dissolution%20rate%20and%20diffusivity%20of%20lime%20in%20steelmaking.pdf

Dissolution Rate and Diffusivity of Lime in Steelmaking

Slag and Development of Fluoride-Free Fluxes

Shahriar Haji Amini

A thesis submitted to The University of New South Wales in total fulfilment of the requirements for admission to the degree of

Doctor of Philosophy

at

The University of New South Wales

School of Chemical Engineering and Industrial Chemistry

&

Commonwealth Scientific and Industrial Research Organization

Division of Minerals

October 2005

i

CERTIFICATE OF ORIGINALITY

I herby declare that this submission is my own work and to the best of my

knowledge it contains no materials previously published or written by another

person, nor material which to a substantial extent has been accepted for the

award of any other degree or diploma at UNSW or any other educational

institutions, except where due acknowledgment is made in the thesis. Any

contribution made to the research by others, with whom I have worked at UNSW

or elsewhere, is explicitly acknowledged in the thesis.

I also declare that the intellectual content of this thesis is the product of my own

work, except to the extent that assistance from others in the project’s design and

conception or in style, presentation and linguistic expression is acknowledged.

(Signed)………………………………(Date)…………………………

ii

To my parents:

Professor Ezatollah Haji Amini

and

Touran Nadimpour

If I have seen further... it is by standing upon the shoulders of giants.

Issac Newton

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ACKNOWLEDGMENT

I would like to express my most sincere thanks to my supervisors; Dr. Sharif Jahanshahi,

for his excellent supervision of the work undertaken in this study, A/Prof. Michael

Brungs for his guidance and support in facilitating my study as a PhD candidate and

Prof. Oleg Ostrovski for his constructive advice throughout the course of this research.

I would like to thank Dr. Ling Zhang for many useful discussions. I am also grateful for

having had the opportunity to discuss my work with Dr. Shouyi Sun.

The work of this project has been aided by the excellent technical support and services

provided by staff at; Commonwealth Scientific and Industrial Research organization

(CSIRO) division of Minerals, The University of New South Wales and University of

Melbourne. I wish to express my appreciation to a number of staff at CSIRO, namely;

Rowan Davidson and Justen Bremmel for laboratory assistance, Howard Poynton, Paul

Fazey and Daniela Varsamakis for chemical analysis, Dr. Angelica Vecchio-Sadus for

OH&S at work place and Damien Hewish for his excellent work on modifying the

experimental apparatus. At The University of New South Wales, my thanks to Barry

Searle for EPMA analysis and John Sharp for laboratory assistance. At University of

Melbourne, my gratitude to Roger Curtin for SEM analysis.

I would like to thank my colleagues and friends at CSIRO Minerals, who gave me

support and advice during the present work. In particular, I would like to thank Dr.

Jakub Bujalski for his valuable suggestions during preparation of my thesis.

The author wishes to thank the financial support from The Australian Research Council,

The University of New South Wales, CSIRO Minerals and Abel Metal Pty Ltd. for the

accomplishment of the present work.

I extend the utmost appreciation to my parents and brothers for their love, support and

understanding over the course of my PhD studies.

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ABSTRACT

A rotating disk technique was used to determine the dissolution rate and

diffusivity of CaO and MgO in slags. The dissolution rate was deduced from the

measured changes in concentration of oxides in slag with respect to reaction

time. The experimental set-up was initially tested with dissolution of magnesia in

the CaO – 55 wt% Al2O3 slag at 1430 ºC and a measured rate of 5107.2 −×

g/cm2.s was obtained. The dissolution rate was increased by slag chemistry and

ranged from 5105.6 −× to 4101.2 −× g/cm2.s.

The dissolution rate of CaO was measured in CaO – 42 wt% Al2O3 – 8% SiO 2

based slag. The measured dissolution rates were found to be strongly dependent

on the slag chemistry and temperature and ranged from 51003.5 −× to 4103.3 −×

g/cm2.s.

The dissolution rates were strongly dependent on the rotation speed and results

indicate mass transfer in the slag phase to be rate- limiting step.

The diffusivity of MgO / CaO was calculated from the dissolution rate and

solubility data, using known mass transfer correlations. The diffusivity of MgO

in the calcium aluminate slag at 1430 ºC was found to be about 5101.1 −× cm2/s.

Additions of 5 and 10 wt% Fe2O3 increased the diffusivity by a factor ~ 1.5 to 3,

respectively. However, with introduction of (CaF2 5 wt% + Fe2O3 5 wt%) and

(CaF2 5 wt% + Fe2O3 10 wt%) in the slag, the diffusivity increased considerably

by a factor of about 29 and 11, respectively.

The diffusivity of CaO in calcium aluminosilicate was measured to be in the

order of 10-6 to 10-5 over a temperature range of 1430 – 1600 ºC. CaF2 increased

the diffusivity by a factor of 3 to 5 while MnOx and FeOx, ilmenite and TiO 2

increased the diffusivity substantially and SiO 2 had an opposite effect. The

measured diffusivities are in accord with published data on comparable systems

and are discussed with reference to Eyring theory.

It was concluded that MnOx, FeOx and ilmenite in the slag increase the

dissolution rate and diffusivity of lime, showing comparable results with respect

to CaF2.

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TABLE OF CONTENTS

CERTIFICATE OF ORIGINALITY .................................................................I

ACKNOWLEDGMENT ...................................................................................III

ABSTRACT........................................................................................................IV

TABLE OF CONTENTS ................................................................................... V

LIST OF FIGURES ...........................................................................................XI

LIST OF TABLES .......................................................................................XVIII

CHAPTER 1. LITERATURE REVIEW ....................................................... 1

1.1 Introduction........................................................................................ 1

1.2 Secondary steelmaking ...................................................................... 1

1.3 Ladle slag and dissolution of lime in the slag.................................... 4

1.4 Fluospar as flux to aid lime dissolution............................................. 5

1.4.1 Use of fluorspar in Australian steel industry ..................................... 7

1.5 Factors affecting dissolution.............................................................. 8

1.5.1 A guide for the literature review........................................................ 8

1.5.2 Rate of flow of the molten slag past the solid oxide .......................... 9

1.5.3 Solubility of solid oxide in the slag ................................................... 9

1.5.4 Physical properties of solid oxides .................................................. 12

1.5.5 Formation of a product layer at the solid oxises/slag interface ....... 14

1.5.6 Viscosity of slag............................................................................... 23

1.5.6.1 Effect of additives on the viscosity of slag...................................... 30

1.5.6.1.1 Effect of CaF2 Substitutes on the viscosity of slag...................... 31

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1.6 Diffusivity in molten slag ................................................................ 36

1.6.1 Liquid state diffusion models........................................................... 75

1.6.1.1 Hydrodynamic theory ...................................................................... 76

1.6.1.2 Hole theory....................................................................................... 78

1.6.1.3 Eyring theory.................................................................................... 78

1.7 General discussion ........................................................................... 82

1.7.1 Questions arising from the literature on diffusivity......................... 83

1.8 Methods for measurement of diffusivity.......................................... 83

1.8.1 Instantaneous plane source method.................................................. 85

1.8.2 Capillary - reservoir method ............................................................ 86

1.8.2.1 Semi – infinite capillary................................................................... 87

1.8.2.2 Finite capillary ................................................................................. 88

1.8.2.3 Diffusion couple method.................................................................. 90

1.8.3 Electrochemical method................................................................... 93

1.8.4 Controlled forced convection method.............................................. 95

1.8.4.1 Rotating disk method ....................................................................... 96

1.8.4.2 Rotating cylinder method............................................................... 101

1.8.4.3 Applicability of rotating disk/cylinder technique .......................... 105

1.8.5 Selection of experimental technique for the present work............. 106

1.9 Objectives of this work .................................................................. 107

CHAPTER 2. EXPERIMENTAL............................................................... 109

2.1 The outline of the experimental work ............................................ 109

2.2 Material preparation....................................................................... 110

2.2.1 Dense CaO / MgO crucible ............................................................ 110

2.2.2 Chemical reagents.......................................................................... 111

2.2.3 Preparation of calcium aluminosilicate master slag....................... 112

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2.2.4 Preparation of calcium aluminate slag........................................... 114

2.3 Experimental apparatus.................................................................. 115

2.4 Experimental procedure ................................................................. 117

2.4.1 Rotating experiments ..................................................................... 117

2.4.2 Static experiments.......................................................................... 119

2.5 Analytical techniques ..................................................................... 119

2.5.1 Scanning Electron Microscopy and Energy Dispersive System analysis (SEM-EDS)...................................................................................... 120

2.5.2 Microprobe analysis ....................................................................... 122

CHAPTER 3. EXPERIMENTAL RESULTS............................................ 125

3.1 Rotating experiments ..................................................................... 126

3.1.1 Dissolution of CaO in calcium aluminosilicate slag...................... 126

3.1.1.1 Effect of rotating speed on dissolution rate ................................... 127

3.1.1.2 Variation of CaO dissolution at various temperatures in the master slag 135

3.1.1.3 Effect of additives on the dissolution of CaO in slag .................... 143

3.1.1.3.1 Effect of CaF2 addition on dissolution of CaO in slag at various temperatures................................................................................................... 144

3.1.1.3.2 Effect of Fe2O3 addition on dissolution of CaO in slag at various temperatures................................................................................................... 147

3.1.1.3.3 Effect of TiO2 addition on dissolution of CaO in slag at various temperatures................................................................................................... 149

3.1.1.3.4 Effect of ilmenite addition on dissolution of CaO in slag at various temperatures ...................................................................................... 151

3.1.1.3.5 Effect of Mn3O4 addition on dissolution of CaO in slag at various temperatures................................................................................................... 153

3.1.1.3.6 Effect of SiO 2 addition on dissolution of CaO in slag at various temperatures................................................................................................... 155

3.1.1.4 Effect of variables on the dissolution rate...................................... 155

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3.1.1.5 Effect of basicity on the dissolution of lime at constant temperature157

3.1.2 Dissolution of MgO in calcium aluminate slag ............................. 160

3.1.2.1 Effect of rotation speed on the rate of dissolution......................... 161

3.1.2.2 Effect of Fe2O3 addition on dissolution of MgO in slag................ 165

3.1.2.2.1 Effect of (Fe2O3 + CaF2) addition on dissolution of MgO in slag166

3.2 Static experiments.......................................................................... 167

3.2.1 CaO experiments............................................................................ 167

3.2.1.1 Solubility of lime in the master slag under various temperatures.. 168

3.2.1.2 Effect of addition of CaF2 on the solubility of lime in the slag..... 171

3.2.1.3 Effect of addition of Fe2O3 on the solubility of lime in the slag.... 172

3.2.1.4 Effect of addition of TiO 2 on the Solubility of lime in the slag..... 174

3.2.1.5 Effect of addition of ilmenite on the solubility of lime in the slag 175

3.2.1.6 Effect of addition of Mn3O4 on the solubility of lime in the slag.. 176

3.2.1.7 Effect of addition of SiO 2 on the solubility of lime in the slag...... 177

3.2.1.8 FactSage thermodynamic modelling.............................................. 178

3.2.1.9 Formation of a reaction layer on the lime/base slag interface ....... 179

3.2.1.9.1 Effect of basicity on the formation of reaction layer on the lime/slag interface .......................................................................................... 186

3.2.2 MgO experiments........................................................................... 189

CHAPTER 4. DISCUSSION ....................................................................... 192

4.1 Diffusivity of CaO / MgO in slag and effect of additives on the diffusivity....................................................................................................... 193

4.1.1 Mass transfer from the rotating disk .............................................. 193

4.1.2 Mass transfer from the rotating cylinder........................................ 196

4.1.3 Total mass transfer from the solid oxide specimen ....................... 198

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4.2 Diffusivity of MgO in calcium aluminate slags............................. 200

4.3 Diffusivity of CaO in calcium aluminosilicate slags ..................... 203

4.3.1 Comparison of CaO diffusivity with literature data ...................... 208

4.4 Diffusion in a Mix – controlled regime ......................................... 216

4.5 Activation energy........................................................................... 230

4.6 Relationship of diffusivity with viscosity...................................... 237

4.7 Ionic conductivity .......................................................................... 239

4.8 Summary of key findings ............................................................... 245

CHAPTER 5. CONCLUSION .................................................................... 247

5.1 Dissolution rate of MgO in calcium aluminate slag and lime in thecalcium aluminosilicate slags ......................................................................... 247

5.2 Solubilities of MgO in calcium aluminate slag and CaO in calcium aluminosilicate slags ...................................................................................... 249

5.3 Diffusivity of MgO / CaO in slags................................................. 250

5.4 Recommendations for future work ................................................ 252

REFERENCES................................................................................................. 254

APPENDIX A. SOLID OXIDES DISSOLUTION DATA...................... 263

A.1 The effect of rotation speed on dissolution of CaO in calcium aluminosilicate slag at 1430 ºC ...................................................................... 263

A.2 Effect of CaF2 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures ................................................. 269

A.3 Effect of Fe2O3 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures ................................................. 274

A.4 Effect of TiO2 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures ................................................. 279

A.5 Effect of ilmenite addition on dissolution of CaO in calcium auminosilicate slag at various temperatures................................................... 284

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A.6 Effect of Mn3O4 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures ................................................. 289

A.7 Effect of SiO 2 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures ................................................. 294

A.8 Effect of Fe2O3 addition on dissolution of MgO in calcium aluminate slag 298

A.9 Effect of (CaF2 + Fe2O3) addition on dissolution of MgO in calcium aluminate slag ................................................................................................ 301

APPENDIX B. MODEL FOR ESTIMATING THE SLAG VISCOSITY304

APPENDIX C. MODEL FOR ESTIMATING THE SLAG DENSITY 307

APPENDIX D. ERROR ANALYSIS ........................................................ 310

APPENDIX E. PRELIMINARY STUDY OF LIME DISSOLUTION INSTATIC SLAG 317

E.2 Experimental.................................................................................. 317

E.1.1 Materials ......................................................................................... 317

E.1.2 Experimental Procedure ................................................................. 318

E.3 Experimental Results and Discussion............................................ 321

E.4 Key findings ................................................................................... 323

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LIST OF FIGURESFigure 1.1: CaO-Al2O3-SiO2 phase diagram in Slag Atlas (Eisenhuttenleute (1995)) ..........10

Figure 1.2: CaO – Al2O3 – MgO phase diagram in Slag Atlas (Eisenhuttenleute (1995)).....11

Figure 1.3: Schematic diagram of distribution of slag components near the interface according to Matsushima et al. (1977) ..........................................................15

Figure 1.4: Effect of concentration of various fluxes on lowering of melting point of dicalcium silicate Singh et al. (1977) ............................................................35

Figure 1.5: Effect of temperature and slag composition on the chemical diffusivity of Ca2+ introduced as Ca45O into slags of A1, A2 and A3 after Johnston et al. (1974) ........................................................................................................39

Figure 1.6: Diffusion coefficient of calcium (upper line) and silicon (lower line) after Towers et al. (1957). ...................................................................................43

Figure 1.7: Tracer diffusivity of Ca45 in CaO – SiO2 melts a function of mole fraction of silica and temperature after Keller et al. (1979b) ...........................................44

Figure 1.8: Electrical conductivity )( 11 −−Ω cm of CaO-SiO2 melts as a function of mole fraction of silica and temperature after Keller et al. (1979b) ...........................45

Figure 1.9: Tracer conductivity and computed conductivity of Ca45 in the CaO – SiO2

melt as function of SiO2 at 1600 ºC after Keller et al. (1979b) ........................47

Figure 1.10: Diffusivities of iron and calcium in silica saturated CaO – FeO – SiO2 melts at 1600 ºC after Keller et al. (1986) ..............................................................48

Figure 1.11: Diffusivity of Ca45 in melts as a function of temperature after Hara et al. (1989) ........................................................................................................49

Figure 1.12: Relationship between logarithm of tracer diffusivities of calcium and iron and reciprocal temperature after Goto et al. (1977)........................................50

Figure 1.13: Diffusion coefficients of Ca45 and Si31 as a function of melt composition at 1600 ºC after Keller et al. (1979a)................................................................51

Figure 1.14: Diffusivities of oxides in CaO-40 wt% SiO2-20 % Al2O3 slag after Ukyo et al. (1982) ...................................................................................................52

Figure 1.15: Diffusivities of oxides in FeOx - 30 wt% CaO - 45 % SiO2 slag after Ukyoet al. (1982) ................................................................................................53

Figure 1.16: The variation of DFe with T in Fe2SiO4 after Agarwal et al. (1975) .................54

Figure 1.17: The variation of DFe with 1/T in CaFeSiO4 after Agarwal et al. (1975)............54

Figure 1.18: Diffusivities of Fe2+, Ni2+, Co2+ and Ca2+ in silica saturated MeO – CaO –SiO2 melts at 1600 ºC after Nowak et al. (1975) ............................................57

Figure 1.19: Self diffusivities of elements in molten slag for blast furnace CaO-40 wt% SiO2-20 % Al2O after Nagata et al. (1982) ....................................................58

Figure 1.20: Self diffusivities of elements in molten slag for steelmaking (25-40) wt% Fe2O3 -(30-40)% CaO-SiO2 after Nagata et al. (1982) ....................................59

Figure 1.21: Tracer diffusivities of CaO in slags with various chemistry on the basis of previous publication (B: basicity , C: CaO, A: Al2O3, Fe: FeO, M: MO).........61

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Figure 1.22: Comparison of alumina diffusivity data according to Henderson et al. (1961) & Cooper et al. (1964) & Taira et al. (1993) & Lee et al. (2001) (B: basicity, A: Al2O3) – B is the basicity, A is Aluminium concentration. ...........67

Figure 1.23: Chemical diffusivity of iron oxide in CaO – 38 wt% SiO2 – 21 % Al2O3

melts in comparison with the results of other studies at 1300 to 1360 ºC and approximately the same base melt composition as a function of the average iron concentration. ......................................................................................75

Figure 1.24: Diffusion of large molecule (B) due to the movement of small solvent molecule (A) ..............................................................................................81

Figure 1.25: Apparatus for measuring diffusivity of elements dissolved in molten slag by capillary – reservoir technique .....................................................................87

Figure 1.26: Diffusion couple, two capillaries..................................................................91

Figure 1.27: Diffusion couple, two capillaries..................................................................92

Figure 1.28: Diffusion couple, one capillary ....................................................................93

Figure 1.29: The relationship between the mass transfer and Reynolds number according to the previous investigations..................................................................... 105

Figure 2.1: Schematic of the experimental apparatus used for the rotating cylinder tests... 116

Figure 2.2: Photo of the CaO/MgO crucible attached with Zirconia paste to the alumina rod........................................................................................................... 117

Figure 2.3: The Philips XL30 used for the SEM analysis ................................................ 121

Figure 2.4: The CAMECA SX-50 Micro Probe used for the EPMA analysis ................... 123

Figure 3.1: CaO-Al2O3-SiO2 system phase diagram from Slag Atlas (Eisenhuttenleute (1995))..................................................................................................... 127

Figure 3.2: The concentration of CaO (wt%) in the melt with increasing the rotation speed at 1430 ºC ....................................................................................... 128

Figure 3.3: Variation of the dissolution rate of CaO versus the square root of rotation speed in air at 1430 and 1600 ºC ................................................................ 134

Figure 3.4: Variation of the dissolution rate of CaO versus the 0.75-th power of rotation speed in air at 1430 and 1600 ºC ................................................................ 134

Figure 3.5: Variation of the dissolution rate of CaO versus 75.05.0 ωω BA + of rotation speed in air. A and B are defined at 1430 and 1600 ºC ................................. 135

Figure 3.6: Concentration of CaO dissolved in base slag at 90 rpm and in air at 1430 °C .. 137



Figure 3.9: Concentration of CaO dissolved in base slag at 90 rpm and in air at 1600 °C . 142

Figure 3.10: Comparison of CaO Concentrations dissolved in slag at 90 rpm and in air at 1430 – 1600 °C ........................................................................................ 143

Figure 3.11: The lime specimen after dissolution in the slag with 5 wt% CaF2 at 90rpm and after reaction time of 20 minutes ......................................................... 145

Figure 3.12: CaO- Al2O3-CaF2 phase diagram according to Mills and Keene (1981)......... 146

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Figure 3.13: Comparison of total CaO content in slag with 5 wt% CaF2 at 90 rpm and in air at 1430 – 1600 °C ................................................................................ 147

Figure 3.14: The lime specimen after dissolution in the slag with 5 wt% Fe2O3 at 90 rpm and after reaction time of 20 minutes ......................................................... 148

Figure 3.15: Comparison of CaO concentrations dissolved in slag with 5 wt% Fe2O3 at 90 rpm and in air at 1430 – 1600 °C........................................................... 149

Figure 3.16: The lime specimen after dissolution in the slag with 5 wt% TiO2 at 90 rpm and after 60 minutes of reaction. ................................................................ 150

Figure 3.17: Comparison of concentrations of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1430 – 1570°C for 1 hour ............................................ 150

Figure 3.18: The lime specimen after dissolution in the slag with 5 wt% ilmenite at 90 rpm and after reaction time of 10 minutes................................................... 152

Figure 3.19: Comparison of concentrations of CaO dissolved in slag with 5 wt% ilmenite at 90 rpm and in air at 1500 – 1600 °C .......................................... 152

Figure 3.20: The lime specimen after dissolution in the slag with 5 wt% Mn2O3 at 90 rpm and after reaction time of 20 minutes................................................... 154

Figure 3.21: Concentration of CaO dissolved in slag with 5 wt% Mn3O4 at 90 rpm and in air at 1430 – 1600 ºC ................................................................................ 154

Figure 3.22: Comparison of concentrations of CaO dissolved in slag with additional 5 wt% SiO2 at 90 rpm in air at 1500 – 1600 °C for 1 hour .............................. 155

Figure 3.23: The rate of dissolution of lime (g/cm2.s) in the slag at various temperatures and with additives..................................................................................... 157

Figure 3.24: The concentration of lime (wt%) in the slag (basicity of 0.9) at various rotation speed at 1500 ºC........................................................................... 158

Figure 3.25: The dissolution rate of CaO with speed 0.5 in slag with basicity of 0.9........... 159

Figure 3.26: The dissolution rate of CaO with speed 07.5 in slag with basicity of 0.9 ......... 159Figure 3.27: CaO-Al2O3-MgO system phase diagram according to Slag Atlas

(Eisenhuttenleute (1995)) .......................................................................... 160

Figure 3.28: Concentration of MgO dissolved in slag at different rotation speed, in air at 1430 °C for 1 hour .................................................................................... 162

Figure 3.29: Dependence of rate of dissolution of MgO with 0.5 -th power of speed........ 163

Figure 3.30: Rate of dissolution of MgO with 0.75-th power of speed............................. 164

Figure 3.31: Variation of the dissolution rate of MgO versus 75.05.0 ωω BA + of rotation speed in air. A and B are defined at 1430 ºC ................................... 164

Figure 3.32: Concentration of MgO dissolved in slag with 5 and 10% Fe2O3 at 90 rpm in air at 1430 °C for 1 hour............................................................................ 165

Figure 3.33: Concentration of MgO dissolved in slag with additives at 90 rpm and in air at 1430 °C for 1 hour ................................................................................ 167

Figure 3.34: Variation of bulk slag composition (wt%) measured by SEM-EDS with the reaction time at 1430 ºC in air.................................................................... 169

Figure 3.35: Interfacial region of CaO in contact with slag at 1430 ºC for the reaction time of 2 hours ......................................................................................... 170

xiv

Figure 3.36: Interfacial region of CaO in contact with slag containing 5 wt% CaF2 at 1430 ºC for the reaction time of 3 hours ..................................................... 172

Figure 3.37: Interfacial region of CaO in contact with slag containing 5 wt% Fe2O3 at 1430 ºC for the reaction time of 3 hours ..................................................... 173

Figure 3.38: Interfacial region of CaO in contact with slag containing 5 wt% TiO2 at 1430 ºC for the reaction time of 3 hours ..................................................... 175

Figure 3.39: Interfacial region of CaO in contact with slag containing 5 wt% ilmenite at 1430 ºC for the reaction time of 3 hours ..................................................... 176

Figure 3.40: Interfacial region of CaO in contact with slag containing 5 wt% Mn3O4 at 1430 ºC for the reaction time of 3 hours ..................................................... 177

Figure 3.41: Interfacial region of CaO in contact with slag containing 5 wt% SiO2 at 1430 ºC for the reaction time of 3 hours ..................................................... 178

Figure 3.42: SEM micrograph of the CaO and slag interface for lime reacting 30 minutes with slag in air at 1430 °C ......................................................................... 180

Figure 3.43: SEM micrograph of the CaO and slag interface for lime reacting 1 hour with slag in air at 1430°C .......................................................................... 181

Figure 3.44: SEM micrograph of the CaO and slag interface for lime reacting 2 hours with slag in air at 1430°C .......................................................................... 181



Figure 3.47: SEM micrograph of the CaO and slag interface for lime reacting 12 hourswith slag in air at 1430°C .......................................................................... 183


Figure 3.49: Thickness of solid layer as a function of square root of time in slag in air at 1430ºC..................................................................................................... 185

Figure 3.50: Interfacial region of CaO in contact with slag (basicity = 0.9) at 1500 ºC for the reaction time of 1 hour ......................................................................... 186

Figure 3.51: Interfacial region of CaO in contact with slag (basicity = 0.9) at 1500 ºC for the reaction time of 2 hours ....................................................................... 187



Figure 3.54: Interfacial region of CaO in contact with slag (basicity = 0.9) at 1500 ºC for the reaction time of 11 hours ..................................................................... 188

Figure 3.55: Interfacial region of CaO in contact with slag (basicity = 0.9) at 1500 ºC for the reaction time of 24 hours ..................................................................... 189

Figure 3.56: SEM micrograph of the magnesia / slag interface from the samples left from the rotation experiments at 90 rpm and 1430ºC ................................... 190

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Figure 4.1: Diffusivity of CaO in CaO – 42 wt% Al2O3 – 8 SiO2 slag with 5 wt% addition of CaF2, MnOx, FeOx, TiO2, SiO2 and ilmenite. The activation energy of diffusion calculated on the basis of the slope of these graphs are compared for the base slag (44 kcal/mol) versus the slag with addition of 5 wt% CaF2 (15 kcal/mol). ........................................................................... 204

Figure 4.2: Diffusiv ity of calcium according to the published data and the deduced diffusivity in the present work for base slag –(B: basicity, C: CaO, Al: Al2O3, Fe: FeO, M:Mg) ............................................................................. 209

Figure 4.3: Influence of addition of FeOx and MnOx on the apparent diffusivity of alumina at 1560-1590ºC according to Lee et al. (2001)................................ 214

Figure 4.4: CaO-Al2O3-SiO2 phase diagram................................................................... 217

Figure 4.5: Estimation of CaO diffusion through a solid layer......................................... 219

Figure 4.6: variation (Thickness2) of magnesiowustite layer as a function of time on the basis of work done by Zhang et al. (1994) .................................................. 221

Figure 4.7: Variation of (thickness2) of wustite layer with time deduced from data according to Allen et al. (1995) .................................................................. 222

Figure 4.8: Variation of the (thickness2) of the spinel layer with time deduced from data according to Allen et al. (1995) .................................................................. 222

Figure 4.9: The CaO concentration predicted by mix-controlled model and the experimental data at30 rpm & 1430 ºC ....................................................... 227

Figure 4.10: The CaO concentration predicted by mix-controlled model and the experimental data at 60 rpm & 1430 ºC ...................................................... 228

Figure 4.11: The CaO concentration predicted by mix-controlled model and the experimental data at 90 rpm & 1430 ºC ...................................................... 228

Figure 4.12: The CaO concentration predicted by mix-controlled model and the experimental data at 120 rpm & 1430 ºC .................................................... 229

Figure 4.13: The CaO concentration predicted by mix-controlled model and theexperimental data at150 rpm & 1430 ºC ..................................................... 229

Figure 4.14: Arrhenius plots for calculation of the activation energy for diffusion of CaO in the master slag and slags with additives.................................................. 231

Figure 4.15: Arrhenius plot for the diffusion of Ca2+ in the CaO – 20 wt% Al2O3 – 42% SiO2, used in the calculation of activation energy on the basis of data from Johnston et al. (1974) ................................................................................ 233

Figure 4.16: Arrehnius plot for the diffusion of Ca2+, F-1 and Fe2+ in the CaO – 20 wt% Al2O3 – 42% SiO2 slag, used in the calculation of activation energy according to data from Johnston et al. (1974) .............................................. 234

Figure 4.17: Arrhenius plot for diffusion of Ca in the CaO – SiO2 slags according to diffusivity data from Keller et al. (1979b) ................................................... 236

Figure 4.18: Investigation of applying Eyring theory in diffusion of CaO in the slag ........ 239

Figure 4.19: Electrical conductivity of CaO – SiO2 slag, measured experimentally calculated as a function of mole fraction of silica at 1600 ºC after Keller et al. (1979b) ................................................................................................ 242

Figure A. 1: Concentration of CaO dissolved in slag at 30 rpm and at 1430°C ................. 264

xvi



Figure A. 4: Concentration of CaO dissolved in slag at 120 rpm and at 1430°C ............... 267

Figure A. 5: Concentration of CaO dissolved in slag at 150 rpm and in air at 1430°C....... 268

Figure A. 6: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1430°C ............................................................................................ 270

Figure A. 7: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1500 °C ........................................................................................... 271

Figure A. 8: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1550 °C ........................................................................................... 272

Figure A. 9: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1600 °C for 1 hour............................................................................ 273

Figure A. 10: Concentration of CaO dissolved in slag with 5 wt% Fe2O3 90 rpm and in air at 1430°C for 1 hour ............................................................................ 275

Figure A. 11: Concentration of CaO dissolved in slag with 5 wt% Fe2O3 at 90 rpm and in air at 1500 °C for 1 hour............................................................................ 276



Figure A. 14: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1430°C for 1 hour ............................................................................ 280

Figure A. 15: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1500 °C for 1 hour............................................................................ 281

Figure A. 16: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1550 °C for 1 hour............................................................................ 282

Figure A. 17: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1570°C for 1 hour ............................................................................ 283

Figure A. 18: Concentration of CaO dissolved in slag with 5 wt% ilmenite at 90 rpm and in air at 1500 °C ....................................................................................... 285


Figure A. 20:Concentration of CaO dissolved in slag with 5 wt% ilmenite at 90 rpm and in air at 1570°C ........................................................................................ 287


Figure A. 22: Concentration of CaO dissolved in slag with 5 wt% Mn3O4 at 90 rpm and in air at 1430°C ........................................................................................ 290

Figure A. 23: Concentration of CaO dissolved in slag with 5 wt% Mn3O4 at 90 rpm and in air at 1500 °C ....................................................................................... 291


xvii


Figure A. 26: Concentration of CaO dissolved in slag with additional 5 wt% SiO2 at 90 rpm and in air at 1500 °C for 1 hour ........................................................... 295



Figure A. 29: Concentration of MgO dissolved in slag with 5 wt% Fe2O3 at 90 rpm in air at 1430°C for 1 hour ................................................................................. 299

Figure A. 30: Concentration of MgO dissolved in slag with 10 wt% Fe 2O3 at 90 rpm in air at 1430°C for 1 hour ............................................................................ 300

Figure A. 31: Concentration of MgO dissolved in slag with addition of 5% CaF2 &5% Fe2O3 at 90 rpm in air at 1430°C for 1 hour ................................................ 302

Figure A. 32: Concentration of MgO dissolved in slag with addition of 5% CaF2 &10% Fe2O3 at 90 rpm in air and at 1430°C for 1 hour .......................................... 303

Figure E. 1: SEM of base slag at 1500 °C for time=0 with 1000 magnification. ............... 325

Figure E. 2: SEM of base slag at 1600 °C for time=0 with 1000 magnification. ............... 325

Figure E. 3: Identified Ca2SiO4 phase by MATLAB program for base slag at 1500 °C for time=0 in a 512 by 512 microns area and 256 by 256 image resolution. ........ 325

Figure E. 4: Identified Ca2SiO4 phase by MATLAB program for base slag at 1600 °C for time=0 in a 512 by 512 microns area and 256 by 256 image resolution. ........ 325

Figure E. 5: The composition of bulk slag at various reaction times in phase diagram for basic slag at 1500 °C................................................................................. 326

Figure E. 6: The composition of bulk slag at various reaction times in phase diagram for basic slag at 1600 °C................................................................................. 327

Figure E. 7: Formation of Ca2SiO4 layer on reaction of lime with master slag at 1600 ºC in the platinum capsule ............................................................................. 328

xviii

LIST OF TABLESTable 1.1: Slag compositions used for the measurements of diffusivity on liquid slags by

Johnston et al. (1974) ..................................................................................38

Table 1.2: Diffusion coefficient of Ca45 in slags studied by Saito et al. (1958) ....................40

Table 1.3: Activation energy of diffusion in the CaO – SiO2 melt as a function of SiO2 content of slag............................................................................................45

Table 1.4: Mass transfer of alumina in the CaO-Al2O3-SiO2 (Al2O3 = 10 wt%) after Taira et al. (1993) and the deduced diffusivity.......................................................65

Table 1.5: Values of mass transfer coefficient after Matsushima et al. (1977) and deduced diffusivity of lime in the slag..........................................................69

Table 1.6: Mass transfer coefficient of dolomite from the Umakoshi et al. (1984b) and deduced diffusivity data for CaO and MgO in the present work.....................72

Table 1.7: The correlations developed previously for mass transfer from rotating solute cylinder to the solvents.............................................................................. 104

Table 2.1: The source and purity of the chemical composition used in the experiment ...... 111

Table 2.2: Chemical composition of ilmenite ................................................................. 112

Table 2.3: XRF analysis of master slag, wt%................................................................. 113

Table 2.4: Chemical composition of various slags for lime dissolution study, wt%........... 114

Table 2.5: composition of slag with additives for magnesia dissolution study, wt%.......... 114

Table 2.6: Standards used in the calibration of Philips XL 30 SEM................................. 122Table 2.7: Standards used in the calibration of SX-50 Micro probe ................................. 124

Table 3.1: The rate of lime dissolution (gr.cm-2.s-1) in the slag at 1430 ºC in air ............... 130

Table 3.2: The rate of dissolution of lime (g/cm2.s) in the slag at various temperatures and with additives..................................................................................... 136

Table 3.3: The variation of CaO concentration in base slag by measurements from XRF analysis at 90 rpm and in air at 1430 °C for 1 hour ...................................... 137

Table 3.4: The variation of CaO concentration in base slag by measurements from XRF analysis at 90 rpm and in air at 1500 °C ..................................................... 140



Table 3.7: The rate of dissolution of MgO in the slag at 1430 °C and with various additives .................................................................................................. 166

Table 3.8: SEM – EDS analysis of the bulk slag at1430 ºC in air ................................... 169

Table 3.9: EPMA analysis of the bulk slag close to the lime/master slag interface in air at different temperatures............................................................................ 171

Table 3.10: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% CaF2 at various temperatures in air .................................. 171

xix

Table 3.11: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% Fe2O3 at different temperatures in air ............................... 173

Table 3.12: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% TiO2 at different temperatures in air................................. 174

Table 3.13: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% ilmenite at different times in air ...................................... 175

Table 3.14: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% MnOx at various temperatures in air ................................ 176

Table 3.15: EPMA analysis of the bulk slag close to the interface of lime/ slag containing additional 5% SiO2 at various temperatures in air ....................... 178

Table 3.16: The solubility of lime in various slags at different temperatures by FactSage (Bale et al. (2003)) modelling.................................................................... 179

Table 3.17: SEM – EDS analysis of the bulk slag at1430 ºC in air................................... 190

Table 3.18: SEM – The solubility of magnesia in various slags ....................................... 191

Table 4.1: The diffusivity of MgO in the CaO – 56 wt% Al2O3 at 1430ºC in air with additives (wt%)........................................................................................ 201

Table 4.2:Results for the measured diffusivity of CaO in the slag and the calculated slag viscosity at various temperatures ............................................................... 205

Table 4.3: Values for mass transfer coefficient, thickness of boundary layer and deduced effective diffusivity of lime in the slag according to Matsushima et al.(1977) ...................................................................................................... 212

Table 4.4: Activation energy for master slag and slag with additives ............................... 231Table 4.5: The activation energy for binary and ternary slags according to Saito et al.

(1958) ...................................................................................................... 235

Table 4.6: Activation energy for diffusion of various oxides in CaO- 40 wt% SiO2- 20 % Al2O3 slag according to Ukyo et al. (1982) ................................................. 236

Table 4.7: Activation energy from diffusivity data of various ions in liquid CaO- 40 wt% SiO2- 20 % Al2O3 slag according to Nagata et al. (1982) ............................. 237

Table 4.8: Estimated Ionic conductivity ( 11 −−Ω cm ) of CaO-Al2O3-SiO2 slag and slags with 5 wt% additives at various temperatures ............................................. 241

Table 4.9: Estimated activation energy of conductivity for master slag and slags with 5 wt% additives........................................................................................... 244

Table A. 1: XRF analysis of the bulk slag when lime dissolves in slag in air at 30 rpm and 1430°C .............................................................................................. 264





xx

Table A. 6: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% CaF2 in air at 90 rpm and 1430°C....................................................... 270

Table A. 7: XRF analysis of the bulk slag when lime dissolves in slag with addit ion of 5 wt% CaF2 in air at 90 rpm and 1500 °C...................................................... 271

Table A. 8: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% CaF2 in air at 90 rpm and 1550 °C...................................................... 272

Table A. 9: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% CaF2 in air at 90 rpm and 1600 °C...................................................... 273

Table A. 10: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Fe 2O3 in air at 90 rpm and 1430°C................................................... 275

Table A. 11: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Fe 2O3 in air at 90 rpm and 1500 °C.................................................. 276



Table A. 14: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1430°C .................................................... 280

Table A. 15: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1500 °C ................................................... 281

Table A. 16: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1550 °C ................................................... 282

Table A. 17: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1570°C .................................................... 283

Table A. 18: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% ilmenite in air at 90 rpm and 1500 °C .............................................. 285


Table A. 20: XRF analysis of the bulk slag when lime dissolves in slag with addition of5 wt% ilmenite in air at 90 rpm and 1570°C ............................................... 287


Table A. 22: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Mn3O4 in air at 90 rpm and 1430°C ................................................. 290

Table A. 23: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Mn3O4 in air at 90 rpm and 1500 °C ................................................ 291



Table A. 26: XRF analysis of the bulk slag when lime dissolves in slag with additional 5 wt% SiO2 in air at 90 rpm and 1500 °C ...................................................... 295

xxi



Table A. 29: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 5 wt% Fe 2O3 in air at 90 rpm and 1430°C................................................... 299

Table A. 30: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 10 wt% Fe2O3 in air at 90 rpm and 1430°C................................................. 300

Table A. 31: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 5% CaF2 & 5% Fe2O3 in air at 90 rpm and 1430°C for 1hour ....................... 302

Table A. 32: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 5% CaF2 & 10% Fe2O3 in air and at 90 rpm and 1430°C ............................. 303

Table B. 1: Equations for B-parameters in Urbain model for viscosity............................. 305

Table C. 1: Recommended values for partial molar volume V of various slag constituents at 1500 ºC.............................................................................. 308

Table E. 1: Chemical compositions of Nepheline Syenite ............................................... 329

Table E. 2: Chemical compositions of ilmenite .............................................................. 329

Table E. 3: Growth of Ca2siO4 layer at 1500 °C............................................................. 330

Table E. 4: Mass (grams) of CaO dissolved in the slags (per 100 grams of slag) at 1600 °C............................................................................................................ 330

1

CHAPTER 1. Literature review

1.1 Introduction

In secondary steelmaking, synthetic slag is used to influence the final chemistry

and residual oxide inclusions in the steel. The most important functions of the

ladle slag are to: prevent direct contact between the liquid steel and oxidizing

atmosphere, desulphurise the liquid steel and absorb oxide inclusions formed as

the result of deoxidation reactions. Lime based slags are used for aluminum

killed steels, to absorb the alumina and silicate inclusions and form a calcium

alumino-silicate slag with low level of other oxides. Fluorspar (CaF2) is

commonly used as an additive to increase the dissolution rate of calcined lime

into this ladle slag as well as reducing the slag viscosity. While fluorspar is

known to be an effective fluxing agent, there are some drawbacks associated

with its use. These include volatilization of fluorine containing species into the

atmosphere, leaching of the residual fluorine from the discard slag, higher

refractory wear rate and relatively high cost of fluorspar. Therefore, an

alternative flux or slag practice, which will promote rapid and complete

dissolution of lime into slag without adverse technical and environmental effects,

is highly desirable.

1.2 Secondary steelmaking

The purpose of secondary steelmaking (also referred to as ladle metallurgy) is to

produce “clean” steel, which satisfies stringent requirements of surface, internal

2

and micro-cleanliness quality and of mechanical properties. Ladle metallurgy is a

secondary step of the steelmaking processes often performed in a ladle after the

initial refining process in a primary furnace is completed.

Increasingly industrial and economic developments in many countries have

increased the demand for high quality steels, such as alloy steels and steels used

in arctic line-pipe and jet aircraft parts. To fulfil their functions these steels must

meet the more stringent requirements that necessitate the use of ladle metallurgy.

With increasing demand for such high quality steels, ladle metallurgy has

became a routine step in the production of steel in the plant.

Although satisfactory for making steels for most applications, conventional

steelmaking and refining practices such as BOP, Q-BOP, open hearth and

electric furnaces could not consistently achieve the high specifications the special

steels had to meet. To remain competitive and maintain production, steelmakers

have accepted the secondary steel refining processes as a crucial part of

steelmaking where it is also the last chance the steelmaker has to improve the

quality of the steel significantly before casting.

Secondary steelmaking processes are adopted primarily to achieve various

objectives. These objectives include:

• Control of gases: degassing (decreasing the concentration of oxygen,

nitrogen and hydrogen in steel);

• Low sulphur contents (normally less than 0.01 wt% and to as low as

0.002 wt%);

3

• Micro-cleanliness (removal of undesired non-metallic inclusions,

primarily oxides and sulphides);

• Inclusion morphology (since steelmakers can not remove undesired

oxides completely, this step allows steelmakers to change the

composition and/or shape of the undesired matter left in the steel to make

it compatible with the mechanical properties of the finished steel).

Although secondary steelmaking processes extend the refining capabilities of

modern steel-producing facilities, various prerequisites must be met for effective

utilization of these processes.

Temperature and chemical composition of the raw steel must meet the

specification in the primary furnace and must be maintained through tap time

into the ladle or secondary vessel to produce quality steel. Accurate assessment

of temperature, chemical composition, and quantity of steel in the ladle are

important. Precise chemical composition control is also dependant on accurate

charge-control measurements and good tapping practices, as is the provisioning

for further processing.

Efficient ladle desulphurization of steel and ladle refining to produce ultraclean

steels are attained only when the steel is treated under a basic, nonoxidizing

“slag”. Ladle-refining methods were also developed whereby the addition of a

nonoxidizing slag to the ladle as a supplement to low-cost argon gas stirring

treatments produced cleaner steel. Synthetic slags must meet the general

requirements such as: low oxygen potential, low melting point, moderate fluidity

4

and large solubility for alumina and sulphur. The slags having these

characteristics are generally found in the CaO – SiO2 – Al2O3 system. Synthetic

slags of this type are added to the ladle during or after tapping to provide refining

of the steel.

The chemistry of synthetic slag plays a major role in the function of ladle

steelmaking and will be presented in the next section.

1.3 Ladle slag and dissolution of lime in the slag

The recovery and impurity content of liquid steel in steelmaking processes is

influenced by the physico-chemical properties of the molten slag and metal as

well as physical processes such as mixing. Synthetic slag is being used in

secondary steelmaking to:

• Remove impurities such as sulphur from the steel.

• Absorb non-metallic inclusions such as Al2O3 or MnO-SiO2 which are

formed as products during of steel.

• Insulate the steel from the atmosphere and reduce heat losses while

suppressing oxygen pick-up from the air, etc.

Lime is one of the ingredients used in making ladle slag, especially when a

calcium aluminate based slag is employed for refining the steel. Usually argon is

used to stir and homogenise the bath, by injection into the steel ladle.

5

When the principal slag component is lime, its main purpose is to de-sulphurise

the steel according to the following reaction:

( ) ][)(][ OCaSSCaO +=+ (1.1)

Where ( ) indicates the species is in the slag phase and [ ] the metal phase.

It is well known that the chemistry of this slag and the progress of slag-metal

reactions in the steelmaking process, is largely influenced by the lime content,

and accordingly by the dissolution rate of solid lime into the slag. The effective

dissolution of solid lime into slag plays an important role in steelmaking

practices. However, lime has a very high melting point of 2570 °C. As,

maintaining high basicity slags for the desulphurisation and dephosphorization of

steel requires close control of lime-silica ratio; therefore, silica, as a flux cannot

be used to aid slag formation.

1.4 Fluospar as flux to aid lime dissolution

With reference to reaction in Equation (1.1), a decrease in slag viscosity

promotes desulphurisation through an increase in reaction kinetics. However, an

increased level of fluidity promotes corrosion/erosion between slag and

refractory. Therefore, a balance must be obtained between a fluid slag, which

promotes adequate refining, and a viscous slag, which provides adequate

refractory protection. Generally, many grades of steel require lime-based slag

with addition of the fluxing agent to increase the rate of lime dissolution.

6

Thus in order to promote favourable chemical reactions during the process while

having a fluid slag, there is a need for an axillary flux. Fluxes are required in

steelmaking basically:

• to lower the melting point of slags so that slags of higher basicity can be

used to reduce the levels of residuals in steel.

• to decrease the viscosity of slags and thus speed up refining reactions.

Calcium fluoride is known to be an effective flux, which accelerates the

dissolution of CaO in the slag by lowering the liquidus temperature and viscosity

of slags (Tribe, Kingston, MacDonald and Caley (1994)). Fluorspar, which

consists of calcium fluoride, is most widely used flux in the steelmaking

industry. Presently, the replacement of fluorspar has become of interest, because

of the associated environmental and economical concerns such as:

• Emission of hazardous fluoride gaseous species, such as SiF4, HF and

NaF, including the vapour species CaF2 (Turkdogan (1985)).

• Leaching of fluorine from generated slags.

• The relatively high cost of fluorspar (Kor (1977)).

• Dwindling accessible supplies. In USA, the industries depend on foreign

supplies of fluorspar from Mexico and other source and in Australia the

supply is partly met by imports from China.

7

For these reasons, there has been effort in developing alternatives to partially or

fully replace fluorspar.

1.4.1 Use of fluorspar in Australian steel industry

Australia has three major steel producers, Bluescope Steel, OneSteel and

Smorgon. Both Bluescope and OneSteel operate integrated steel works, in which

iron ore is reduced in blast furnaces to produce liquid iron, which is then

converted to steel. Smorgon on the other hand operates only Electric Arc

Furnaces (EAF). The process uses mainly steel scraps as feed material. OneSteel

also has a mini-mill in Sydney, which has no primary iron making and operates

EAF using scraps for steel making only.

Bluescope uses about 1 kg fluorspar per tonne of steel in the BOS furnace. In the

ladle, they use much less, about 0.1 kg per tonne and are trying to eliminate the

use of fluorspar. Apparently they do not measure the off gases from fluorspar

addition; however, it is noted that there is a mass imbalance (loss) when they

measure what ends up in a known mass of slag from a given amount added,

indicating that the fluoride partially reports to the fume/dust. Leachate is

measured at various sites surrounding the slag processing area. Further

information on these data has been requested but is not available at the time of

this report.

In Onesteel, fluorspar is currently used in the ladle metallurgy furnaces (LMF).

They used fluorspar in the past in the BOF practice but it showed drawbacks, so

the practice was stopped. (There is no detail publicised.) For the LMF typically

8

40 kg of spar is added in a total addition of fluxes around 2 tonne. It was reported

that no environmental work has been done in measuring the off-gases or on the

measurement of leachate from the slag to the surroundings.

A rough estimate indicates that the tonnage of fluorspar utilized is in the order of

5 - 10 kt/a between BlueScope and OneSteel.

1.5 Factors affecting dissolution

Generally, the rate of dissolution of solid oxides such as lime into a molten slag

is affected by:

• Solubility of solid oxide in the slag;

• Rate of flow of the molten slag past the solid oxide;

• Physical properties of the solid oxide;

• Possible formation of a solid phase at the interface between solid oxide

and slag;

• Viscosity of slag;

• Diffusion of solid oxide in the liquid slag.

1.5.1 A guide for the literature review

During the next section of this chapter, the available published data on the factors

affecting the dissolution of lime/magnesia will be investigated and the tools for

9

prediction of these effects will be studied. As CaF2 is currently being used in

ladle slag to promote the dissolution of lime, the published data on the effect of

this flux and potential substitute oxides on the factors affecting the rate of lime

dissolution in slag will be investigated.

1.5.2 Rate of flow of the molten slag past the solid oxide

Many of the secondary steelmaking processes make use of argon bubbling

treatment to stirr the steel bath, to promote bulk movement of the liquid steel for

chemical and thermal homogeneity and to promote intimate slag and metal

mixing for refining operations. The injection of an inert gas into steel offers a

simple and inexpensive method to decrease the thickness of the stagnant slag

boundary layer by convective mixing in the bulk slag, and thus improves the rate

of mass transfer.

1.5.3 Solubility of solid oxide in the slag

The dissolution of solid oxides in molten slag is directly related to the saturation

level of solid oxides in the slag. The higher the solubility of solids in the slag the

larger the driving force for the solid oxide to dissolve in the slag. For the purpose

of the present work, the solubility of lime in the CaO – SiO2 – Al2O3 slag and

magnesia in CaO – Al2O3 slag at various temperatures can be found by from

ternary phase diagram according to Figure 1.1 and Figure 1.2.

The solubility of lime in the low silica ladle slag could be determined from the

intersection of the line connecting the composition of bulk slag to the corner of

CaO and the liquidus lines for various temperatures in the phase diagram. The

10

dashed lines show the estimated liquidus boundaries in the phase diagram. The

effect of additives investigated in the present work, on the liquidus temperature

might be studied in the quaternary phase diagrams of CaO – SiO2 – Al2O3 – X,

where X = CaF2, FeOx, TiO2, ilmenite, MnOx, etc.

Figure 1.1: CaO-Al2O3-SiO2 phase diagram in Slag Atlas (Eisenhuttenleute(1995))

11

Figure 1.2: CaO – Al2O3 – MgO phase diagram in Slag Atlas (Eisenhuttenleute (1995))

The tentative liquidus surfaces in the system Al2O3 – CaO – SiO2 - FeOx was

measured by Kalmanovitch and Williamson (1984) & (1986) but they did not

consider slags with low concentration of silica.

Baisanov, Takenov, Gabdullin and Buketov (1983) and Takenov (1987)

investigated liquidus surface in Al2O3 – CaO – MnOx – SiO2 where the focus was

mainly on the coexisting phases in the melt.

12

The liquidus surface in the system of Al2O3 – CaO – SiO2 – TiO2 was measured

by Pierre (1954) & (1956) but they just considered the slags with 10 and 20 wt%

Al2O3.

Nadyrbekov, Akberdin, Kulikov and Kim (1980) studied the crystallisation

temperatures in the Al2O3 – CaF2 – CaO – SiO2 system with 2, 4, 6, 8, 10 mass %

CaF2 and the deduced the information from viscosity versus temperature curves.

But they did not consider slag with low silica content.

In the case of MgO, one can find the solubility of MgO in the established CaO –

Al2O3 – MgO phase diagram, but for slag with addition of FeOx and CaF2, no

data was found in the published literature.

The solubility of solid oxides in the slag can also be determined from the

thermodynamic modelling, although its accuracy greatly depends on the

verification of the results by the experimental data.

Therefore, there are gaps in the published data on the measured solubility of lime

in ladle slag with the above mentioned additives and the solubility of magnesia in

the calcium aluminate slags with the mentioned additives.

1.5.4 Physical properties of solid oxides

Natalie and Evans (1979) studied the relationship between lime properties and

the rate of dissolution in molten slags. They subjected lime samples to a series of

tests such as; water reactivity test, mercury penetration porosimetry and surface

area measurement aimed at the characterizing their structure. They applied the

13

water ASTM test and the rotating lime in slag test to estimate the reactivity of

different lime samples. In these water ASTM tests, the reactivity is assessed from

the temperature rise in water. The authors found that the pre-treatment of the

lime in the kiln had significant effect on the reactivity result, with hard burnt

lime the least reactive and soft burnt lime the most reactive. According to their

mercury penetration porosimetry results, the soft burnt lime had the highest

porosity and also the soft-burnt lime had larger pores compared with other limes.

The lime samples with higher reactivity had higher porosity and total pore

volumes. Then the rate of dissolution of lime samples was examined by rotating

lime specimen in the CaO – FeOx – SiO2 slag at 1350ºC. The rate of dissolution

was measured on the basis of the reduction in diameter of the cylindrical lime

samples. It appeared that soft burnt limes dissolved more rapidly in the slag

compared with other samples and the rate of dissolution was found to be directly

dependent on the pore surface area. They postulated that the dissolution of lime

takes place within pores by penetration of slag into the lime, this dissolution

process would thus result in faster dissolution of porous, soft burnt lime. They

concluded that more reactive porous limes dissolve more rapidly in the slag.

Umakoshi, Mori and Kawai (1984b) studied the dissolution of burnt dolomite

with the apparent porosities of 20 to 35% into the molten FeOx – CaO – SiO2 in

the temperature range of 1350 to 1425ºC. They found that the dissolution rate

was increased by about 20% when the apparent porosity was increased, although

the mass flux into the slag was scarcely changed. It was postulated that the

penetration of molten slag into burnt dolomite pores increased with increasing

apparent porosity.

14

1.5.5 Formation of a product layer at the solid oxises/slag interface

According to phase equilibria data and observations made by researchers, (Slag

Atlas (Eisenhuttenleute (1995)) formation of a solid layer of oxide e.g.

2CaO.SiO 2 takes place at solid oxide/ slag interface, which may prevent the

direct contact of solute with the slag. Formation of such a layer lowers the rate of

dissolution because of the lower mass transfer rate through the solid.

Natalie et al. (1979) performed experiments in which the lime samples with

various porosities were dissolved in two types of slag, i.e. (FeOx – 12 wt% SiO2

– 10 % CaO) at 1350ºC and (FeOx – 18 wt% SiO2 – 27 % CaO – 10 wt% CaF2)

at 1400°C. They reported that a layer of dicalcium silicate was formed a few

micrometers away from the lime. It is postulated that this observed layer might

have been anchored to its position by chemical or electrochemical bonding

phenimena. This layer was reported to be discontinuous in the presence of FeOx.

The formation of this layer appeared to have a substantial effect on the

concentration profile. However they did not report the effect of slag composition

on the morphology of this layer.

Matsushima, Yadoomaru, Mori and Kawai (1977) studied the mechanism of

dissolution of a static solid lime in a slag, by dipping a single crystal of lime into

slag bath of CaO – 40 wt% SiO2 – 20 % Al2O3 and CaO – 40 wt% SiO2 – 20 %

FeOx at 1400 – 1500 ºC. They used the crystal of CaO to avoid the complexity

due to the porosity of the sintered lime. It was observed that a layer of

2CaO.SiO 2 formed at places slightly apart from the interface, which retarded the

dissolution. The slag near the interface was enriched in Al2O3 or FeO as shown

15

in Figure 1.3. It was also observed that the lime dissolution rate into slags

containing high FeO and low SiO 2 was greater than rates for slags with low FeO

and high SiO2. This observation was explained on the basis that formation of

2CaO.SiO 2 and 3CaO.SiO 2 layers in slag of high FeO was discontinuous and

thus had small retarding effect on the dissolution rate of lime, whereas in slags of

high SiO2 and low FeO, the layer was dense and continuous hence retarded the

rate of dissolution markedly.

Figure 1.3: Schematic diagram of distribution of slag components near the interface according to Matsushima et al. (1977)

Noguchi, Ueda and Yanagase (1976) studied the rate of dissolution CaO crystals

into the CaO – 45 wt% SiO2 melt at 1500 ºC using a hot stage microscope. They

observed a layer of 2CaO.SiO 2 formed around the CaO, grew with time. They

also studied the effect of addition of FeO (2 to 40 wt%) on the morphology of the

reaction layer. It was shown that by increasing FeO content of slag, some cracks

formed on the 2CaO.SiO 2 layer and the formation of 3CaO. SiO 2 layer and (Ca,

Fe) O solution were also observed between lime and 2CaO.SiO 2 layer.

16

Williams, Sunderland and Briggs (1982) investigated the dissolution of lime and

dolomite in iron-silicate melts at 1300°C and reported the existence of four

distinct zones. The iron-silicate melt became separated from the lime specimen

by a zone of 2CaO.SiO 2 and FeO rich region. Initially a granular form of

2CaO.SiO 2 was precipitated which gradually sintered and formed a continuous

barrier around the lime sample. In case of a soft burnt lime an FeO rich, two

phase region between 2CaO.SiO 2 and lime sample was formed. After 120

seconds, the 2CaO.SiO 2 layer lost its appearance and produced a solid irregular

shaped layer. Soft burnt lime produced greater proportion of FeO-rich liquid

between 2CaO.SiO 2/lime interface than hard burnt lime. Addition of 5 wt %

MgO to iron-silicate melt produced an extensive and dispersed zone of

2CaO.SiO 2 which was discontinuous and no longer formed a barrier to melt

penetration.

Umakoshi et al. (1984b) reported that when burnt dolomite was immersed and

rotated into stagnant molten slag of (15 – 40 wt%) CaO - (15 – 50 %)SiO2 - (20 –

70 %) FeOx, a solid solution film of 2CaO.SiO 2 and (Ca, Fe)O was formed at a

short distance from the surface of dolomite and at the same time CaO and MgO

began to dissolve individually. But due to the difference in crystal structure of

CaO and MgO, 2CaO.SiO 2 detached easily and dispersed into bulk slag phase

under forced convection. The molten slag rich in FeO penetrated into gaps and

formed dense (Fe, Mg)O film, hence dissolution of MgO proceeded through the

dissolution of (Fe, Mg)O solid solution formed on the surface.

17

Satyoko and Lee (1999) studied the dissolution of doloma and dolomite at

1350ºC in the stagnant melt of CaO – 4 wt% MgO – 30 % SiO 2 – 30 % FeOx – 6

% MnOx. Their results showed that molten slag penetrated into the doloma

through pores and/or cracks, then reacted with MgO and CaO forming low

melting phases of ((Fe, Mg)O) and dicalcium ferrite (2CaO.Fe2O3). The

formation of these phases indicated the breakdown of the 2CaO.SiO 2 layer

formed at the lime/slag interface, making it easier for slag to penetrate through.

In the dissolution of dolomite, the formation of CO2 claimed to act as a barrier

for further dissolution. Also the formation of 2CaO.SiO 2 was shown to be

accelerated by localized cooling due to CO2 gas evolution. On the basis of this

work; Satyoko, Lee, Parry, Richards and Houldsworth (2003) suggested iron

oxide enrichment of doloma using mill scale as a substitute material for normal

doloma in a BOF flux charge.

Kor, Martonik and Miller (1986) investigated the effect of temperature and

degree of calcination of lime on its dissolution rates in the slag. They found that

lime calcined at 900ºC dissolves about twice as fast in a FeO – 30 wt% SiO 2 slag

as lime calcined at 1200ºC. However, the calcination temperature hardly affected

the dissolution rate in FeO – 25 wt% SiO2 – 15 % CaO slags. They explained

their observations by making use of the lime dissolution mechanism in FeO –

SiO2 – CaO slags as proposed by Oeters and Scheel (1971). This mechanism is

based on the counter diffusion of CaO and SiO 2 and relates the dissolution rates

of lime to the formation of a dicalcium silicate phase within the slag phase, a

certain distance away from the lime-slag interface. The magnitude of this

distance, according to the proposed mechanism, is determined by the relative

18

magnitude of the diffusive fluxes of CaO and SiO 2. The lower the diffusive flux

of CaO with respect to that of SiO 2, the further away from the lime-slag interface

the formation of the Ca2SiO4 phase takes place. For slags containing 70 wt%

FeO, the thickness of the 2CaO.SiO 2 phase was small and was expected to be less

coherent for lime calcined at 900 ºC. This was explained as small particles would

detach early from the lime spheroid calcined at 900 ºC and this would form an

incoherent 2CaO.SiO 2 phase, causing the CaO to more rapidly diffuse into the

slag phase. This mechanism was claimed not to occur in lime calcined at 1200 ºC

and explained why the dissolution of calcined at 1200 ºC was slower than that for

lime calcined at 900 ºC. The authors also show that the degree of calcination of

the lime (amount of CO2 remaining) has a significant effect on the lime

dissolution rate. For lime containing residual quantities of CO2 (degree of

calcination <100%), the faster dissolution rate observed which was claimed to be

attributed to CO2 bubbles disturbed the 2CaO.SiO 2 layer and generally increased

the mass transfer coefficient through agitation of the melt.

According to the analysis by Turkdogan (1983), the penetration of iron oxide

rich slag through the cracks in the solid layer to the surface of lime particles

provides a passage for calcium and oxygen ions to diffuse into the slag bulk, thus

facilitating the rate of dissolution. With porous lime the depth of slag penetration

into the reacted zone is greater, and the rate of dissolution is much faster, as

would be expected from an increase in the solid/liquid contact area. Slag

penetration into the pores and between the lime and dicalcium silicate also

contributes to the disintegration of the particle and thus accelerates the rate of

lime dissolution.

19

Finn, Cripps and McCarthy (1973) investigated the dissolution of burnt lime in

the basic oxygen steelmaking slags and proposed the concept of coating lime

with iron ore during calcination. They explained that the structure of burnt lime

is dependant on the raw limestone and more importantly, on the temperature

reached during calcination. Hard – burning, at temperatures of order of 1400ºC,

produces a relatively coarse- grained, chemically unreactive, sintered structure

with large pores and fissures. Soft – burning, at about 1000ºC, yields a finer,

more porous structure, with a larger, more reactive, surface area. However,

during the steelmaking process, as the temperature rises from 1400 to 1600 ºC,

solid lime remaining in the slag tends to become hard – burnt. The authors

mentioned that at the lime/slag interface, there are two competing reactions

possible:

• Absorption of iron oxide on solid lime to form low melting point calcium

ferrite.

• Reaction with silica in the slag to form solid silicates, mainly dicalcium

silicate, 2CaO.SiO 2.

The first reaction was claimed to bring the lime into solution while the second

tends to form a solid layer around the lime inhibiting the solution of lime in the

slag. The difference in the rate of solution of hard and soft burnt limes was

related to the first reaction. They argued that the denser structure of hard burnt

lime inhibits the absorption of FeO and formation of liquid ferrite; instead, it

provides a continuous foundation for an adherent 2CaO.SiO 2. Conversely, FeO is

readily absorbed in the porous structure of soft burnt lime, dissolves it, dilutes

20

the CaO and inhibits the formation of a continuous layer of 2CaO.SiO 2. This

layer decreases the rate of further reaction until it is dissolved or mechanically

broken or removed. The authors mentioned that the dissolution of this protective

layer could be promoted by addition of fluxes to the slag, which lowers the

liquidus temperature at the 2CaO.SiO 2 end of the pseudo – binary mixture with

that flux. High FeO slags could promote the dissolution of lime directly and also

the dissolution of 2CaO.SiO 2, but in practice, FeO concentrations are not

sufficient unless the lime is burnt at low temperature. It was explained that

Fluorspar was a standard flux for promotion of lime dissolution but

environmental concerns associated with the use of this flux, increasing demands

and decreasing availability of metallurgical grade fluorspar have led the steel

companies to an intensive search for suitable alternatives. The authors proposed

that an alternative approach to the problem was to prevent the formation of

dicalcium silicate layer rather than attempt to dissolve it once formed. From

consideration of the mechanism of lime dissolution, it was postulated that, if each

lime particle were surface impregnated with iron oxide prior to contact with the

BOS slag, this layer, at temperatures, would form an intermediate liquid phase

between the lime and the slag preventing the formation of an adherent layer of

dicalcium silicate. It was also postulated that this phase would advance into the

lime particle ahead of its external surface as solution progressed. The authors

carried out laboratory tests, during which the coated and uncoated lime samples

were immersed for the required time in the slag at 1400ºC and then rapidly

removed from the crucible. The samples were mounted and sectioned for XRD

and microscope examination to identify the various phases. For the coated lime,

as it absorbed sufficient iron oxide ahead of its contact with silicates, the

21

particles assumed a structure of FeO in solid solution in lime (C (W)) grains in a

largely continuous matrix of low melting point dicalcium ferrite, which rendered

it mechanically weak and therefore readily disintegrated in the slag. Also SiO 2

present in the solution, or as 2CaO.SiO 2, formed 3CaO.SiO 2, which precipitated

as separate hexagonal prisms and these provided less resistance to further

absorption of liquid slag. However, in the uncoated hard – burnt lime, a layer of

C (W) formed on the surface with insufficient dicalcium ferrite being produced

to weaken the particle mechanically or react the 2CaO.SiO2 layer with lime. Also

the FeO in the solid solution layer was a firm basis on which 2CaO.SiO 2 formed

a continuous layer, which prevented further reaction. Their results confirmed the

postulated mechanisms and indicated that a preliminary coating with iron oxide

can provide sufficient calcium ferrite to alter the mechanism radically and

thereby obtain rapid solution of the lime into the slag. Finally, the authors

indicated the feasibility of manufacturing coated lime with iron oxide in a rotary

kiln providing proportion and size and kiln temperature are controlled.

Zhang and Seetharaman (1994) studied the dissolution of MgO in CaO – FeO –

CaF2 – SiO2 slags in the temperature range 1573-1673 K under static conditions.

They identified formation of a magnesiowustite solid solution layer at the

MgO/slag interface. They measured the thickness of the product layer, change in

the dimension of MgO sample and the concentration profile of Mg in the product

layer and in the melt. It was shown that the thickness of the product layer was

changing linearly with time. The effect of CaF2 on the dissolution of MgO in the

slag was also studied. The dissolution of MgO increased with CaF2 content in the

slag. The thickness of the solid-solution layer also increased with the

22

concentration of CaF2 below 15 wt% and decreased substantially at higher levels

of CaF2. Based on the experimental observation, the authors proposed that the

dissolution of the magnesiowustite layer in the slag was faster than its growth

rate in the early stages of the dissolution. In later stages, it was shown that the

dissolution of solid solution in the slag was slower than its growth. It was

concluded that the mechanism of MgO dissolution is consist of two parallel

steps:(a) the formation of solid solution Mg1-x FexO and (b) the dissolution of

solid solution in the slag and proposed that the rate of growth of the

magnesiowustite layer could be the rate-controlling step in the dissolution of

MgO in slags.

Bygden, DebRoy and Seetharaman (1994) studied the dissolution of dense MgO

in (10 – 25 wt%) CaO – (45 – 60 %) FeO – (30 – 45 %) SiO 2 slag in the

temperature range of 1473-1673 K. They found that a layer of Wustite, (Fe,

Mg)O, and a silicate layer formed surrounding the MgO. They also suggested

that slag attack of MgO was in three steps; first the formation of the

magnesiowustite solid solution, followed by diffusion of the core MgO into the

(Fe.Mg)O layer and then chemical dissolution of this layer that increased linearly

with square root of time , suggesting that it was solid diffusion controlled. The

dissolution of MgO increased with the increase of FeO, and decreased with the

increase of CaO content in slag.

Sandhage and Yurek (1988) & (1990) investigated the dissolution of sapphire in

slag of CaO – 20 wt% Al2O3 – 40 % SiO2 – 5 % MgO with variable amount of

MgO. It was found that at lowest amount of MgO (5 wt%) and at 1450°C and

23

1550 °C, sapphire dissolved directly and without formation of any layer in the

slag, as it was observed that only isolated particles of spinel was formed in the

sapphire/melt interface. It was found by the authors that the dissolution was

slowed down by formation of a layer of spinel at 1450°C when the magnesia

content of the slag was 10 – 15 wt% and also at 1550 °C when the magnesia

content was more that 5 wt%, so the dissolution was continued in an indirect

way. They argued that the process of steady-state, indirect sapphire dissolution

into the melt consisted of two components, which operated in parallel: the rate of

formation of the spinel reaction product, and the rate of dissolution of the spinel

reaction product. It was postulated that the solid-state diffusion of a reactant or

product species was the slowest step in formation of the spinel and that the

liquid-phase diffusion of a reactant or product species was the slowest step in the

dissolution of the spinel.

It can be concluded that solid oxide dissolution often involves the formation of

an intermediate solid oxide reaction product which itself dissolves into the melt.

Formation and stability of these solid phases are in accord with established phase

diagrams for slag systems, thus in general the formation of any product layer at

solid oxide/slag interface for a given slag composition and temperature can be

predicted by studying the phase diagram and application of the thermodynamic

models.

1.5.6 Viscosity of slag

Viscosity is one of the key properties, which can influence the dissolution of lime

in slag. Viscosity affects the mass transfer of ions through the liquid slag, to and

24

from the solid oxides and slag interface. Another aspect of furnace performance,

which is influenced by slag viscosity, is refractory life, since the rate of attack by

a potentially corrosive slag is reduced if that slag is very viscous. Therefore

requirements dictate that slags should achieve a ‘rheological balance’ between

being adequately fluid, to have the rate of reaction high, and not being too fluid

to cause excessive corrosion/erosion of the refractory.

The viscosity of slag depends on composition and temperature, and since the

viscosities of metallurgical slags have an important influence on furnace

operation, then accurate experimental data and predictive models of the viscosity

of slags have always been desirable. There are many published data on the

viscosity of CaO – Al2O3 – SiO2 which has been measured experimentally.

Methods used to determine viscosity of slags include: Capillary method, Falling

body method, Rotating cylinder method, Oscillating method. It was shown by

various experimental data that the prime source of experimental uncertainties

were:

• Changes in the composition of the melt due to the reaction between the

melt and graphite, where graphite crucibles are used.

• To lesser extend, errors in temperatures of the melt.

According to the published data, most viscosity measurements were subject to

experimental uncertainties of ± 25%, where in some cases experimental

uncertainties could be %50±> , although experimental uncertainties of ± 10%

could be achieved by careful calibration of viscosimeters with high and low

25

temperature reference materials. Viscosity of some slags are available in the

literature, such as in Slag Atlas (Eisenhuttenleute (1995)).

It is often the case, however, that experimental information on the slag viscosities

is not available for the particular composition and conditions of interest to a

particular practice. In this event, mathematical models can be used to predict the

trends in viscosity as a function of the key variables, and so assist in the selection

of process conditions and the optimization of the performance of the system of

interest. The viscosity models normally utilize the temperature and composition

dependency of the viscosity in various forms.

A number of viscosity models make use of Arrhenius Equation (1.2) to describe

the temperature dependence of silicate viscosity;

⎟⎠⎞⎜

⎝⎛=

RTEA A

A expη (1.2)

Where η is the viscosity, E is the activation energy, R is the gas constant, and

T is the temperature in K. Viscosity-temperature data are, on the basis of the

above equations, usually presented in the form of ηln as a function of reciprocal

temperature (T-1). It is, however important to point out that the viscosity-

temperature plots for silicates usually show a slight curvature.

Many viscosity models are based on the Weymann – Frenkel (WF) kinetic theory

of liquids. In many cases, these models have been found to give better agreement

with experimental data than can be achieved using the Arrhenius expression:

26

⎟⎠⎞⎜

⎝⎛=

RTE

TAw expη (1.3)

The modified WF equation for slag viscosity developed by Urbain (1987) &

Urbain and Boiret (1990) is given by the following expression:

⎟⎟⎠

⎞⎜⎜⎝

⎛=

TB

AT310

expη (1.4)

Where A and B are compositionally dependant parameters. These classes of

oxides are introduced in the Urbain model as: glass formers, modifiers, and

amphoterics. Silicon dioxide (SiO 2) is an example of a glass – forming

component, which is characterized by a net structure and very high viscosity.

Modifier oxides containing e.g., Na+, K+, Ca2+, Fe2+ and Mg2+ ions modify or

break the net structure and lower the viscosity. Oxides such as Al2O3 or Cr2O3

can behave either as modifier or glass former, depending on the concentrations of

other constituents of slag. From the analysis of experimental data, Urbain

postulated that the parameter B increases proportionally to the third power of XG;

(XG, XM and XA are the corresponding molar fractions of glass – forming,

modifier, and amphoteric components). At a given XG, the parameter B has a

maximum value at the intermediate ratio of modifier to amphoteric fraction, XM/(

XM + XA ), this latter compositional dependence can be described by the second

power parabola. The parameter A is linked to B by the “compensation law”:

nmBA +−=ln , where m and n are constants.

27

Riboud, Roux, Lucas and Gaye (1981) using Urbain formalism which corrected

compositional dependence of A and B, successfully applied the model to

describe the viscosities of some industrial mold fluxes. It was reported that

between these two models, the model of Urbain gives a slightly better fit than the

Riboud model according to Slag Atlas (Eisenhuttenleute (1995)).

Hu and Reddy (1988) used a Weyman – type Equation (1.2) to describe the

viscosities of slags (Reddy model). The compositional dependence was estimated

by hole theory and “atomic pair model” of the slag structure. The Reddy model

has been applied to some binary systems and some ternary borosilicates.

Seetharaman and Sichen (1994) & Sichen, Bygden and Seetharaman (1994)

developed a KTH model, for estimation of viscosities of multi-component slags.

This model adopts the Arrhenius Equation (1.2) and Eyring equation for the

description of viscosities by estimation of the Gibbs energies of activation for

viscosities of pure components and in the case of multi-component solutions, the

non- linear variation of the activation Gibbs energies are included. The activation

energy for viscous flow was modelled in analogy with the modelling of Gibbs

energy.

The quasi – structural models have been developed to take into account the

complex internal structures of molten slags. Zhang and Jahanshahi (1998b) &

(1998a) developed a structurally related viscosity model, which, was originally

applied to three binary and two ternary melts. The temperature dependence of

viscosities was described by the Weyman Equation (1.3) but linked the

parameters to the concentrations of bridging, non – bridging, and free oxygens,

28

which were calculated using a thermodynamic “cell model” of slag structure. The

composition effect in the slag was also modelled by expressing the activation

energy of the slag as a function of structural parameters, namely, the fraction of

bridging and free oxygen ions, which relate directly to the bonding environment

in the silicate melts. The results from this model showed that it can be used to

calculate the viscosity of homogeneous multi-component silicate melts over the

broad temperature and composition ranges according to Sun, Zhang and

Jahanshahi (2003).

Mills and Sridhar (1999) developed the NPL model, which uses the Arrhenius

equation for temperature dependence of slag viscosity, but links the

compositional dependence to the corrected optical basicity of the slag, which in

turn can be obtained from experimental data or estimated. This model was

successfully applied to a range of metallurgical slag compositions as well as

mold fluxes, although it can be used only in limited compositional ranges.

Iida, Sakai, Kita and Shigeno (2000) & Iida and Kita (2002) used a quasi-

structural approach towards the modelling of slag viscosities as functions of

composition. Their model was based on an Arrhenius-type equation, wherein a

“modified basicity index” is used to link so-called structurally related “ network

parameters” to the viscosity. This model was used to describe experimental

viscosity measurements on mold fluxes.

Kondratiev and Jak (2001b) & (2001a) have revised and expanded the Urbain

formalisation so that separate model parameters can be included for the various

chemical components. The major advantages of this modified Urbain model is

29

that it enables the difference in chemistry of individual components to be taken

into account while retaining the strength of the Urbain assumptions, i.e. the

silicate slag viscosity increases with third power of the glass former

concentration and exhibits parabolic behaviour with varying proportions of

amphoterics and network modifiers

In the recent work by Seetharaman, Mukai and Sichen (2004) a set of

compositions for binary, ternary, quaternary, and multicomponent slag systems

was distributed to the authors of various models. The authors obtained the

corresponding experimental results by the rotating cylinder method. The

experimental results were compared with the results of the viscosity data, which

was carried out by the modellers themselves. It was shown that the various

models were able to approximately predict the order of magnitude of viscosities

for the various systems. In most cases, Idia’s model was able to predict the

viscosities close to the experimentation while the KTH model also seemed to

predict the viscosities of the binary, ternary and quaternary slags reasonably well.

The other models did not seem to deviate drastically from the experimental

values.

The discrepancies between the experimental values and the predicted values are

of the order of 25-30%, which are similar to the experimental uncertainties for

the viscosity measurements. Therefore the viscosity of molten slag can be

predicted by using one of the established models.

30

1.5.6.1 Effect of additives on the viscosity of slag

The effect of additives like, CaF2, FeO and TiO2 on the viscosity of CaO – Al2O3

– SiO2 slags has been reported widely in the literature on the basis of the

experimental work. Mills (1977) and Slag Atlas (Eisenhuttenleute (1995)), have

reviewed and complied the published data, all the mentioned additives decreased

the viscosity of slag but the effect of CaF2 is much more pronounced compared

to FeOx and TiO2.

While there are data on effects of additives on viscosity of slags, they do not

always cover the composition range of interest. Thus, one needs to use models

for predicting the values in composition range that data is lacking.

The viscosity of slags with addition of various additives can be predicted by

using the viscosity models. For example the model developed by Zhang et al.

(1998b) & (1998a) predicted that addition of metal-oxide components, tends to

reduce viscosity, so the developers of this model proposed that the effect of

cations on viscosity may be attributed to the strength of interaction between the

M2+ cation and oxygen ion. It was claimed by the authors that, the stronger

interaction between M – O atoms in the melt would cause the more difficult

movement of atoms, which consequently increases the viscosity.

Calcium fluoride as the main component of fluorspar is being used currently in

steelmaking to dissolve the lime in slag efficiently, through lowering the melting

point of the slag and decreasing the viscosity of the slag. The addition of calcium

fluoride to a silicate melt disrupts the polymeric constitution of the melt more

effectively than basic oxide additions according to Baak (1958) & Turkdogan

31

and Bills (1960) & Bills (1963). This is attributed to the fluorine anion replacing

the oxygen anion in the matrix owing to the F- ion having a greater affinity for

the Si4+ cation according to Gammal and Stracke (1988). The liberated oxygen

anion may then re-enter the structure, breaking yet another bond. With

depolymerisation of the slag, melt fluidity increases. Through the breakdown of

silicate networks, metal cations are produced, and their subsequent behaviour

depends on the system into which they are incorporated. If the refractory material

containing the slag is not compatible, these cations may react with the container

lining.

1.5.6.1.1 Effect of CaF2 Substitutes on the viscosity of slag

CaF2 is proved to decrease the viscosity of slag effectively, however there are

certain drawbacks associated with using CaF2. The research in the past by

Shimizu, Suzuki, Jimbo and Cramb (1996) & Shimizu and Cramb (2002) has

indicated that a significant amount of fluorine may evaporate from slags in the

form of toxic fluoride vapours such as SiF 4 and HF. Fluoride evaporation is not

only concerned with the environment but is also associated with interfacial

phenomena such as surface tension and adsorption. Also the steel industry has

been facing the dwindling supplies and increase in prices of fluorspar due to use

of more costly mineral processing methods, such as floatation cells.

The effect of additives on the viscosity of slag, and in particular, replacement of

CaF2 with other minerals has been evaluated by a number of researchers.

Tribe et al. (1994) & Tribe, Kingston and Caley (1997) performed a rheological

study of the CaO – SiO2 – MgO – CaF2 system to determine the influence of the

32

various mineralogical species on slag rheology and to access the possible

replacement of fluorspar in this system with an alkali-aluminosilicate tailing

material, Nepheline Syenite Tailing (NST) with the composition of 50 wt% SiO 2

- 20 wt% Al2O3 - 15 wt% (Na2O and K2O) - 10 wt% FeO - 3 wt% CaO. They

reported that basic slags with fluorspar exhibited both high fluidity levels, and

well-defined solidification temperature. In contrast, the acidic slags were less

fluid and, as might be expected, solidified over a wide temperature range. It was

also shown that the freezing point of slags in which Nepheline Syenite Tailing

replaced fluorspar was less-defined than for the basic fluorspar slags. This was

attributed to the higher concentration of acidic components, such as SiO 2, in the

NST slags. With respect to the replacement of fluorspar with NST, it was shown

that NST can effectively replace fluorspar, thereby sacrificing a lower overall

level of slag fluidity while gaining a slag with a broader solidification

temperature range. Whereas the fluidity was somewhat reduced, no problems

with respect to either slag retention or reaction kinetics were evident during

industrial testing.

MacLean, Kingston, MacDonald and Caley (1997) investigated the possibility of

replacement of fluorspar with Nepheline Syenite in the CaO-MgO-SiO2 system

at ladle furnace practice. The Nepheline Syenite used came from a rock, which

was consisted of three minerals, nepheline (NaAlSiO 4), microline (KAlSi3O8),

and albite (NaAlSi3O8). In the slag rheology tests, nepheline syenite proved to be

very effective. Although slags containing this mineral did not achieve the same

degree of fluidity as a fluorspar containing slag, the difference was not

considered to be significant at steelmaking temperature. The presence of Na2O

33

decreased the melting point of the slag considerably, a result of formation of

lower melting point minerals in the NaO-CaO-SiO2 system. Investigation on the

corrosive effect of adding the various minerals to the slag showed that fluorspar

to be the most aggressive towards the refractory and Nepheline Syenite proved to

be slightly less corrosive than the fluorspar. However, no experiment was

conducted to investigate the volatisation of species from the slag due to the use

of Nepheline Syenite.

Singh, Ravat, Chatterjee and Chakravarty (1977) conducted extensive laboratory

and industrial trials and showed that ilmenite, can be successfully used instead of

fluorspar as a fluxing agent in open-hearth steelmaking. As ilmenite is a

compound of FeO and TiO2 (FeTiO3), so they initially showed the effect of FeO

and TiO2 on slag liquidus temperature and compared it to CaF2. It was claimed

that as the concentration of the fluxing agent increases, there is a decrease in the

liquidus temperature of the slag. However, it was notable that there is no marked

difference between CaF2 and TiO2 at lower concentrations. They proposed that if

ilmenite with much lower melting point than TiO 2 (1470°C compared with

1830°C), is used, it can be expected to be more effective than TiO 2 alone. They

also compared effect of concentration of various fluxes on lowering melting

point of dicalcium silicate as it is shown in Figure 1.4 and mentioned that the

curve corresponding to ilmenite was expected to lie between the curves for TiO 2

and CaF2. Therefore, it was suggested that there should be no appreciable

difference between ilmenite and fluorspar as far as the fluidity action of the slag

is concerned, if the relative quantities of these fluxes are not very large. They

measured the relative fluidity of slags with ilmenite and fluorspar, and showed

34

that there was no difference between the fluidity of ilmenite and fluorspar.

However, the action of ilmenite was found to be slower than that of fluorspar.

This problem was overcome by adding ilmenite at the earlier stage of

steelmaking than fluorspar. This sluggishness in the action of ilmenite was

reported to be due to its higher meting point (1470°C), compared with that of

fluorspar (1400°C). One of the advantages of using ilmenite instead of fluorspar

is that, while fluorspar liberates harmful fluorine gas, ilmenite does not

contribute to atmospheric pollution. As ilmenite was replaced fluorspar

completely with a replacement of about 2:1, so the authors concluded that if

ilmenite would be cheaper than fluorspar then ilmenite would be a more

attractive flux.

Poggi and Lee (1974) measured the viscosity of ilmenite and fluorspar and found

out the high grade ilmenite (with low amount of SiO 2) has a similar viscosity and

melting point as the fluorspar. They also showed that the dissolution rate of lime

in liquid ilmenite is about 2.5 times faster than in fluorspar, however it was found

that to dissolve the same amount of lime, 30% more ilmenite than fluorspar must

be used as a flux.

35

Figure 1.4: Effect of concentration of various fluxes on lowering of melting point of dicalcium silicate Singh et al. (1977)

Rheological investigations into the use of Nepheline Syenite and ilmenite as

suitable fluxing additions for secondary steelmaking slags have shown promising

characteristics when compared to fluorspar. In testing the corrosive properties of

the fluxing agents, Nepheline Syenite showed less corrosive behaviour than

fluorspar, and no published literature was found on the effect of ilmenite on the

refractory. Although Nepheline Syenite could be a source Na emission due to the

presence of Na2O in this flux, there is no published study to consider this hazard.

However, a previous investigation showed that there is no environmental concern

with respect to utilizing ilmenite instead of Fluorspar in steelmaking.

36

1.6 Diffusivity in molten slag

The mass transfer of any solute in the solvent can be described by Fick’s first law

of diffusion as in Equation (1.5):

dxdC

Dj ii −= (1.5)

The proportionality constant D is called the diffusion coefficient or diffusivity of

i in the solvent. With the diffusion flux of species i, ij is in mol.m-2.s-1 and the

concentration gradient iC in mol.m-3, the diffusion coefficient has the unit of

m2.s-1. Therefore the dissolution of lime on the slag is greatly dependant on the

diffusion coefficient of CaO in the liquid melt.

The diffusion coefficient of a solute in a melt is a fundamental quantity required

to characterize mass-transport rates. Diffusion is the movement of the

components or constituent species of melt from point to point within melt.

In order to present the results in the literature and assess their practical

significance, it is necessary to define various diffusivities based on the possible

driving force for diffusion.

Generally, a thermodynamic gradient acts as a force for diffusion causing a net

flux of the diffusing species in a direction such as to diminish that gradient.

Chemical diffusion coefficients describe diffusion taking place under a gradient

of chemical composition. The limiting case of chemical diffusion, where the

thermodynamic gradient has been reduced to zero is self – diffusion in which

37

diffusion is the continuous interchange that takes place between species of the

same type in a medium of uniform composition. It is measured using stable or

radioactive isotopes(“tracers”) so that ideally, diffusion occurs down a gradient

of only isotope composition.

Based on these types of diffusion, the diffusion coefficient can be measured by

various methods such as: instantaneous plane source method, capillary reservoir

method, diffusion couple method and rotating disk technique (Kubicek and

Peprica (1983)). These methods are briefly explained in this section with the

relevant diffusivity data. The detailed description of each method and the criteria

for selection of the technique used in the present study will be explained in the

next section.

In the instantaneous source method, a small amount of radioactive tracer is

deposited on the surface of slag capillary specimen. The diffusion coefficient is

obtained by plotting the concentration of radioactive atoms with time.

In the capillary method, the diffusing species is held in a capillary, which is

immersed in the melt and diffusion occurs between the contents of the capillary

and liquid. The capillary is moved after a set of time and the distribution of the

species determined.

The diffusion couple consisted of two melts of identical composition except that

one contains the tracer element. The diffusion coefficient can be derived by a

linear regression of concentration versus distance.

38

The rotating disk method will be explained after presenting the published data on

the above-mentioned methods.

Johnson (1970) & Johnston, Stark and Taylor (1974) used radioactive tracers in

their experiments and measured the diffusion coefficients of calcium in the slag

under varying conditions of temperature and composition. They adopted two

methods; instantaneous plane source method where a small amount of

radioactive tracer was deposited on to surface of the slag capillary specimen

(called by the authors; chemical diffusivity) and capillary reservoir technique

where a small amount of labelled finely powdered slag of the same composition

as the slag in capillary was placed on the capillary surface (self diffusivity). The

calcium allowed diffusing under conditions of chemical diffusion, or more

strictly through a thermodynamic gradient, the gradient was so small that it could

in most cases probably be ignored.

They measured the chemical diffusivity of Ca45 in three slags with compositions

tabulated in Table 1.1. Conditions of self-diffusion, where the composition was

uniform throughout the sample, were established on slag A2.

Table 1.1: Slag compositions used for the measurements of diffusivity on liquid slags by Johnston et al. (1974)

CaO Al2O3 SiO2

A1 50.1 49.9 -A2 38 20 42A3 23.5 14.5 62

Chemical composition (wt%)Slag

39

Inspections of their results as shown in Figure 1.5 revealed that the diffusion

coefficient of Ca45 is higher in slag A1, compared to slags with higher silica

contents of A2 and A3. The values of diffusivity for slags with and without SiO 2

at 1450 ºC was reported to be 6108.4 −× cm2s-1 in slag A2 and was 5109.1 −×

cm2.s-1 in the slag of A1.

Figure 1.5: Effect of temperature and slag composition on the chemical diffusivity of Ca2+ introduced as Ca45O into slags of A1, A2 and A3 after Johnston et al. (1974)

The authors also compared the self diffusivity and chemical diffusivity of Ca45 in

slag A2 and found that the results are identical within the limits of experimental

error. The fluorine ion F18 was introduced with Ca45 as Ca45F218 into the slag of

CaO – 42 wt% SiO2 – 20% Al2O3 and the simultaneous diffusion of Ca45 and F18

was measured. It was shown that the introduction of fluorine ions into the melt

had a marked effect on the diffusivity of Ca45 and increased it by a factor of two

40

or more, however the activation energy for diffusion remained constant. Johnston

et al. (1974) also measured the chemical diffusion coefficient of iron as Fe59O in

slags containing 10 wt% and 1 wt% calcium fluoride. The results indicated that

the presence of the high-diffusivity fluorine ion in the melt considerably

increased the iron diffusivity. Their results also showed that different levels of

CaF2 content in the slag did not affect the rate of diffusion iron in the slag.

Saito and Maruya (1958) measured self-diffusion of calcium in molten slags of

CaO-SiO2, CaO-Al2O3, CaO-SiO2-Al2O3 and CaO-SiO2-Al2O3-MgO systems.

They performed the experiments by method of semi- infinite medium where two

specimens, one with Ca45O and the other without, were brought into contact at

the melting point of the slags. The results are shown in Table 1.2.

Table 1.2: Diffusion coefficient of Ca45 in slags studied by Saito et al. (1958)

The authors also compared the trend of diffusivity data with published data on

the viscosity and specific electrical conductivity. As it was found that there is no

large difference between the diffusivity, viscosity and electrical conductivity

CaO SiO2 Al2O3 MgO CaO/SiO2 1350 1395 1420 1440 1485 1510 1530 1540 1565 1575

55.2 44.8 - - 1.24 1460 - - - - 7.1 8.7 11 - - -

48.7 - 51.3 - - 1415 - - 3.3 5 7.8 - - - - -

39.8 41.2 19 - 0.97 1300 3.9 6.9 - 10 - - - - - -

43 37.2 20.2 - 1.15 1400 - - - 8 - 19 - - - -

48.9 39.4 11.7 - 1.24 1390 - - - 11.5 - 17 - - - -

45.2 36.3 18.6 - 1.24 1430 - - - - 8.5 9.9 - - -

45.6 34.1 20.3 - 1.33 1440 - - - 3.8 7.1 8.4 10.3 - - 13

48.4 31.3 20.3 - 1.55 1530 - - - - - - - 5.5 8.1 -

43.4 31.8 19.5 5.4 1.36 1480 - - - - 8.4 9.8 11.7 - - -

Slag composition wt% Meltingpoint(C)

Diffusion coefficient *10-7(cm2/s) of Ca45 ion in molten slag at various temperatures ( C )

41

between CaO-SiO2 and CaO-Al2O3 slags, the authors proposed that in the

neighbourhood of the composition CaO:Al2O3=1:1, the greater part of Al2O3

exists as the tetrahedra structure of aluminate ion AlO 45- similar to that of SiO 4

4-

in basic CaO-SiO2 slags. Diffusivity, conductivity and their activation energies in

aluminate melts were larger than in silicate melts. The viscosity of aluminate

melts was about the same as or slightly smaller than corresponding silicate melts.

Thus there was a good relationship between diffusivity and conductivity and

reciprocal of viscosity. For the purpose of studying the behaviour of Al2O3 in

liquid slags, diffusivity of CaO – SiO2 slags (CaO/SiO 2=1.24) were compared

with those of CaO-SiO2-Al2O3 (CaO/SiO2=1.33, Al2O3=20.3%). The authors

mentioned that according to the previously published data, it had been considered

that Al2O3 had an intermediate properties between acidic and basic elements, and

at low Al2O3 concentrations in acid slags, Al2O3 might dissociate into Al3+ and

O2- ions and showed basic properties (network modifier), but in strong basic

slags, Al2O3 became aluminate ion such as AlO 33- or AlO4

5-, etc. and showed a

trend of acidity (network former) regardless of the concentration of Al2O3. As the

addition of 20% Al2O3 scarcely changed the values of diffusivity, it was

postulated that the trend and the degree of formation of network structure of

aluminate ions were not so strong as those of silicate ions. It was also found that

addition of 5 wt% MgO, increased the diffusion coefficient of Ca2+ by about

10~15% in the slags with similar basicity, so the authors postulated that Mg2+ ion

dissociated from MgO might behave as a network–modifier, increasing the

activity or mobility of Ca2+ ion under the reducing condition in their experiment.

They supported their theory by looking at the published viscosity data, as

viscosity decreased 15% due to addition of 5% MgO at the composition

42

CaO/SiO2 = 1.2. Generally the magnitude of self-diffusion coefficient in liquid

slags was about 10-6~10-7 cm2/s and it was shown that the data had a good trend

with changes of electric conductivity and the reciprocal of viscosity coefficient

based on the compositions of slag.

Towers and Chipman (1953) & (1957) measured the diffusion coefficient of

calcium and silicon ions in the slag consisting of CaO – 40.5 wt% SiO2 – 20.9%

Al2O3 by tracer technique. They used two techniques for measuring diffusivities,

one contacting two slags of same composition with one of them containing the

radioactive tracer and in the other technique, slag capillaries to which tracer had

been added, were brought into contact with a relatively large volume of the

master slag. After the diffusion, concentration of tracer along the capillary was

measured, which resulted in the calculation of diffusion coefficient. Their results

are shown in Figure 1.6, where diffusivity is plotted against 1/temperature. The

values of silicon diffusivity were about one tenth that of calcium diffusivity. The

average values of Ca45 diffusion coefficient at 1350, 1400 and 1450°C, were

7105.3 −× , 7101.2 −× and 6104.3 −× cm2.s-1 respectively, with the activation

energy of 70 kcal/mole. The average diffusivities of Si31 ion was calculated at

1365 and 1430ºC to be 8107.4 −× and 71005.1 −× cm2.sec-1, respectively.

43

Figure 1.6: Diffusion coefficient of calcium (upper line) and silicon (lower line) after Towers et al. (1957).

Keller, Schwerdtfeger and Hennesen (1979b) measured the tracer diffusivity and

electrical conductivity of Ca45 in the CaO-SiO2 melts, where SiO 2 content of slag

varied between 0.448 to 0.634 (mole fraction) in the temperature range of 1500

to 1700 ºC, using capillary technique. The average diffusivity values were in of

the order of magnitude of 10-6 cm2/s. Their results showed that the diffusivity

was decreased by increasing the silica content of the slag as it is illustrated in

Figure 1.7.

44

Figure 1.7: Tracer diffusivity of Ca45 in CaO – SiO2 melts a function of mole fraction of silica and temperature after Keller et al. (1979b)

Their diffusivity values agreed best at the same basicity with those measured by

Towers et al. (1953) & (1957) in slag with the composition of (CaO - 40 wt%

SiO2 – 20 % Al2O3) but higher than results from Saito et al. (1958) and lower

than those obtained from Johnston et al. (1974), although the diffusivity data

show the order of magnitude of 10-6. The authors measured the activation energy

of diffusion and it was shown that the activation energy was increased by

addition of silica content of the slag, as it is tabulated in Table 1.3. The authors

also measured the electrical conductivity of Ca with AC current of variable

frequency using the four-pole method. The results are shown in Figure 1.8.

45

Table 1.3: Activation energy of diffusion in the CaO – SiO2 melt as a function of SiO2 content of slag

Composition of melt Mole (SiO2)

Activation energy(kcal g atom-1)

0.448 29

0.488 34

0.530 34

0.587 30

0.634 35

Figure 1.8: Electrical conductivity )( 11 −−Ω cm of CaO-SiO2 melts as a function of mole fraction of silica and temperature after Kelleret al. (1979b)

As it can be seen, the electrical conductivity was decreased by increasing the

mole fraction of SiO 2. The activation energies for diffusion of Ca45 (average 32

kcal g-atom-1) and for electrical conduction (average 26 kcal g-atom-1) as

46

determined from the slopes of the straight lines in Figure 1.7 and Figure 1.8. This

indicates the same mechanism for diffusion and conduction. The authors also

computed the electrical conductivity from the Nerst – Einstein Equation (1.6) on

the basis of the assumption that conduction was solely due motion of Ca2+ ion

and also validity of Nerst – Einstein equation as:

RTFDCz

k CaCa22

= (1.6)

Where z is the charge of the Ca2+ ion, Cca the concentration in moles.cm-3 of the

Ca2+ ions, and F the Faraday constant. A comparison of the computed values of

electrical conductivity with the measured values at 1600 ºC as presented in

Figure 1.9 shows that the calculated values of conductivity are lower than the

measured data. The difference is small at low SiO 2 content, but it increases with

increasing SiO 2 content. Hence, it appeared that in the CaO rich slag, most of the

current was transported by Ca2+ ions, which is in agreement with the published

transference numbers of cations by Bockris, Kitchener and Davis (1952).

47

Figure 1.9: Tracer conductivity and computed conductivity of Ca45 in the CaO – SiO2 melt as function of SiO2 at 1600 ºC after Keller et al. (1979b)

Keller and Schwerdtfeger (1986) also measured the tracer diffusivities of Ca45

and Fe59 in silica saturated (0 – 15.9 wt%)FeO – (33.8 – 23.2 wt%) CaO – (66.2

– 60.9 wt%) SiO 2 melts at 1600 ºC. They deployed the porous frit technique,

where the frits consisted of a packing of silica powder, which was sintered into

vitreous silica tubing and the pores of the first were filled with pre-melted silica

saturated slag. Diffusion into the slag was from a thin layer of the same chemical

composition but doped with Fe59 or Ca45. It was shown that the diffusion of iron

was much faster than that of calcium as the average value of diffusivity obtained

were about 6102 −× cm2.s-1 for Ca45 and 5101 −× cm2.s-1 for Fe59as it is also

illustrated in Figure 1.10.

48

Figure 1.10: Diffusivities of iron and calcium in silica saturated CaO –FeO – SiO2 melts at 1600 ºC after Keller et al. (1986)

The authors compared their results with electrochemically determined Fe

diffusivity data by Nowak and Schwerdtfeger (1975) at most compositions, the

data (Keeler) were smaller about a factor of two. It was motioned that the

electrochemical method yields self – diffusivities which were related directly to

the mobility of the iron and the tracer – diffusivity must be smaller than the self-

diffusivity due to the correlation factor, which in silicate melts is about 0.5. The

authors also claimed that the difference between data could be due to difficulty in

the diffusivity measurement in liquid slags and deviation by a factor of two

between data obtained with different techniques is about normal. Their

investigation showed that the frit technique could be used to produce diffusivity

data at high temperatures, however it was mentioned that its application was

49

limited to the slag compositions, which are in thermodynamic equilibrium with

the frit material.

Hara, Akao and Ogino (1989) measured the self diffusivity of Ca45 in FeO- 33

wt% SiO2- 7% CaO slag and mutual diffusivity of Ca45 in FeO- 32 wt% SiO 2

melt equilibrated with solid iron in the temperature range 1270 to 1450ºC. They

used the capillary reservoir method with Ca45 as the radioactive tracer. Their

results are shown in Figure 1.11.

Figure 1.11: Diffusivity of Ca45 in melts as a function of temperature after Hara et al. (1989)

Goto, Kurahashi and Sasabe (1977) measured the tracer diffusivities of calcium

and iron in a steelmaking slag of CaO – 27 wt% SiO 2 – 40% Fe2O3 under varying

oxygen pressure in the gas phase, by the instantaneous plane source method. The

50

tracer diffusivities were measured at 1360, 1410, and 1460ºC with an oxygen

activity of 10-1 to 10-8 atm. The results are shown in Figure 1.12. Their results

indicated that the diffusivity of iron was about 2 to 3 times larger than that of

calcium. The ratio of Fe+3/(Fe+3+Fe+2) in their slag was measured to be in the

range of 0.1 to 0.6. It was shown than the diffusivity had a direct relationship

with this ratio.

Figure 1.12: Relationship between logarithm of tracer diffusivities of calcium and iron and reciprocal temperature after Goto et al. (1977)

Keller and Schwerdtfeger (1979a) measured the tracer diffusivity of Si31 ion in

CaO-SiO2 melts with capillary technique, where the silica content of slag varied

(mole fraction of silica NSiO2 = 0.484-0.634) at 1600 ºC. They reported that

diffusivity of Si31 decreases with increasing silica content of the slag, as it is

51

shown in Figure 1.13. The authors also compared the silica diffusivity with their

previous publication on Ca45 diffusivity Keller et al. (1979b) and showed that the

values of Si31 diffusivity was lower than that of Ca45 by approximately one order

of magnitude in the silica rich melt. The difference decreased with decreasing

silica content. The results measured by these authors agreed with the results

published by Towers et al. (1957) at lower temperatures in the slag with

composition of CaO – 40 wt% SiO – 21 % Al2O3 slag.

Figure 1.13: Diffusion coefficients of Ca45 and Si31 as a function of melt composition at 1600 ºC after Keller et al. (1979a)

Ukyo and Goto (1982) measured the Quasi- inter-diffusivities of several solute

oxides in liquid CaO-SiO2-Al2O3 slag of 4:4:2 of charge weight ratio and liquid

FeOx-CaO-SiO2 slag of 2.5:3:4.5 of charge weight ratio. The slags were

equilibrated with air and the measurements were done using the diffusion couple

52

method at 1350 to 1450ºC. After diffusion runs of 20 or 40 min, the sample was

quenched to glassy state and analysed by a X – ray micro-analyser. According to

Figure 1.14, their results revealed that, MgO in the slag of CaO – SiO2 – Al2O3

had the highest diffusivity with an order of magnitude of 10-5 and P2O5 and TiO2

had the lowest diffusivity with an order of magnitude of 10-7. Also the diffusivity

data for MnO showed an average of 10-6 while diffusivity of FeOx was proved to

be about 10-5. For the slag containing FeOx their result is illustrated in Figure

1.15, where MgO still was the fastest oxide and the other oxides had a similar

order of magnitude to slags without FeOx.

Figure 1.14: Diffusivities of oxides in CaO-40 wt% SiO2-20 % Al2O3 slag after Ukyo et al. (1982)

53

Figure 1.15: Diffusivities of oxides in FeOx - 30 wt% CaO - 45 % SiO2slag after Ukyo et al. (1982)

Agarwal and Gaskell (1975) measured the self diffusion of iron in Fe2SiO4 and

CaFeSiO4 melts in the temperature range of 1250 to 1540ºC using Fe59 as the

radio tracer and the capillary – liquid reservoir method of diffusion measurement.

Their results are plotted as diffusivity of Fe versus 1/temperature for the two

compositions and are shown in Figure 1.16 and Figure 1.17. Based on their data,

the activation energy for diffusion was 3.24.17 ± kcal/mole for Fe2SiO4 and was

8.29.24 ± kcal/mole for CaFeSiO 4 slag.

54

Figure 1.16: The variation of DFe with T in Fe2SiO4 after Agarwal et al. (1975)

Figure 1.17: The variation of DFe with 1/T in CaFeSiO4 after Agarwal et al. (1975)

55

The self diffusivity of Fe in 61 wt% FeO – SiO2 melt was measured by Yang,

Chien and Derge (1959) at12 50, 1270 and 1304 ºC using the capillary –

reservoir method with Fe55,59 as the radioactive tracer. The iron diffusivity values

obtained were 510)3.09.7( −×± cm2/s at 1250 ºC, ( ) 5102.06.9 −×± cm2/s at 1275

ºC and 410)1.02.1( −×± cm2/s at 1304 ºC. Their results are presented in Figure

1.16, which are more than an order of magnitude higher than the results by

Agarwal et al. (1975).The activation energy for diffusion, evaluated from the iron

diffusivity was about 40 kcal/mole, while the activation energy for electric

conduction, calculated from Wejnarth (1934) data for melt of similar

composition was about 16 kcal/mole. The authors concluded that the diffusion

and electric conduction were operating on different mechanism in that melt.

Simnad, Yang and Derge (1956) developed an electrochemical radioactive tracer

method for using for the direct determination of ionic mobility in a molten

electrolyte. They immersed a radioactive iron electrode and supplied a current.

The distribution of the radioactivity in the quenched slag was measured in the

vicinity of the electrode. The ionic mobility of Fe2+ in silica – saturated iron

silicate is found to be 0 4109 −× cm2/volts.s, which corresponds to a diffusion

coefficient of 5108.5 −× cm2/s at 1250 ºC for the melt of FexO – 34 wt% SiO2 in

equilibrium with solid iron and silica. Their results agreed well with the data

from Agarwal et al. (1975) in which the diffusion coefficient was 5109.7 −×

cm2/s at the same temperature.

Mori and Suzuki (1969) measured the inter-diffusivities of iron in iron oxide

melts by the capillary method over the temperature from 1430 to 1550 ºC and the

56

composition range from ∑ == + 12.0)/( 3 FeFer to 0.42. Agarwal et al. (1975)

applied Darken’s diffusion equation to the their inter-diffusivity results using the

thermodynamic data of Darken and Gurry (1946) for iron oxide melts, and the

deduced diffusivity data is presented in Figure 1.16. Their values were in

excellent agreement with the work done by Agarwal et al. (1975), which is in

shown in Figure 1.16.

Nowak et al. (1975) used a galvanostatic technique to determine the mobility of

Fe2+, Co2+, Ni2+, and Ca2+ ions in silicate melts at 1600 ºC. The cell used was

made of quartz glass. Hence, the liquid silicates obtained the composition of the

silica saturation isotherm in the systems MeO – CaO – SiO2 (Me = Fe, Co, Ni).

Three electrodes (anode, cathode, reference electrode) were located at the bottom

of the cell. They consisted of the liquid metal Me contained in a capillary. When

current was passed through the cell, the concentration gradient caused an

increase of the voltage measured between anode (or cathode) and reference

electrode. The mobility of the Me2+ and Ca2+ ions were calculated from an

analysis of the voltage current relationship. The results are shown in Figure 1.18,

where the obtained diffusion coefficients are plotted versus the MeO – content of

the silicate melt. It can be seen that the diffusivity for the Ca2+ - ion is about one

order of magnitude smaller than those of the Me2+ ions.

57

Figure 1.18: Diffusivities of Fe2+, Ni2+, Co2+ and Ca2+ in silica saturated MeO – CaO – SiO2 melts at 1600 ºC after Nowak et al. (1975)

Nagata, Sata and Goto (1982) reviewed and compared the diffusivities of various

elements in molten slag for blast furnace and molten slag for steelmaking. The

self – diffusivities of elements in molten slag of CaO – 40 wt% SiO 2 – 2 % Al2O3

are summarized in Figure 1.19.

The Mg, Fe and Mn were shown to the fastest elements in the melt compare to

the rest of elements. It is evident from Figure 1.19 that of the elements studied,

Mg, Fe and Mn have the highest self-diffusivities. This could result from their

lower charge and hence weaker interaction with the oxygen anions and also the

size of ions.

58

Figure 1.19: Self diffusivities of elements in molten slag for blast furnace CaO-40 wt% SiO2-20 % Al2O after Nagata et al. (1982)

The diffusivity of Ca in the temperature range of 1388-1533ºC was in an order of

magnitude of 10-7 to 10-6 cm2/s. Also the self-diffusivity of elements in

steelmaking slag with composition of (25-40 wt%) Fe2O3 - (30-40 wt%) CaO-

SiO2 was reviewed by the same authors according to Figure 1.20. Again Fe was

shown to have the highest diffusivity, while Ti was the slowest diffusing species.

The calcium diffusivity in the temperature range of 1300-1550 ºC was in an order

of magnitude of 10-5.

59

Figure 1.20: Self diffusivities of elements in molten slag for steelmaking (25-40) wt% Fe2O3 -(30-40)% CaO-SiO2 after Nagata et al. (1982)

The diffusivity of lime in slags with various chemistries and at different

temperatures is summarized in Figure 1.21. These results are from published data

by Towers et al. (1957) & Saito et al. (1958) & Johnston et al. (1974) & Goto et

al. (1977) & Keller et al. (1979a) & Keller et al. (1979b) & Keller et al. (1986).

All results in this figure are on the basis of diffusivity measurements with

different techniques such as diffusion couple, capillary and instantaneous plane

technique. It can be seen that by increasing the temperature, the diffusivity

increases. Apart from the results from Saito et al. (1958), which are lower than

the rest of published data, the basicity of slag affects the diffusivity of lime. By

increasing the basicity, the diffusivity of lime in the slag increases. The effect of

additives such as FeOx and CaF2 shows an increase in the diffusivity of lime in

60

the slag. It can be seen that the there is no published data on the diffusivity of

lime in the ladle type slag where the basicity is around 5~6, furthermore, the

effect of other oxides on the diffusivity of lime in the slag has not been

quantified in the past. The poor reproducibility of diffusion results with the

methods mentioned above at high temperatures required that a large number of

experimental measurements had to be carried out in order to obtain statistically

significant data. Also, the experimental difficulties and hence the inaccuracies

recorded in results increased with increasing temperature. Moreover, the

diffusivity measurements in liquids using the above-mentioned method could

easily be in error because of convection in the melt.

In general, the data are incomplete even for the most important systems because

only selected compositions and only some of the transport properties have been

investigated. Further, the results obtained by different authors often disagree

considerably. Thus, it is desirable to extend some of the experimental studies to

cover broader compsotion range while determining effects of chemistry on

diffusivity and its activation energy.

61

Figu

re1.

21: T

race

r diff

usiv

ities

of C

aO in

slag

s with

var

ious

che

mis

try

on th

e ba

sis o

f pre

viou

s pub

licat

ion

(B: b

asic

ity ,

C: C

aO,

A: A

l 2O3,

Fe: F

eO, M

: MO

)

62

Some of the researchers measured the dissolution rate and mass transfer of solid

oxides in the slag under forced convection using a rotating disc/cylinder

technique, where a solid sample is rotated in a liquid slag capable of dissolving

the solid under reproducible conditions of fluid mechanics. A well-described

flow that affects dissolution in a known way is produced by rotating a

disk/cylinder in the melt. By applying the non-dimensional correlations of the

mass transfer, the diffusivity of oxides in the slag could be evaluated. The mass

transfer coefficient is essentially cons tant across the disk/cylinder surface,

simplifying the subsequent mass transfer analysis. A detailed description of this

method will be explained in this chapter.

Cooper and Kingery (1964) were the first who applied the rotating disk method

to measure the rate of dissolution and diffusion of sapphire in molten slag of 20

wt% CaO- 40 wt%Al2O3- 40 % SiO2 under forced convection at a temperatures

range of 1345-1550 °C. They calculated the rate of dissolution by measuring the

diameter change of the sapphire samples in the melt and found that the

dissolution of sapphire was controlled by mass transport in the molten liquid.

They also estimated the diffusivity of alumina in the slag, using the solutions for

mass transport from rotating disk into the melt. The estimated diffusion

coefficients were in the range of 810486.0 −×− cm2/s in which the diffusion

coefficient increased with temperature. These results are compared to the results

by Henderson, Yang and Derge (1961), who measured the self–diffusion of

aluminium by capillary – reservoir technique in two types of CaO – SiO2 – Al2O3

slag with basicity = 1 and Al2O3 = 6 and 12.5 mole %, in the temperature range

of 1400 to 1520ºC. They found that by decreasing the alumina amount of slag,

63

the diffusion coefficient was increased. The comparison with extrapolated data

from Henderson et al. (1961) to higher temperatures shows that both set of data

have an order of magnitude of 10-7 and are in a very good agreement (Figure

1.22).

Lee, Sun, Wright and Jahanshahi (2001) studied dissolution of dense alumina

discs in slags with composition of (28 – 48 wt%) CaO – (16 – 25 %) Al2O3 – (7 –

32 %) SiO2 – MgO (5 %) at 1575°C, by rotating disk method. The dissolution

rate was determined by sampling the melt at regular time intervals and measuring

the amount of solute dissolved in the slag. It was shown that the dissolution was

controlled by the mass transfer in the liquid phase. They also looked at the effect

of addition of FeOx and MnOx on the dissolution rate of alumina in the slag. It

was shown that addition of mentioned oxides had little effect on activity of Al2O3

and the driving force of alumina did not change across the liquid boundary layer.

They considered the total alumina mass transfer as the combination of the mass

transfer from the disk and cylinder side of the immersed sample and it was found

that reduction of viscosity due to the addition of transition metal oxides had little

effect on the increase of total mass transfer coefficient. However, the authors

showed that the increase in the rate of dissolution and mass transfer coefficient

were likely to be due to the increase in the diffusion of alumina in the slag phase.

So the apparent diffusivity of alumina was obtained (a magnitude of 10-6 cm2/s)

and it was found that addition of transition metal oxides had a considerable effect

on increasing the diffusivity of alumina in the slag. (a factor of two for addition

of 5 wt% FeOx and a factor of about four for 5 wt% MnOx addition). These data

are compared to the extrapolated results from Henderson et al. (1961) on self –

64

diffusivity of alumina, where the diffusion coefficient for slag of 12 wt% Al2O3

and basicity = 1. It appears that for slag without addition of FeOx and MnOx, the

diffusivity is slightly lower than Henderson et al. (1961) data but with addition of

transition metals, the diffusivity values have the same order of magnitude. The

comparison of data is shown in Figure 1.22.

Taira, Nakashima and Mori (1993) used the rotating cylinder technique to

investigate the kinetic behaviour of dissolution of sintered alumina into CaO-

SiO2-Al2O3 slags (basicity from 0.64 to 1.25, Al2O3 10 wt%) in the temperature

range from 1500 to 1580 ºC. They also looked at the effect of addition of NaF

and CaF2 on the dissolution behaviour. They examined the effect of revolution

speed, temperature and slag composition on the dissolution rate of alumina into

the molten slag. The rate of dissolution was obtained from the reduction in

diameter of the alumina specimen in the melt. The dissolution rate increased with

increasing revolution speed, temperature and CaO/SiO 2 ratio as well as by

addition of NaF and CaF2. It was concluded that the rate controlling-step during

the dissolution process of alumina into molten CaO-SiO2-Al2O3 slag is the

diffusion of solute in the slag boundary layer. The dissolution rate of alumina in

slags with 15 wt% NaF or CaF2 were 2 to 6 times higher than those for CaO-

SiO2-Al2O3 slags with the same ratio of CaO/SiO 2. They evaluated the mass

transfer coefficient on the basis of dissolution rate, however they did not measure

the mass transfer coefficient when the additives were added to the slag, as the

effect of additives on solubility of alumina in their slag was not investigated. The

diffusivity of alumina in the slag is deduced by the present author on the basis of

the mass transfer dimensionless correlation for rotating cylinder derived by

65

Kosaka and Minowa (1966). The results of mass transfer coefficient and

diffusivity are listed in Table 1.4. It appears that there is no trend in change of

diffusivity with basicity of slag, but the order of magnitude of diffusion is about

10-7 for temperature of 1500 ºC and 10-6 for the higher temperatures. These

results are in good agreement with results from Henderson et al. (1961) shown in

Figure 1.22, where the diffusion coefficient at 1485 ºC in slag of CaO/SiO 2 = 1,

Al2O3 = 12 wt%, was measured to be 7101.6 −× cm2/s and the deduced

diffusivity value on the basis of rotating cylinder experiments and for slag of

similar composition (slag D) at 1500 ºC is 7101.6 −× cm2/s.

Table 1.4: Mass transfer of alumina in the CaO-Al2O3-SiO2 (Al2O3 = 10 wt%) after Taira et al. (1993) and the deduced diffusivity

*Calculated by the present writer

Slag CaO/SiO2temperature

(K) rpm mass tranafer (cm/s)

diffusion*(cm2/s)

A 0.64 1823 200 3.00E-05 1.1E-06200 1.52E-05 3.1E-07100 2.86E-05 1.8E-06200 3.49E-05 1.1E-06400 8.41E-05 1.9E-06600 1.11E-04 1.8E-06

1853 200 4.16E-05 1.4E-06C 0.9 1823 200 5.62E-05 1.8E-06

1773 200 3.09E-05 6.1E-07100 3.86E-05 1.8E-06200 5.71E-05 1.5E-06400 1.23E-04 2.2E-06

1853 200 8.31E-05 2.7E-06E 1.25 1823 200 6.12E-05 1.5E-06

D 1 1823

B 0.8

1773

1823

66

Yu, Pomfret and Coley (1997) investigated the dissolution of alumina in the slag

of CaO – 16.1 wt% Al2O3 – 47 % SiO2 – 2.9 % Na2O – 3.7 % CaF2 system at

1530ºC using the rotating disk method. The rate of dissolution of alumina was

calculated from the change in the alumina concentration of slag. They applied the

boundary layer correlations in rotating disk and estimated the effective

diffusivity of alumina in the slag. The diffusivity data were in the range of

8102.7 −× to 7108.6 −× cm2/s changing directly with the amount of Na2O in the

slag, which was in the range of 2.9 to 11 wt%. The comparison of these results

with the data from Henderson et al. (1961) in Figure 1.22 shows the same order

of magnitude, where the Na2O content of slag is greater than 4 wt%.

67

Figu

re1.

22: C

ompa

riso

n of

alu

min

a di

ffusi

vity

dat

a ac

cord

ing

to H

ende

rson

et a

l. (1

961)

& C

oope

r et a

l. (1

964)

& T

aira

et

al. (

1993

) & L

ee e

t al.

(200

1) (B

: bas

icity

, A: A

l 2O3)

– B

is th

e ba

sicity

, A is

Alu

min

ium

con

cent

ratio

n.

68

Matsushima et al. (1977) applied the rotating cylinder technique and determined

the dissolution rate and mass transfer coefficient of rotating lime into CaO – SiO2

– Al2O3 and FeO – CaO – SiO2 slags. They found that the dissolution rate was

increased with revolution speed, temperature and reaction time. The authors

calculated the boundary layer thickness ( )δ form the mass transfer coefficient

( )k ,kD=δ where the diffusion coefficient ( )D was used from the previously

published data by Johnston et al. (1974). It should be noted that Johnston’s data

was on self-diffusivity but here we are looking at chemical diffusivity, which

may be much greater than self-diffusivity. Boundary layer thickness was

estimated from the equation derived by Kosaka et al. (1966), which was obtained

by the method of dimensional analysis. A comparison of boundary layer

thickness calculated from the two methods, showed a good agreement,

supporting the postulation that the rate-determining step was the mass transfer

through a slag phase boundary layer.

The dissolution rate into slags containing FeO was several times greater than that

into slags without FeO. Since the authors calculated the mass transfer of CaO in

the slag from the dissolution rate data, the diffusivity of CaO in two types of slag

is deduced in the present work from their mass transfer data and on the basis of

Kosaka’s mass transfer correlation. The results are tabulated in Table 1.5.

69

Table 1.5: Values of mass transfer coefficient after Matsushima et al. (1977) and deduced diffusivity of lime in the slag

Slag Temperature( ºC )

Revolutionspeed (rpm)

K(cm/s)

D(cm2/s)

1500 200 2.90×10-4 6.67×10-6CaO – 40 wt% SiO2 –20% Al2O3 1500 400 5.30×10-4 1.01×10-5

1400 200 9.70×10-4 2.62×10-5CaO – 40 wt% SiO2 –20% FeO 1400 400 1.71×10-3 3.08×10-5

These diffusivity results for slag without iron oxide are compared with the data

by Johnston et al. (1974) on chemical diffusivity of Ca45O in the CaO – 62 wt%

SiO2 – 14.5 % Al2O3 where the diffusivity of lime was about 6105.5 −× cm2/s at

1500 ºC. The CaO diffusivity results in the slag containing iron oxide are also

compared with the data from Hara et al. (1989), where the self diffusivity of Ca45

in the slag of FeO – 33 wt% SiO2 – 7% CaO at 1400ºC, is 5107.2 −× cm2/s. This

comparison proves a very good agreement from the lime diffusivity results by

rotating disk technique and previously published data.

Umakoshi et al. (1984b) studied the dissolution rate of burnt dolomite in CaO-

FeO-SiO2 slag (CaO/SiO 2=1, FeO = 20 to 70 wt%) at 1350 to 1425ºC using the

rotating cylinder technique. The dissolution rate increased exponentially with the

increased stirring rate of the refractory cylinder suggesting that the dissolution

rate was controlled by the mass transport. With mass transport in the boundary

layer of liquid as the rate – controlling step for the dissolution of solid in liquid,

the mass flux for the dissolution, J was expressed as:

70

)( bs nnkJ −= (1.7)

Where,

=k mass transfer coefficient (cm/s)

=bs nn , contents of solute at the interface and in the bulk of molten slag (g/cm3)

The mass flux J (g/cm2.s) and the dissolution rate dtdr /− were defined

according to:

⎟⎠⎞⎜

⎝⎛−=

dtdr

J c .ρ (1.8)

Where cρ is the bulk density in g/cm3.

They substituted Equation (1.7) into Equation (1.8), which leads to the following

rate equation:

( ) ( )bsc

bbbss

s

cck

cckdtdr −=−=−

ρρ

ρρρ 100100 (1.9)

Where;

=c Concentration of solute (%)

=bs ρρ , Densities of molten slag (g/cm3) at the interface and the bulks

71

It was impossible to determine the mass transfer coefficient of burnt dolomite by

Equation (1.9), since CaO and MgO might individually dissolved from the

surface of burnt dolomite. Therefore the authors proposed that if the dissolution

of CaO in burnt dolomite was much slower than that of MgO, the dissolution rate

was controlled by the mass transfer of CaO in the boundary layer of molten slag

and the mass flux would be expressed as:

CaOCaO

MgO JMM

J .1 ⎟⎟⎠

⎞⎜⎜⎝

⎛+= (1.10)

On the contrary, if the dissolution rate was controlled by the mass transfer of

MgO, the mass flux would be expressed as:

MgOMgO

CaO JMM

J .1 ⎟⎟⎠

⎞⎜⎜⎝

⎛+= (1.11)

Where MgOCaO MM , are the molar weights of CaO and MgO, respectively and

MgOCaO JJ , are the mass fluxes for the dissolution of sintered CaO and MgO

cylinders determined from the previously publications by Matsushima et al.

(1977) & Umakoshi, Mori and Kawai (1981). By establishing the plots of

Equation (1.10) and (1.11) and also checking the linearity of the variables in the

two sides of the equations, the authors concluded that Equation (1.10) was valid

for the slag with 20 wt% FeO (CaO/SiO 2 = 1) and Equation (1.11) for slags of

higher FeO. Therefore, the mass transfer coefficient of dolomite in low FeO slag

at 1400ºC was calculated from Equation (1.12):

72

( )CaOk

MM

J b

CaO

MgO %.100

.1 Δ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ρ(1.12)

While the mass transfer coefficient for the other slags from the Equation (1.13).

( )MgOk

MM

J b

MgO

CaO %.100

.1 Δ⎟⎟⎠

⎞⎜⎜⎝

⎛+=

ρ(1.13)

The authors calculated the driving force of CaO and MgO according to the

relevant phase diagrams. The results of mass transfer coefficients are tabulated in

Table 1.6. The diffusivity of CaO and MgO on the basis of the mass transfer

coefficient are deduced in the present work by utilizing the dimensionless mass

transfer correlation for rotating cylinder developed by Kosaka et al. (1966). The

estimated diffusivity results are also listed in Table 1.6.

Table 1.6: Mass transfer coefficient of dolomite from the Umakoshi et al. (1984b) and deduced diffusivity data for CaO and MgO in the present work

SlagBasicity=1

FeOwt(%)

viscosity(poise)

density(g/cm3)

Mass tranafer (cm/s)

9.15E-049.77E-049.15E-046.81E-04

B 30 1 3.2 6.45E-04C 40 0.5 3.4 8.53E-04

7.89E-047.43E-04

20

50

1.6

0.4

A

D

3.1

3.5

73

The diffusion coefficient of CaO in slag with 20 wt% FeO was compared to the

interdiffuion coefficient of CaO, ( 5107.2 −× cm2/s) in the FeO – SiO2 slag

measured by Hara et al. (1989) and the diffusion coefficient of MgO in other

slags, compared to the MgO diffusivity data of ( 5.1 to 5108.1 −× cm2/s),

according to Umakoshi et al. (1981).

Effect of additives on the dissolution rate of lime has been investigated in the

past by Hamano, Horibe and Ito (2004).They studied the dissolution rate of lime

in the slag of FeO – 30 wt% CaO – 40% SiO2 at 1573ºC. They investigated the

effect of 10 wt% addition of CaCl2, Al2O3 and B2O3 on the dissolution rate of

lime. The dissolution rate of lime was estimated from the reduction in the

diameter of the rod used as the solute in their experiments. It was shown that at

constant temperature and a given slag composition, the dissolution rate of CaO

was governed by the mass transfer in the bulk liquid phase. The dissolution rate

of CaO increased with increasing FeO concentration and with basicity of the

melt. The effect of additives to the melt was an increase in the dissolution rate of

CaO in the order of: CaF2>CaCl2>B2O3>Al2O3.

Umakoshi et al. (1981) applied rotating cylinder method and measured the

dissolution rate of sintered MgO into molten FetO-CaO-SiO2 slags at

temperatures from 1350 to 1425 ºC. It was shown that the dissolution rate of

MgO increased with the rotating speed of cylinder and with temperature, and was

found to be controlled by mass transport in the boundary layer of molten slag.

The authors measured the mass transfer coefficients and utilized the non-

dimensional correlation in order to deduce the values of diffusion coefficient of

74

MgO into molten slags. The diffusivity of MgO in the molten slag was estimated

to be 51035.1 −× to 51075.2 −× cm2/s at 1400 ºC. Their findings agree well with

MgO diffusivity data by Ukyo et al. (1982), where the diffusivity of MgO in

FeOx – CaO – SiO2 slag between 1350 to 1450 ºC varies between 51097.1 −× to

51005.3 −× cm2/s.

Xie and Belton (1999) measured the chemical diffusivity of iron oxide in CaO –

38 wt% SiO2 – 21 % Al2O3 slag at 1360 ºC by a rotating disc of solid iron.

According to the authors, there is good agreement with the value at near to iron

saturation from the galvanostatic studies of Nagata et al. (1982), however, the

chemical diffusivity from work of Johnston et al. (1974) and the quasi – binary

diffusivity determined by Ukyo et al. (1982) are a factor of 5 to 6 higher (Figure

1.23).

It can be seen that the deduced lime diffusivity data obtained from this method

agree well with the data from the other techniques.

75

Figure 1.23: Chemical diffusivity of iron oxide in CaO – 38 wt% SiO2 –21 % Al2O3 melts in comparison with the results of other studies at 1300 to 1360 ºC and approximately the same base melt composition as a function of the average iron concentration.

1.6.1 Liquid state diffusion models

The understanding of diffusion phenomena in liquids is inferior in most respects

to that of either gaseous or solid state diffusion (Walls and Upthegrove (1964)).

The lack of accurate comparison of these and other related transport phenomena

in liquids is a consequence of a less complete knowledge of the liquid state. The

understanding of diffusion processes in liquids is further complicated by the

experimental difficulties encountered in attempting to test the various theories

proposed to describe diffusion and to predict the effect of relevant system

variables upon these phenomena.

76

Researchers have proposed mechanistic models for diffusion in liquids as an

attempt to enhance the understanding of liquid diffusion phenomena. These

models are reviewed in the following part:

1.6.1.1 Hydrodynamic theory

One of the best known equations relating diffusion and viscosity is that of

Einstein (1905). In this theory (Poirier and Geiger (1998)), the diffusing species

are non-reacting spherical particles of radius R moving through a continuos

medium of viscosity η with a steady-state velocity ∞V . The development of this

theory is based on Stokes’ law, which predicts the terminal velocity of the

relatively large un-attracting, hard spheres through a liquid. Therefore, the force

on a sphere moving at steady state in laminar flow is:

∞= VRF ηπ6 (1.14)

And upon Einstein’s equation, expressing the self-diffusion coefficient as a

function of the mobility as:

kTMD = (1.15)

Where the mobility, M, is the average velocity of the diffusing particle per unit

force acting on that particle. To obtain the Stokes-Einstein equation, the mobility

is determined from Stokes’ law as F

V∞ and the resulting expression is introduced

into Equation (1.15) to give:

77

μπrkTD

6= (1.16)

Although the Stokes-Einstein equation is derived on the assumption of large

solute particles diffusing a continuos medium, the radii of some liquid metal

atoms calculated from this equation show comparatively close agreement with

the values of crystallographic ionic radii. In view of the inconsistency between

the Stokes-Einstein model and the supposed structure of liquid metals, this

agreement is frequently described as merely fortuitous. Indeed, the agreement

between crystallographic radii and those calculated using the Stokes-Einstein

equation should not be accepted as an unequivocal verification of the validity of

the equation to describe diffusion except in an empirical manner. There are

several reasons for this conclusion. First, the crystallographic radii are very much

dependant upon the rather arbitrary assignment of a radius to one element either

from experimental data where the calculated radii are based on the assumed

additive nature of ionic radii to give interionic distance in halide and oxide

compounds. Second, examination of the radial probability functions from

quantum mechanics indicates that no absolute significance should be given to the

concept of radii, since these probability functions tail off zero for an infinite

radial distance. Third, the reported agreement between Stokes-Einstein radii and

crystallographic radii are achieved by judicious selection of the solid state radius

value and by subsequently assuming that a given ionic radius is identical in both

the liquid and solid state. The fact that the Stokes-Einstein equation does predict

approximately the diffusion behaviour in liquid metals implies that Stokes’ law

does provide a good estimate of the mobility. Since the mobility is a ratio of the

78

average velocity (taken to be the terminal value) to the force acting on the

particle, both the velocity and the force could be subject to compensating errors

and give an approximate value for the mobility.

1.6.1.2 Hole theory

The oldest structural picture of a liquid is the hole theory, which presumes the

existence of holes or vacancies randomly distributed throughout the liquid and

providing ready diffusion paths for atoms or ions. The concentration of these

holes would have to be very great in order to account for the volume increase

upon melting, thus resulting in much higher diffusion rates in liquids than in

solids just below the melting point. The hole theory has been used to estimate the

activation energy for self-diffusion in a liquid, by assuming that this energy is

equal to that required to form a hollow sphere (hole) of a diameter on the order of

a fraction of a nanometre.

1.6.1.3 Eyring theory

Eyring used his activated state theory (Glasstone, Laidlev and Eyring (1941)) to

explain the mechanism of diffusion, which worked reasonably well for diffusion

in solids and liquids. According to Eyring if the mechanism of activation in

diffusion can be assumed identical with that of viscous flow, the relation between

the self-diffusion coefficient and viscosity in liquids is given by:

79

32

1

λλλη =

kTD

(1.17)

Where 1λ is the distance between two adjacent layers and 2λ and 3λ are the

distances between two neighbouring molecules in the moving layer

perpendicular to and in the direction of moving, respectively. Since it is

reasonable to put the λ ’s as the average intermolecular distances, Equation

(1.17) reduces to:

λη 1=

kTD (1.18)

Based on the Eyring’s theory, when a large molecule or ion diffuses or migrates

under the influence of an electric field, in a solvent consisting of relatively small

molecules, it is unlikely that the rate-determining step will be the jump of the

solute molecule from one equilibrium position to the next, since the work

required to produce the necessary space would be very large. It is much more

probable, that the jump of the solute in one direction is the rate-determining

process; the large molecules of solute then moves in the opposite direction into

the space left vacant as a result of the motion of the solvent molecule.

Thus the rate-determining mechanism for large molecules diffusing through a

liquid composed of small molecules is the diffusion of the smaller molecules

around the oncoming large ones by the same mechanism, which these small

molecules use in diffusing around other smaller molecules. In Figure 1.24, a

80

small molecule is indicated by A and the large molecule it must diffuse around,

is indicated by B. Also, B’ is for the alternative case of a molecule of the same

kind as A. Now B’ or B will each be advanced the same distance when A in one

case flows around B’ and in the other around B. But the ratio of the distances

which A must travel in the two cases is ra2

λ , where the undetermined number, a,

will vary with the path followed by A in passing around B or B’. We thus expect

the ratio of the diffusion coefficients to be:

)2( raDD λ=

′ (1.19)

Where the diffusion of small molecule around other small molecule is defined

from Equation (1.18), we obtain the diffusion of molecule as:

η)2( rakTDl = (1.20)

81

Figure 1.24: Diffusion of large molecule (B) due to the movement of small solvent molecule (A)

Fluctuation theory: Cohen and Turnbull (1959) have proposed an alternative

theory for liquid state diffusion based upon the free volume, hard sphere model.

This theory, assumes that hard sphere atoms moves randomly within a free

volume cell until a fluctuation opens up a path, which permits diffusive

displacement of the contained atom. This theory can be regarded as an activation

volume analog of the more conventional Botlzmann activation energy concept.

This model has been tested by Cohen et al. (1959) using available self-diffusion

data to evaluate the radii for the critical free volume per cell required for

diffusion. These radii have been shown to be comparable to solid state ionic radii

and this result has been taken to support the contention of Glasstone et al. (1941)

that the ionic cores are the diffusing particle in liquid melts. The Eyring’s

equation has been used successfully by several researchers (Eisenhuttenleute

BA

2r

B’

λ

82

(1995)) but values of λ in Equation (1.18) slightly greater than 2r were needed

to obtain good agreement with experimental data.

1.7 General discussion

The above review of the literature revealed that the rate of dissolution of a solid

oxide into a molten slag has often been observed to be affected by solubility of

solute in the slag, viscosity of the melt, the agitation of bath, formation of a

reaction layer of the solute/solvent interface and diffusivity of the solute in the

solvent. The formation of the solid product layer is related to thermodynamic and

kinetic factors involved in the dissolution process, which can be predicted by

thermodynamic modelling or studying the relevant phase diagrams. The viscosity

data are available form the published data or can be predicted by viscosity

models. Given the fact the diffusivity of lime plays a significant role in the

dissolution of lime in the ladle slag, there is no published data on the lime

diffusivity in low silica slag system as all the previous work focused on the high

silica slag systems. Therefore, in order to fully understand the mechanism of lime

dissolution, there is a need to determine the data for diffusivity of lime in such

slags. The understanding of lime diffusivity could also shed lights on the impact

of various additives on the diffusivity and possibility of utilizing environmental

friendly fluxing agents for enhancing the process of lime dissolution.

In reviewing the diffusivity data by various experimental methods, it has become

apparent that the results obtained by different authors often disagree

considerably. This is due to inherent experimental difficulties at elevated

temperature. In measuring the tracer diffusivity, mass transport by diffusion

83

processes occurs at a very much slower rate than by gross convection processes,

which may interfere with measurements of self-diffusivity. Accordingly,

experimental methods are required to either minimize convective transport

processes or incorporate these effects as a part of the experimental technique

under controlled condition.

1.7.1 Questions arising from the literature on diffusivity

• What are the diffusivity and dissolution rate of lime and magnesia in the

ladle type slag?

• What are the effects of additives (like, CaF2, FeOx, TiO2, ilmenite and

MnOx) and temperature on the diffusivity of lime in the ladle type slag?

• What are the criteria for selection of experimental technique for

measuring diffusivity and which method is the appropriate for the present

study?

• What are the conditions governing the formation and stability of a solid

phase layer at the lime/ladle slag interface and how to monitor the impact

of this phase formation on the dissolution rate of lime and diffusivity?

1.8 Methods for measurement of diffusivity

Various experimental techniques for measuring the diffusivity are based on the

two classes of diffusion phenomena: self-diffusion (tracer diffusion) and

chemical diffusion.

84

Self diffusion involves movement of the various species present in the melt due

to the random motions. Self diffusion occurs continuously in any melt and can

not be measured because there are no physical manifestations of the process.

Tracer diffusion is the same process as self diffusion, except that a fraction of

one or more of the species in the melt is isotopically labelled to establish tracers.

The diffusive process can then be monitored by observing the movement of the

labelled species. In tracer diffusion both net fluxes and concentration gradients

are present, but only for the tracer component.

Chemical diffusion is the movement of species in response to chemical potential

gradient in the melt. Such gradients could be created by a number processes

including dissolution. Therefore, the diffusivity can be measured experimentally

by a tracer or creating a chemical potential in the melt.

The theoretical and mathematical description of the diffusion measurement

methods is based on Fick’s first and second laws for linear diffusion (in the x-

direction), whereby the equation of diffusion can be expressed as:

[ ]⎭⎬⎫

⎩⎨⎧

∂∂

∂∂

=∂

∂x

txCtxCD

xttxC ),(

),(),(

(1.21)

Where ),( txC is the concentration of diffusing species, x is the special coordinate

along the path of diffusion, t is time and D is the diffusion coefficient. Unlike

diffusion in solid phases, when diffusion in melts is considered, it is usually

85

assumed that the diffusion coefficient is independent of concentration. The

equation of diffusion can then be written as:

2

2 ),(),(x

txCDt

txC∂

∂=∂

∂(1.22)

The main methods used in the past in measuring diffusivity in melts are outlined

below.

1.8.1 Instantaneous plane source method

In this method a tracer (usually radioactive) is deposited as a thin later at one end

of long column, and the diffusion coefficient can be derived by the use f the

appropriate solution of Fick’s law as:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

Dtx

DTQ

C4

exp.2

π (1.23)

Where;

=C Concentration of radioactive atoms at a distance x from the deposit

=Q number of radioactive atoms deposited on the surface

=D diffusion coefficient of radioactive species

=t time for diffusion

The diffusion coefficient may therefore be obtained by plotting Cln versus x2.

86

1.8.2 Capillary - reservoir method

In this method, a long capillary tube containing slag is immersed in a large

reservoir of the same molten slag with a known content of the element whose

diffusion rate is to be measured. The temperature of the system is selected in

advance and must be kept constant. After a certain time, during which diffusion

takes place, the capillary tube is removed and cooled down (alternatively the

whole system may be cooled) and the sample is analysed along its length. The

inside diameter of the capillary tube is normally chosen so as to eliminate

convection, and is usually 1 – 3 mm. The capillary is tens of millimetres long, i.e.

longer than the distance to which the diffusing species has penetrated. The time

allowed for diffusion is usually 103 – 104 s. A schematic set-up for this

technique is illustrated in Figure 1.25.

87

Figure 1.25: Apparatus for measuring diffusivity of elements dissolved in molten slag by capillary – reservoir technique

1.8.2.1 Semi – infinite capillary

In this method, the initial and boundary conditions for diffusion are, from

Equation (1.22):

Water-cooledvacuum seal

Mullitereaction tube

chamotte tube

furnace

Heating elements

Graphite crucible

Reservoir melt

Graphite capillary sample holder

crucible support

thermocouple

Water cooled vacuum sealed

88

0)0,( =xC ∞<< x0

0),0( CtC = 0>t(1.24)

Thus, the concentration of the diffusing species is assumed to be constant in the

mouth of the capillary tube. For a semi – infinite capillary tube the solution of

Equation (1.22) using the conditions given in Equation (1.24), can be written as:

⎥⎦

⎤⎢⎣

⎡= 2/10 )(2

),(Dt

xerfCtxC (1.25)

1.8.2.2 Finite capillary

For a finite length l of the column of melt in the capillary tube, comparable with

the distance over which the species in the capillary tube has diffused in the

course of the experiment, the initial and boundary conditions for Equation (1.22)

are:

0)0,( =xC lx ≤<0 (1.26)

0),0( CtC = 0),( =∂

∂x

tlC 0>t

The solution of Equation (1.22), using the condition given in Equation (1.26), is

to be found in Crank (1975). The mean concentration )(tC of a diffusing species

may be written as:

89

∫=1

0

),(1

)( dxtxCl

tC (1.27)

When inserting the solution for ),( txC into Equation (1.27), we again obtain the

infinite series that, provided experimental conditions are suitably chosen,

converges rapidly. Therefore only the first term of the series need to be

considered when calculating the diffusion coefficient, and under such conditions

one can obtain

[ ]⎭⎬⎫

⎩⎨⎧

−⎟⎟⎠

⎞⎜⎜⎝

⎛=

)(18

ln4

20

2

2

tCC

tl

Dππ (1.28)

Equation (1.28) is specially suitable for calculating the diffusion coefficient D

since it is sufficient to know the mean concentration of the diffusing component

)(tC in the capillary tube; here, it is not necessary to know the entire

concentration curve as it could be altered and/or displaced, for example by

processes taking place during solidification. However, Capillary – reservoir

methods suffer from a number of shortcomings:

Convection: This increases the apparent value of the diffusion coefficient.

Convection may occur:

• During immersion of the capillary tube.

• Because of differences in density, unless the species with the higher

density is placed in the bottom part of the system.

90

• Because of mechanical effects such as vibration.

• Because of unfavourable temperature gradients.

To prevent convection it is necessary to use capillary tubes of small diameter,

less than 1 – 3 mm. On the other hand, with such small diameters wall effects

may become significant. For example, the diffusing species may attack the wall

and so leave the melt, as occurs when oxygen diffusing in molten slag in a

capillary with alumina walls reacts with alumina to form phases.

Boundary conditions: The boundary conditions for diffusion as given by

Equations (1.24) and (1.26) are not satisfied exactly. At the boundary of the

diffusion system the concentration 0C is not constant because of the diffusion in

the static melt. Moreover, it is not possible to determine exactly the position

0=x .

Changes on solidification: The samples are analysed in the as-cooled state, so

errors arise from the redistribution of solute during solidification and solid – state

transformations.

1.8.2.3 Diffusion couple method

This method uses the combination of semi- infinite and finite capillary tubes. It is

based on bringing into contact two capillary tubes of the same size filled with

slag having different concentrations of the diffusing species in the form of

radionuclides (Figure 1.26). To ensure good contact, the two surfaces of the open

ends of the capillary tubes are polished.

91

Figure 1.26: Diffusion couple, two capillaries

An alternative experimental arrangement is shown in Figure (1.23). A capillary

tube of 100 – 200 mm long is filled under vacuum with melt to half its height.

After solidification, the remaining half of the column is filled with melt

containing the species whose diffusion is to be investigated (the second column

having been prepared in another capillary tube). The tube is heated to allow

diffusion to occur, and after solidification the sample is analysed along its length.

In the finite - source method, the second column of the melt containing the

diffusing species is substantially shorter (Figure 1.28).

Capillary tube

Melt containing different concentrations of diffusing species

Capillary tube

92

Figure 1.27: Diffusion couple, two capillaries

In evaluating the diffusion methods that make use of a combination of semi –

infinite capillary tubes, it is necessary to take into account the following factors:

• The boundary conditions for Equation (1.22) are more closely approached

than in the capillary – reservoir method in that the undesirable

phenomena associated with immersion of the capillary tubes are

eliminated.

• Convection, and hence mixing, may occur after melting down the

samples.

• Wall effects are still present.

capillary tube

melt containing different diffusing species

melt

93

• The distribution of concentration of the diffusing species can change

during solidification; in some cases rapid quenching can be applied to

minimize problems arising from segregation on freezing.

Figure 1.28: Diffusion couple, one capillary

1.8.3 Electrochemical method

The electrochemical methods most widely used for studying diffusion in melts

are chronopotentiometry, linear voltametry, chronoamperometry, voltametry

with rotating-disk electrode (RDE), and polarography. All these processes are

controlled by the depolarizer (i.e. the ions of the diffusing species) that has to

reach the electrode by either diffusion (as in voltametry, chronopotentiometry,

and chronoamperometry) or forced convection (as in RDE and polarography).

Transport by migration, i.e. the motion of ions under the electric field in solution,

is not usually considered in view of the high electrical conductivity of the melts.

capillary tube

melt containing differentdiffusing species

melt

94

The electrochemical method is especially suitable for measuring diffusion in

melts as convection is either eliminated or controlled. The experiments last only

a few seconds, in contrast to the several hours needed for the capillary methods,

and wall effects are not encountered. Of these methods, chronopotentiometry and

RDE are most important in the study of diffusion in melt.

Chronopotentiometry is a galvanostatic method in which pulse of constant

current density is used to perturb a system from its equilibrium. The response of

the system is measured in terms of the dependence of the potential of the

investigated electrode on time. The accuracy of the chronopotentiometric method

in determining diffusivity varies with experimental conditions. At medium

temperature it may be 2 – 30 %, while at high temperature the accuracy is

unknown.

An electrochemical cell is established which contains a metal electrode

containing the diffusing species and the molten slag composition of interest and

electrolysis is carried out at uniform current (I). If the electrode reaction is

controlled by diffusion, Equation (1.29) can be used to derive the diffusion

coefficient as;

0=⎟⎟⎠

⎞⎜⎜⎝

⎛=

ydydCZFDI (1.29)

Where, Z is the valence of the diffusing species, F is the Faraday constant; D is

the diffusion coefficient and ⎟⎟⎠

⎞⎜⎜⎝

⎛dydC is the concentration profile.

95

The Rotating disk electrode (RDE) is the electrochemical variant of the rotating

method which will be described in the next section, and is known as voltametry

with RDE. An increasing voltage is applied to the RDE and the current is

measured. The increase in voltage is very slow owing to the diffusion processes

and thus the phenomenon is quasistationary. Voltametry with RDE has been

applied more in aqueous solutions than in melts.

Generally, serious difficulties have been faced in the mentioned methods to

accurately measure diffusion coefficients in liquid slags at elevated temperatures.

The main difficulty is to avoid mass transport by bulk motion of the fluid caused

by natural convection, unless the fluid flow is a part of the measuring method.

This fluid flow is driven by the buoyancy force produced by any temperature and

concentration gradients, which leads to a decrease in liquid density with depth.

1.8.4 Controlled forced convection method

In these methods the errors due to convections are minimised by imposing

controlled forced convection where the hydrodynamic conditions are well

defined. A sample of solid oxide is rotated in the molten slag and the diffusion

coefficient is deduced from the measured rate of dissolution with knowledge of

chemical driving force and boundary layer thickness. Since the hydrodynamics

of rotating disk is well established, a rotating disk or cylinder can be used.

Advantages of this method include:

• The experimental conditions, including slag dynamics are exactly

reproducible.

96

• The slag is agitated to a sufficient degree to render a comparison with the

conditions in the real industrial practice.

The mass transfer from the solid oxides to the slag under forced-convection has

been modelled successfully in the past by many researchers. The rotating sample

of solid oxide used in this method could be in the forms of a disk or a cylinder.

The following part will explains the hydrodynamic conditions involved in each

type.

1.8.4.1 Rotating disk method

In this method dissolution of a rotating solid disc in a static melt is measured; the

rate of rotation is chosen so that laminar flow is achieved. The diffusion

coefficient is determined from the dissolution rate, angular velocity, and from the

time of dissolution. The dissolution rate is obtained from either the loss of the

weight of the disk or the reduction in diameter of the rotating disk or the increase

in the concentration of dissolving solid oxide in the melt. The diffusion boundary

layer is right next to the surface of rotating disk; the matter is considered to be

transferred by molecular diffusion. Equations for the tangential, radial, and axial

contributions to fluid flow near the surface of a rotating disk have been derived

by Cochran (1934). With the use of Cochran’s equations, Levich (1962) obtained

the equations for boundary layer thickness of a solute species dissolving from a

rotating disk. The diffusion boundary layer is not sharply delineated, and its

thickness δ varies with the hydrodynamic conditions, i.e. with the thickness 0δ

of the hydrodynamic (Prandtl) layer and with the value of the diffusion

coefficient:

97

0

3/1

5.0 δν

δ ⎟⎠⎞⎜

⎝⎛= D

0δδ ≤

2/1

0 6.3 ⎟⎠⎞⎜

⎝⎛=

ωνδ

(1.30)

Where ν is the kinematic viscosity and ω is the angular velocity of rotation of

the disk. Under common experimental conditions, δ and 0δ have values of ~1

and ~0.01 mm, respectively.

To solve the diffusion equation, it is necessary to know the velocity of the

vertical ( )y direction:

22/13

)(51.0)( yyνωυ −≈

2/1

⎟⎠⎞⎜

⎝⎛<<

ωνy

δ≤y

(1.31)

ωνυ 2/189.0)( −≈y ∞→y (1.32)

Transport due to simultaneous convection and diffusion can be determined when

the convective flow in the melt is known. The equation of convective diffusion

(i.e. mass transfer due to diffusion and convection) in one dimension is:

98

2

2

yCD

yC

tC

y ∂∂=

∂∂+

∂∂ υ (1.33)

Where, yυ is the flow rate in the y-direction and C is the concentration.

The equation for convection-disc method is a stationary example of the mass-

transport equation for convection and diffusion, i.e. 0=∂∂

tC in Equation (1.33):

2

2 )()()(dy

yCdDdy

ydCy =υ (1.34)

The boundary conditions are:

satCyC == )0( 0)(lim =∞→

yCy (1.35)

Where satC is the equilibrium concentration at the disc/melt boundary, or the

concentration of saturated solution at the disk surface. Equations (1.31) to

(1.35) are fundamental formulas for the rotating-disk method.

By solving Equation (1.34) under the boundary conditions given by

Equation (1.35), and with the velocity )( yυ given in Equation (1.31), it can be

shown that:

99

⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢

⎣

⎡

∞→

−=)(

)(1)(

δ

δyf

yfCyC sat (1.36)

Where;

∫=δ

ξξδ

/

0

2 )exp()(y

dy

f

8934.0)( =∞→δyf

(1.37)

To determine the diffusion coefficient by the rotating disk method, it is necessary

to know the flux density j of material from the disc surface dissolving into the

melt:

0

)(

=⎥⎦

⎤⎢⎣

⎡−=

ydyydCDj (1.38)

Substituting of Equations (1.30), (1.36) and (1.37) into Equation (1.38) gives:

satCDj 2/16/13/262.0 ων −= (1.39)

The Levich correlation (1.39) was used by many to prove that the dissolution is

controlled by liquid-phase diffusion. When that is the case, the dissolution rate

should be proportiona l to the square root of the angular velocity of the disk. The

100

diffusion coefficient D is determined from experimentally derived values of j, i.e.

from the rate of dissolution.

Sandhage et al. (1990) studied the dissolution of sapphire in calcia-magnesia-

alumina-silica melts at 1450 and 1550 ºC. Prior to performing the sapphire

dissolution experiments in melts, they conducted a low-temperature modelling

study, involving glycerol as the model fluid and aluminium cylinders as

“specimens”, in order to determine the proper specimen and crucible dimensions.

The most ideal flow pattern was observed for a 1.3 cm diameter cylinder stirred

at less than 2000 rpm in glycerol contained in a 7.6 cm diameter crucible. For the

mentioned dimension, when alumina cylinder rotated in the glycerol, the glycerol

rose toward the cylinder along an inner, helical path about the rotation axis.

When the liquid was near the bottom of the rotating cylinder, it was thrown

radially outward. The liquid then sank along an outer, helical path. Thus, the

flow pattern near the bottom of aluminium cylinder was consistent with the

velocity distribution predicted by Cochran (1934).

The key benefit of the rotating disk is that the mass flux in the axial direction

from the disk is not a function of radial position, and is therefore, constant over

the entire disk face. This uniformity of the mass flux across the disk surface,

simplifying the subsequent analysis and makes the rotating disk ideal for mass-

transfer experiments. Therefore, The rotating disk is employed largely in

electrochemistry and is convenient for studying chemical kinetics under

laboratory conditions.

101

1.8.4.2 Rotating cylinder method

Generally, the mass-transfer coefficient is a function of geometry and fluid

properties of flow through the use of dimensionless numbers such as the

Reynolds number (Re) and Schmidt number (Sc). These dimensionless numbers

are defined as μ

ρVd=Re andD

Scρμ= , where ρ is the density, V is the linear

velocity, d is the characteristic length, μ is the viscosity and D is the

diffusivity of species in the fluid.

Chilton and Colburn (1934) by analogy with heat transfer, developed an

approximation relationship between these variables in terms of a mass-transfer

)( j and dimensionless numbers as:

nD bSc

Vkj −== Re3/2

(1.40)

Where

=Dj mass-transfer j factor from the cylinder side of the crucible

=V linear (peripheral) velocity of rotating disk

=Sc Schmidt number

=k mass transfer coefficient of the cylinder

=Re Reynolds number based on the peripheral velocity of the cylinder

102

The constants, b and n, can be determined from experimental data. Generalized

relationships of mass transfer coefficient have been obtained experimentally for

many specific geometries. Eisenberg and Tobias (1955) measured rates of mass

transfer at circular cylinders rotating about their axes in the centre of stationary

cylinders by means of solid dissolution and electrolytic reactions. Benzoic and

cinnamic acids cast into cylinders were dissolved into water and water-glycerol

solutions. The characteristic length dimension for the Reynolds number,

μρldu

=Re , was found to be the diameter of the rotating cylinder, instead of the

gap between the concentric cylinders. Their study involved a large variation of

cylinder diameters (1.94 to 5.02 cm). For the diameters studied, the magnitude of

the gap was found not to affect the rates of mass transfer even under turbulent

flow conditions. They also covered a range of Schmidt numbers from 835 to

11490 and of Reynolds numbers from 112 to 241000. The functional dependence

of the mass transfer coefficient on physical properties of the system was found to

be represented by finding factors b and n of Equation (1.40). Therefore,

Eisenberg et al. (1955) obtained a general correlation of the mass transfer

coefficient as Equation (1.41), which is a function of Reynolds number based on

the rotor diameter.

3.0644.0 Re0791.0 −== ScV

kj cylinder

cylinder (1.41)

Where;

=cylinderj mass-transfer (j factor) from the cylinder side of the crucible

103

=V peripheral velocity of rotating disk

=Sc Schmidt number

=cylinderk mass transfer coefficient of the cylinder


Kosaka et al. (1966) developed a correlation for the mass transfer from a rotating

metal cylinder into liquid metal at about 1400°C (Equation (1.42)). In their

research, they employed Steel-Al, Steel-Zn, Cu-Pb, Zn-Hg and Sn-Hg as the

combination of solid metal cylinder-liquid metal bath.

25.0644.0 Re065.0 −== ScV

kj cylinder

cylinder (1.42)

A number of researchers measured experimentally the relationship between the

mass transfer (J- factor) from the rotating cylinder with the Reynolds number.

The solute and the properties of the solvent vary in different experiments as

shown in Table 1.7.

104

Table 1.7: The correlations developed previously for mass transfer from rotating solute cylinder to the solvents.

Solute Solvent Mass transfer coefficient & Reynolds relationship Researcher

Salt Water – organic liquid 5.0Re664.0 −=j Eisenberg et al. (1955)

Metals Liquid metal 25.0Re065.0 −=j Kosaka et al. (1966)

Dolomite FeOx-CaO-SiO236.0Re152.0 −=j Umakoshi et al

(1984a)

MgO CaO-FeOx-SiO230.0Re126.0 −=j Umakoshi et

al. (1981)

CaO CaO-SiO2-Al2O331.0Re495.0 −=j Matsushima et

al. (1977)

Al2O3 CaO-SiO2-Al2O319.0Re048.0 −=j Taira et al.

(1993)

The logarithmic relation of J- factor and Reynolds number is also shown in Figure

1.29. Umakoshi, Mori and Kawai (1984a) explained the reason for larger values

of J-factor compare to the data obtained by Eisenberg et al. (1955) and Kosaka et

al. (1966). They claimed that such differences may be caused by the

underestimation of the net area for the dissolution process which may be larger

then the geometric one because the rotating cylinder is porous. They also claimed

that high J- factor of lime dissolution obtained by Matsushima et al. (1977)

compared to the other solid oxide dissolutions could be explained by spalling,

i.e., the mechanical separation of CaO particles from sintered lime during

dissolution. Taira et al. (1993) measured the dissolution of alumina into molten

CaO-SiO2-Al2O3 slags. They claimed that relationship between J- factor and

Reynolds number shown in Figure 1.29, is close to extension of line for Kosaka

relation.

105

Figure 1.29: The relationship between the mass transfer and Reynolds number according to the previous investigations.

Umakoshi et al. (1981) measured the dissolution of MgO into molten FeOx-CaO-

SiO2 slags at temperatures from 1350 to 1425 ºC. They applied the correlation

developed by Kosaka in their calculations to measure the mass transfer

coefficient. Therefore, the Kosaka correlation might be applicable to the

dissolution of a cylindrical solid oxide into the molten slag.

1.8.4.3 Applicability of rotating disk/cylinder technique

A number of researchers utilized the rotating disk/cylinder technique to

determine the dissolution rate and mass transfer and diffusivity of solid oxides in

the slag. It was shown in the previous section that data on diffusivity of alumina

obtained with this method by Cooper et al. (1964) & Taira et al. (1993) & Lee et

106

al. (2001) were in a good accord with the results from Henderson et al. (1961)

measured by capillary-reservoir technique in a slag of similar chemistry.

Although there is no published data on the determination of diffusivity of lime by

rotating disk/cylinder method, Matsushima et al. (1977) & Umakoshi et al.

(1984b) applied this method to measure the dissolution rate and mass transfer

coefficient of lime and dolomite in the slag. As it was shown in the previous

section, the deduced values of apparent diffusivity on the basis of non-dimension

analysis of mass transfer data shows a very good agreement with the data from

direct measurement of diffusivity with instantaneous plane source and capillary-

reservoir techniques by Johnston et al. (1974) & Hara et al. (1989), respectively,

with similar slag chemistries.

The excellent agreement on values of diffusivity of MgO obtained with rotating

cylinder technique by Umakoshi et al. (1981) and inter-diffusivities data of MgO

with diffusion couple method by Ukyo et al. (1982), is also another proof on the

reliability of this technique for measurement of diffusivity in the slag.

The comparison between the diffusivity of iron oxide measured by Xie et al.

(1999) with a rotating disc of solid iron in the slag and data on the galvanostatic

diffusion studies of Nagata et al. (1982) shows a very good agreement .

1.8.5 Selection of experimental technique for the present work

In general, one can conclude the appropriateness of the rotating disk/cylinder

technique for measurement of diffusivity of solid oxides in the slag as:

107

• The error caused by convection in measuring tracer diffusivity is

minimised by creating a forced convection under well-defined

hydrodynamic condition.

• The experimental conditions, including slag dynamics are exactly

reproducible.

• The slag is not static and is agitated to a sufficient degree to render a

comparison with conditions in steelmaking process.

Furthermore, according to Levich equation, if dissolution rate of rotating solid

oxide is controlled by mass transfer, then varying the rotation speed will vary the

thickness of the liquid boundary layer adjacent to the disk and hence change the

mass transfer coefficient in the slag phase (Lee et al. (2001)). For a given rotation

speed, the effects of slag chemistry (such as addition of CaF2 and transition

metals) and temperature on the dissolution rate, mass transfer and hence the

diffusivity can also be determined by this technique.

1.9 Objectives of this work

• Determine the diffusivity of lime in CaO – 42 %Al2O3 – 8 % SiO2 slag by

the method of rotating disk/cylinder technique.

• Examine the effects of formation of a solid reaction product on the

slag/lime interface on the dissolution rate and develop a model of

dissolution in the presence of a solid layer.

108

• Quantify the effects of additives such as CaF2, Fe2O3, TiO2, Mn3O4, SiO2

and ilmenite on the dissolution rate, diffusivity and solubility of lime in

the slag.

• Quantify the diffusivity of magnesia into the CaO – 55 wt% Al2O3 slag

and investigate the impact of additives such as Fe2O3 and (CaF2 + Fe2O3)

on dissolution rate, diffusivity and solubility of magnesia in the slag.

109

CHAPTER 2. Experimental

This chapter explains the experimental setup and material used in this work.

Firstly, the outline of experimental work for measurement of diffusivity is

described. Secondly, details of the material and equipment used in this work are

presented. Thirdly, the procedures used to perform dynamic and static dissolution

experiments are given. Finally, the methods used to analyse the samples are

described.

2.1 The outline of the experimental work

The dissolution rate of CaO and MgO in the slag was determined using rotating

disk/cylinder technique. The rate of dissolution was obtained by measuring the

concentration of dissolving oxide in the melt at different time intervals by

sampling of the melt. The diffusivity of CaO/MgO was deduced from the

dissolution rate data.

According to the literature review, the rotating sample in this technique is either

a cylinder or a disk. In the case of the rotating disk, the effects of the edge of the

disk on the hydrodynamic mass transport of material from the disk surface have

not been precisely quantified. On the other hand, it is often very difficult to

immerse the disk in melt in a way to just have the flat bottom of the disk in the

liquid and the effect of walls on the fluid dynamics and mass transfer would

cause an error. Also in the case of a rotating cylinder, the researchers normally

cover the end part of the cylinder (as a disk) with a cap, so that the dissolution of

110

the solute would proceed only at the side surface of the cylinder; however, the

bottom of the cylinder affects the fluid dynamics of dissolution. Thus, it was

decided to use a cylindrical crucible and combine the effect of dissolution of disk

and cylinder sides of the sample in the process of dissolution, which will be

discussed in detail in Chapter 4. The dense lime/magnesia crucible had low

porosity in order to minimize the effect of porosity on the diffusivity. The base

slag considered in the present study has the composition of CaO – 42 wt% SiO 2 –

8 % Al2O3 with addition of 5 wt% CaF2, FeOx, TiO2, ilmenite, MnOx and SiO2,

where we have some knowledge of their phase diagram, viscosity and density

over the temperature range that was investigated.

In the experiments for measuring the diffusivity of MgO, a dense magnesia

crucible was used and the slag investigated was a CaO – 55 wt% Al2O3 slag.

2.2 Material preparation

2.2.1 Dense CaO / MgO crucible

Dense CaO crucibles, 20 mm ID, 16 mm OD and 30 mm high, were supplied by

Rojan Ceramics Pty Ltd. in Australia. The crucibles had low porosity (< 1%) and

contained more than 96.3 wt% CaO with 2.9 wt% of MgO as grain bonding

phase. These crucibles were used as cylinders in the rotating experiments.

Dense MgO crucibles; with the same dimension as lime crucibles were provided

by Fuji Sho Inc. Japan.

111

2.2.2 Chemical reagents

The master slags were prepared from Reagent grade chemicals. Table 2.1 details

the chemicals (CaCO3, SiO2, Al2O3, CaF2, Fe2O3, TiO2 and CaF2) used in this

work. The purity and powder size of these chemicals are also included in this

table. All reagents were dried at 120ºC for at least 12 hours before use to remove

moisture resulting in accurate weight. All the materials were weighted with an

electronic balance to a precision of 0.001 grams.

Table 2.1: The source and purity of the chemical composition used in the experiment

Chemical Supplier Comments

CaCO3Ajax Finechem Company, Inc.

Purity > 99%Analytical reagent

SiO2Consolidation Chemical,

Inc. Purity ~ 99.8%

Al2O3Ajax Finechem Company, Inc.


Fe2O3Alrich Chemical Company, Inc.

Purity ~ 99%Analytical reagent

TiO2Alrich Chemical Company, Inc.

Purity > 99.9%Analytical reagent

CaF2Ajax Finechem Company, Inc.

Purity > 97%Laboratory reagent

MnO2Alrich ChemicalCompany, Inc.


Table 2.2 provides the chemical composition of ilmenite used in this study.

Ilmenite was provided by Cable Sands Pty Ltd. Australia.

112

Table 2.2: Chemical composition of ilmenite

ilmenite

Oxides Wt%

TiO2 55.3

Fe2O3 24.1

FeO 16

MnO 1.48

Al2O3 0.58

SiO2 0.93

Cr2O3 0.045

P2O5 0.03

2.2.3 Preparation of calcium aluminosilicate master slag

Master slags were prepared in a way to represent the composition of ladle type

slag. The calcium aluminosilicate master slag was made in a 15 KW, 450 KHz

induction furnace at 1500 °C in air. The starting materials for the slags were

reagent-grade CaCO3, SiO2, and Al2O3 that were dried at 120ºC for 12 hours.

The required materials were then weighed and then mixed in a plastic container

on a rotating mill for 1 hour. The mixed powder was melted in a graphite

crucible (90 mm OD and 300 mm high) contained in a clay bonded graphite

susceptor, which was heated to 1500 °C with a heating rate of 600°C per hour.

The slag was held at 1500 °C for half an hour as the graphite crucible was

charged with the remaining powder. After all the slag powder was charged into

the graphite crucible, nitrogen gas was injected to mix the molten slag, by

blowing through an alumina lance into the slag for half an hour. The slag was

113

cooled down in the graphite crucible and then the slag was separated from the

crucible by breaking the graphite crucible. The slag was then initially crushed in

a jaw crusher and then in a tungsten carbide ring mill. The resultant very fine

slag powder was again mixed in a plastic container on a rotating mill for one

hour to ensure the homogeneity of slag. As the slag contained some graphite

particles, it was de-carbonized in a platinum dish heated in air in a muffle

furnace at 800°C for 12 hours. The master slag was analysed by XRF analysis at

CSIRO, division of minerals and the results are shown in Table 2.3.

Table 2.3: XRF analysis of master slag, wt%

Sample CaO Al2O3 SiO2 Fe2O3 CuO K2O MgO Na2O P2O5 SO3 Sum

Master slag 48.8 42.2 7.8 0.2 0.01 0.01 0.04 0.04 <0.005 <0.005 99.1

The slags with additives were made by pre-melting mixtures of reagent-grade

CaF2, Fe2O3, TiO2 and MnO2 with the master slags. The additives were dried at

120°C for 12 hours. After weighing and mixing the material, the mixture was

melted in a platinum crucible in a muffle furnace, which was programmed to

attain 1500 °C with a ramping rate of 300ºC per hour, the atmosphere inside the

muffle furnace was air. The melt was then poured onto a cold copper plate to

quench. The quenched slag was then pulverized in a tungsten carbide ring mill.

The final composition of slags were analysed using the XRF technique, the

results are shown in Table 2.4.

114

Table 2.4: Chemical composition of various slags for lime dissolution study, wt%

Sample CaO Al2O3 SiO2 CaF2 FeOx TiO2 MnOx

slag + CaF2 5% 47.79 39.8 8.09 4.82 - - -

slag + FeO 5% 47.3 40.3 7.52 - 5.09 - -

slag + TiO2 5% 47.5 40.3 7.76 - - 4.93 -

slag + ilmenite 5% 47.3 39.8 7.94 - 2.13 2.82 -

slag + MnOx 5% 47.6 40.3 7.84 - - - 4.6

slag + SiO2 5% 47.4 40.2 12.8 - - - -

2.2.4 Preparation of calcium aluminate slag

The calcium aluminate master slag for the study of dissolution of magnesia, was

prepared in the same method described above. The composition of base slag and

slags with additives are listed in Table 2.5.

Table 2.5: composition of slag with additives for magnesia dissolution study, wt%

Sample CaO Al2O3 FeOx CaF2

master slag 45 55 - -

slag + FeO 5% 42 50.7 5.4 -

slag + FeO 10% 40.2 48.7 9.7

slag + CaF2 5% +FeOx 5% 41.5 49.0 5.3 3.6

slag + CaF2 5% +FeOx 10% 39 45.8 9.9 3.7

115

2.3 Experimental apparatus

The dissolution kinetic experiments were carried out in a vertical tube furnace. A

schematic diagram of the furnace arrangement is shown in Figure 2.1. A

Pythagoras furnace tube (50mm ID and 800 mm high) was heated by three U-

shaped MoSi2 heating elements. The temperature was controlled with type R

thermocouples (Pt/ Pt-13% Rh) positioned outside the Pythagoras furnace tube

and connected to a Eurotherm Controller, which maintained temperatures to ±

1°C. Both ends of the Pythagoras tube were sealed by water-cooled brass end-

caps. A type-R thermocouple was used for measuring the temperature of the

crucible. This thermocouple was cemented to the alumina platform that the

platinum crucible sat on.

116

Figure 2.1: Schematic of the experimental apparatus used for the rotating cylinder tests

117

2.4 Experimental procedure

2.4.1 Rotating experiments

Dissolution rate of dense CaO/MgO in slags with additives was measured by

carrying out experiments using the rotating disk method in a tube furnace. The

experimental set-up is shown in Figure 2.1. The lime/magnesia crucible (20 mm

OD and 30 mm high) was cemented with Zirconia paste to the end of an alumina

tube (8 mm OD), which was then cemented to a stainless steel shaft (Figure 2.2).

Figure 2.2: Photo of the CaO/MgO crucible attached with Zirconia paste to the alumina rod

The steel shaft was driven by an electric stirrer at constant speed. The rotation

speed of the motor could be varied between 20 and 900 rpm. The speed of stirrer

was checked regularly with a digital tachometer.

118

In each experiment about 60 grams of slag was used. The slag was contained in a

Pt – 10% Rh crucible (40 mm in diameter and 44 mm in height) placed on a

platform that could be manually lowered and raised to adjust the immersion

depth of the sample in the slag. An R-type thermocouple positioned beneath the

platinum crucible was used to monitor the temperature of the melt.

The tip of the lime crucible was located in the centre of the hot zone and the

platinum crucible was positioned 10 mm below the lime crucible during the

furnace heat-up, at a rate of 120 ºC/hour. After reaching the target experimental

temperature, the slag was allowed to homogenize for 1~2 hours. Dried air was

used to control the atmosphere in the tube furnace.

The platinum crucible was then raised to immerse 15 ~ 20 mm of the lime

sample so that there was always 10 mm distance between the bottom of the lime

crucible and bottom of platinum crucible; and then the rotation was started. The

molten slag was sampled at regular time intervals using a cold 2-mm-diameter

platinum rod attached to a stainless steel tube from the top of the furnace. The Pt

rod was dipped into the melt, and quickly removed from the furnace. The slag

attached to the tip of the Pt wire was rapidly quenched in water. Then the slag

sample was crushed and dried for 1 hour to remove any moisture. The slag

samples were crushed fine for XRF analysis. The XRF results were then used to

measure the concentration of the CaO dissolved in the slag. The dissolution rate

of CaO was determined from the variation in composition of slag with time.

After the last sampling for the required period, the Pt crucible was lowered and

the furnace was cooled down at the rate of 180 ºC per hour. A similar procedure

was used for measuring the dissolution of MgO into slags.

119

2.4.2 Static experiments

The solubility of lime in the slag and also the possible formation and growth rate

of solid phases formed on the CaO crucible/slag interface were studied by

carrying out the series of static experiments. The experiments were carried out

using a muffle furnace. In each experiment a platinum capsule was used to

contain the slag and a piece of lime. The small platinum capsules used in the

experiments (15 mm ID by 32 mm height) were made by welding two sides of a

thin platinum foil. About 0.5 gram of slag and 0.6 ~ 0.7 gram of dense chipped

CaO from crucible pieces (which was used for rotating experiments) was

contained in the platinum capsule and were placed in the shallow holes drilled in

refractory bricks in order to hold the platinum crucibles vertically. After reaching

the target temperature and staying at temperature for the required reaction time,

the platinum capsule were taken out of the muffle furnace and rapidly quenched

on a brass plate, which was also cooled by an air flow on its back surface. The

platinum capsule with their contents were mounted in resin and then cut and

polished for SEM analysis.

2.5 Analytical techniques

Approximately 0.5 grams of the finely ground, oven dried slag power resulted

from sampling was accurately weighed into an 95% Pt – 5% Au crucible with

approximately 6 grams of 12:22 lithium tetraborate/metaborate flux. The mixture

was fused into a homogeneous glass over an oxy-propane flame at a temperature

of approximately 1050 ºC. The molten material was poured into a 32 mm

diameter 95% Pt – Au mould heated to a similar temperature. The melt was then

120

cooled by air jets for approximately 300 seconds. The resulting glass discs were

analysed on a Philips PW2404 XRF system using a control program developed

by Philips and algorithm developed at CSIRO Minerals by P.G.Fazey. Oxygen in

the XRF analysis was calculated by assuming stoichiometry for the oxides

species. The error involved in the XRF analysis in the present work was within ±

1% for the analysis of the low concentration components.

2.5.1 Scanning Electron Microscopy and Energy Dispersive System analysis (SEM-EDS)

The samples from static experiments were mounted in epoxy resin and cut with a

diamond saw, then they were ground initially with the Struers waterproof silicon

carbide paper at consecutive grits sizes of 600, 800, and 1200 mμ using a Struers

Labopol-5 grinding machine at 300 rpm. Since the samples were very sensitive

to moisture, kerosene was used as the lubricating fluid. Diamond polishing of the

specimen was done using polycrystalline diamond paste of 6, 3 and 1μm microns

consequently on Chemo-textile Cloth (Leco-PAN-W). A LECO G25 Rotary

Polisher was used for the final stage of polishing. Finally, the samples were

coated with carbon layer (thickness:~ 200 A) using a vacuum evaporator to

provide a conducting surface.

A Philips XL30 Scanning Electron Microscopy (Figure 2.3) at School of

Chemical Engineering, University of Melbourne equipped with an Oxford Link

ISIS Energy Dispersive System and an ATW Pentafet SiLi detector was used for

the SEM analysis of examination of mounted samples. The electron optical

system accelerating voltage was 20 KV. The various phases present in the

121

samples were identified from the different crystal forms and colour intensities

displayed in back-scattered electron (BSE) images generated by SEM. The EDS

was then used to quantify the chemical composition of the phases. The EDS was

calibrated with Bedrock Scientific Ltd standard reference block SB 1/a. The

standards were carefully selected to be free of line overlaps and were stable

inorganic compounds or single elements. Table 2.6 lists the standards used in the

calibration of the EDS in this work.

Figure 2.3: The Philips XL30 used for the SEM analysis

122

Table 2.6: Standards used in the calibration of Philips XL 30 SEM

Elements Standards

Ca CaSiO3

Al Al2O3

Si SiO2

Mg MgO

Fe FeS2

Ti Ti

Mn MnSiO3

F LiF

O SiO2

2.5.2 Microprobe analysis

A CAMECA SX50 electron probe micro-analyser (EPMA) at the Electron

Microscopy Unit, The University of New South Wales was used in quantitative

analysis of the samples (Figure 2.4). It is a fully automated instrument employing

four wavelength dispersive spectrometers in order to analyse various elements.

These elements were analysed with the TAP, PCO and PET crystals. All samples

were examined using an accelerating voltage of 15 KV, a beam current of 20 nA

and a beam size of 1 micron. The instrument was operated with SAMx

application software. X-ray intensity distributions were acquired for the main

constituents to produce elemental analysis across the area of interest. The

calibration was performed by taking peak and background measurements on a

123

standards listed in Table 2.7. All standards are in the Austimex Block, which was

polished under perfect sample preparation by Mr. Rad Flossman at UNSW.

Figure 2.4: The CAMECA SX-50 Micro Probe used for the EPMA analysis

124

Table 2.7: Standards used in the calibration of SX-50 Micro probe

Elements Standards

Ca Diopside

Al Sanidine

Si Diopside

Mg Diopside

Fe Haemetite

Ti Rutile

Mn Rhodonite

F Calciumfluoride

O Diopside

125

CHAPTER 3. Experimental results

The results of the present work are detailed in this chapter. The results are

presented in two main sections: rotating disk experiments in section 3.1, and

static experiments in section 3.2. The results from dissolution of CaO in calcium

aluminosilicate based slag under forced convection in air are presented in section

3.1.1. The effects of variables such as rotation speed, temperature and slag

chemistry (additives; CaF2, TiO2, Fe2O3, Mn2O3, ilmenite and SiO 2) on the

dissolution of lime are also presented in this section. The apparent dissolution

rate was deduced from the variation of dissolved lime concentration in the slag

with time and the effect of variables on the dissolution rate is presented in this

section. Finally, results from dissolution of MgO in calcium aluminate based slag

in air, at 1430 °C and under forced convection are presented in section 3.1.1.5.

The variation of dissolution with rotational speed and effects of additives such as

Fe2O3 and (CaF2 + Fe2O3) on the dissolution rate are summarized in this section.

The results from experiments carried out under static condition are presented in

section 3.2, reaction of lime with base slag produced a solid phase at the

lime/slag interface and the growth rate of the layer is deduced. The

measurements on solubility of lime in the base slag and slags with additives such

as (CaF2, TiO2, Fe2O3, Mn2O3, ilmenite and SiO 2) at various temperatures are

presented in this section. This section also contains the results from solubility of

MgO in calcium aluminate based slag and slags with addition of Fe2O3 and

(CaF2+ Fe2O3) at 1430°C.

126

3.1 Rotating experiments

3.1.1 Dissolution of CaO in calcium aluminosilicate slag

The CaO dissolution in the calcium aluminosilicate slag was investigated by

rotating a lime sample in molten slag in a platinum crucible. The initial slag

composition was CaO – 42 wt% Al2O3 – 8% SiO2 as shown in Figure 3.1. Lime

crucible was used as the rotating samples in melt with dimensions of 20 mm in

diameter and 30 mm in height. The selection of this slag chemistry was based on

the consideration of phase diagram and typical ladle slag in steelmaking. The

experiments were carried out in air, initially at 1430 °C, with rotational speeds

ranging from 30 to 150 rpm and with the reaction time of up to 1 hour. These

experiments were followed by investigation on the effect of temperature and slag

chemistry, i.e. addition of CaF2, TiO2, Fe2O3, Mn2O3, ilmenite and SiO2 on the

dissolution of lime at constant speed. The amount of slag used in each test was

about 60 grams. The CaO concentrations in the bulk slag were determined by

sampling of molten slag at time intervals. The lime dissolved in the slag was

analysed using XRF, with the estimated error being within ±0.2 – 0.3 wt% in the

slag phase. All the concentration data were smoothed by Rational curve fitting

using Curve Fitting Toolbox in MATLAB (MATLAB (2000)). The raw

experimental data are presented in CaO (wt %) versus time graphs in the form of

dot points throughout this chapter and also in Appendix A. The curve fittings are

also presented in the form of continuous curves going through the experimental

data in each graph. Both raw experimental data and corresponding curve-fitted

values are tabulated as separate columns in tables relevant to the CaO

concentration versus time graphs.

127

Figure 3.1: CaO-Al2O3-SiO2 system phase diagram from Slag Atlas (Eisenhuttenleute (1995))

3.1.1.1 Effect of rotating speed on dissolution rate

These experiments were carried out to study the effect of increasing the rotation

speed from 30 to 150 rpm on the dissolution/dissolution rate of lime in the master

slag in air and at a temperature of 1430 ºC. It was observed that by increasing the

rotation speed from 30 rpm to 150 rpm, the dissolution rate was increased by a

factor of 13.5. The fact that the dissolution rate was increased with the rotation

speed implies that mass transfer in the slag played a significant role in the

dissolution of lime in the slag phase.

128

The curve-fitted results are shown in Figure 3.2. The raw data are detailed in

Appendix A.1. The initial lime concentration was a bit different for various

speeds, where the slag made for each experiment had slightly different slag

chemistry as the target lime content of slag was about 50 wt%.

Figure 3.2: The concentration of CaO (wt%) in the melt with increasing the rotation speed at 1430 ºC

The initial dissolution rate (g/(cm2.s)) was derived from the slope of CaO

concentration curves with respect to dissolution period and on the basis of

Equation (3.1):

129

60100 ×××=

Awsloperate (3.1)

Where; w is the weight (g) of slag and A is the surface area (cm2) of the lime

crucible in contact with the slag. The slope of the dissolution curves were

obtained by fitting a straight line through the initial experimental concentration

data using MATLAB. The lime crucible used in the experiments, geometrically

consisted of a disk at the bottom of crucible and a cylinder at the wall, therefore

the total area of the lime sample was taken as area of disk and area of cylinder in

contact with the slag. The calculation of the area is detailed in Chapter 4. In

calculation of the area of lime samples, the height of a sample was considered as

the depth of lime crucible immersed in the melt which was about 15~20 mm. The

radius of the lime sample changed with temperatures and slag chemistry during

dissolution. To simplify the calculation, the area of the sample was assumed to

be constant. This may cause an error, which is detailed in Appendix D. This is

one of the reasons that the initial CaO concentration data only was included for

the dissolution rate calculations, as the area of the lime crucible was steadier

during the early stages of rotation of lime in the melt. The errors associated in

calculation of rate of dissolution is about 15~20%, which is detailed in Appendix

D.

The rate of lime dissolution is tabulated in Table 3.1, which shows an overall

increase in the rate of dissolution by increasing the rotational speed.

130

Table 3.1: The rate of lime dissolution (gr.cm-2.s-1) in the slag at 1430 ºC in air

Slag Static rpm = 30 rpm = 60 rpm = 90 rpm = 120 rpm = 150Master slag 4.78×10-6 3.18×10-5 2.23×10-5 5.03×10-5 4.78×10-5 6.37×10-5

As mentioned before, the lime sample used in the experiments was in the form of

a cylinder and a disk. The mass transfer from the disk side of the sample can be

calculated by the following Equation (3.2):

)(61.0 2/16/13/2 CbCsDj −= − ων (3.2)

Where, j (g/cm2.s) is the mass flux, sC and bC (g/cm3) are the saturation and

bulk liquid slag concentration, D (cm2/s) is the diffusion coefficient of lime in

the slag, ν is the kinematic viscosity of the melt (cm2/s), and ω (rad/s) is the

angular velocity of the disk. The mass transfer coefficient diskk (cm/s) from the

disk side of crucible can be written as:

6/12/13/2621.0 −= νωDk disk (3.3)

Equation (3.2) describes the dissolution that is rate limited by mass transfer

through a concentration boundary layer in the melt.

The mass transfer from the cylinder side of the sample can be calculated by the

following Equation (3.4):

131

3.0644.0 Re0791.0 −== ScV

kj cylinder

cylinder (3.4)

Where j (g/cm2.s) is the mass flux, cylinderk is the mass transfer coefficient of the

cylinder, V is the peripheral velocity of rotating disk, Sc is Schmidt number and

Re is the Reynolds number. The mass transfer coefficient cylinderk (cm/s) from the

cylinder side of crucible can be written as:

75.041.0

)(065.0 ων

⋅⎟⎠⎞⎜

⎝⎛= rDkcylinder (3.5)

Where r is the radius of the rotating cylinder (cm).

The total mass transfer from the rotating sample to the slag can be calculated

according to Equation (3.6), which will be explained in detail in Section 4.1.3.

cylinderdisktotal khr

hkhr

rK ⋅+

+⋅+

=2

22

(3.6)

Thus, if mass transfer in liquid phase plays a significant role in the dissolution of

lime in the slag phase, then the mass transfer coefficient and consequently the

dissolution rate should be proportional n-th power of a stirring speed, where n is

0.5 for the disk and 0.75 for the cylinder as two boundary conditions. Figure 3.3

and Figure 3.4 show a linear dependence of the dissolution rate with the 0.5 and

0.75 – th power of rotation speed in the speed range of 30 to 150 rpm. Based on

Equation (3.6), and by calculation of kinematic viscosity of slag at 1430 ºC

132

(according to the models explained in Appendix B and C) and the area of disk

and cylinder in contact with slag, the total mass transfer and consequently the

dissolution rate is proportional to the rotation speed according Equation (3.7):

75.05.0 027.0095.0 ωω +≈totalRate (3.7)

The result in Figure 3.6 shows a linear relationship between the dissolution rate

and the correlation of rotation speed expressed in Equation (3.7). The apparent

linear dependence of the initial rate on the ( 75.05.0 ωω BA + ) provides an

evidence that liquid phase mass transfer played a significant role in controlling

the dissolution of these samples over the rotation speed of 30 to 150 rpm. As it

will be explained later in this chapter, in static experiments at 1430 ºC formation

and growth of a solid layer on the surface of lime specimen were observed, while

at higher temperature this phase was not stable and did not form. It is thus

reasonable to consider that the measured dissolution rates at 1430 ºC were in a

mixed controlled regime of liquid phase mass transfer and diffusion in the solid

layer formed.

The variation of dissolution rate with 0.5 and 0.75 –th power of rotation speed as

two boundary conditions was also investigated at 1600 ºC at 30, 60 and 90 rpm

(Figure 3.3 and Figure 3.4). The total dissolution rate is related to the rotation

speed according to Equation (3.8), with calculation of kinetic viscosity of slag at

1600 ºC.

133

75.05.0 043.0115.0 ωω +≈totalRate (3.8)

A linear relationship holds between these two variables (Figure 3.5). The

observed effect of temperature on destabilising the solid layer separating the lime

and slag at 1600 ºC from the present work is in agreement with the CaO – Al2O3

– SiO2 phase diagram which does not show the formation of any reaction layer

while lime is dissolving in the slag at 1600 ºC. Therefore, the dissolution rate

data for various rotation speed at 1600 ºC in the present work suggesting that the

dissolution is controlled by the mass transferred into the liquid phase and not in

the mix-controlled regime due to the formation of a solid layer.

The measured data under static condition, i.e zero rotation speed should

correspond to the rate of lime dissolution under any natural convection and

agitation caused by sampling the melts. As the rotation speed of 90 rpm was in

the middle range of the speeds at 1430 and 1600 ºC, where there is a linear

relationship between the dissolution rate and 0.5 and 0.75 –th power of rotation

speed and their combination, 90 rpm was chosen as the constant speed for the

rest of experiments, where the influence of temperature variation and additives in

the slag were investigated

134

Figure 3.3: Variation of the dissolution rate of CaO versus the square root of rotation speed in air at 1430 and 1600 ºC

Figure 3.4: Variation of the dissolution rate of CaO versus the 0.75-th power of rotation speed in air at 1430 and 1600 ºC

135

Figure 3.5: Variation of the dissolution rate of CaO versus 75.05.0 ωω BA +of rotation speed in air. A and B are defined at 1430 and 1600 ºC

3.1.1.2 Variation of CaO dissolution at various temperatures in the master slag

Experiments were carried out to study the dissolution of lime in master slag at

temperatures of 1430, 1500, 1550 and 1600 °C in air and a rotating speed of 90

rpm. The results show an increase in dissolution rate of lime when the

temperature was increased from 1430 to 1600 °C as it is shown in Table 3.2. At

1600 °C the dissolution rate was increased by a factor of 2.

At 1430 °C, the variation of CaO concentrations with reaction time at rotating

speed of 90 rpm is illustrated in Figure 3.6 and also presented in Table 3.3. The

concentration data have the error of about 0.2 – 0.3 wt% (absolute) in XRF

136

analysis of the slag samples. The dissolved CaO concentration in slag increased

more rapidly in the first 10 minutes and then dissolution of CaO slowed.

Although the lime crucible was not fully dissolved in the slag after the

completion of the experiment, CaO reached a level of 52 wt%, which is still far

from the saturation level of about 59 wt%. This observation suggests the

formation of a stable solid layer, which hindered further dissolution of lime

under the given experimental conditions.

The formation of a product layer at the lime/slag interface was investigated and

confirmed by performing static reaction of lime with slag at 1430 °C and the

results are presented in Section 3.2. The results for rate of dissolution of lime in

the slag for all experiments at different times and various additives are tabulated

in Table 3.2.

Table 3.2: The rate of dissolution of lime (g/cm2.s) in the slag at various temperatures and with additives

Temperature ( ºC ) 1430 1500 1550 1600

master slag 5.03×10-5 6.37×10-5 8.83×10-5 1.27×10-4

slag + CaF2 - 2.31×10-4 2.72×10-4 3.30×10-4

slag + Fe2O3 1.34×10-4 1.63×10-4 1.85×10-4 2.23×10-4

slag + TiO2 7.96×10-5 1.21×10-4 1.34×10-4 1.72×10-4

slag + ilmenite - 9.55×10-5 2.10×10-4 2.55×10-4

Slag + Mn3O4 9.55×10-5 1.40×10-4 1.66×10-4 2.17×10-4

slag + SiO2 - 6.61×10-5 1.01×10-4 1.34×10-4

- slag likely to contain solid phase

137

Figure 3.6: Concentration of CaO dissolved in base slag at 90 rpm and in air at 1430 °C

Table 3.3: The variation of CaO concentration in base slag by measurements from XRF analysis at 90 rpm and in air at 1430 °Cfor 1 hour

XRF analysis of bulk slag (wt%)Reactiontime (min)

SiO2 Al2O3 Fe2O3 MgO CaO

CaO from curvefitting

0 8.06 42.0 0.31 0.09 49.83 49.83

5 7.91 41.9 0.18 0.08 50.50 50.31

10 7.83 41.7 0.20 0.09 51.00 50.65

15 7.83 41.6 0.15 0.10 51.10 50.91

20 7.74 41.3 0.14 0.11 51.07 51.11

25 7.77 41.3 0.15 0.12 51.34 51.27

30 7.74 41.0 0.14 0.11 51.39 51.40

35 7.74 41.1 0.12 0.13 51.60 51.51

40 7.71 40.8 0.13 0.13 51.46 51.60

45 7.80 41.2 0.15 0.14 51.66 51.68

50 7.72 40.8 0.19 0.13 51.82 51.75

55 7.70 40.6 0.13 0.14 51.71 51.81

60 7.69 40.7 0.13 0.15 51.95 51.86

138

In experiment at 1500 °C, the lime dissolution was increased with reaction time.

Results in Figure 3.7 show that after one-hour reaction time, the dissolved lime

in the slag had not reached the lime saturation limit of about 59 wt%. At 1500 ºC

and after the completion of the experiment, a substantial reduction in diameter of

the lime sample was observed, which was due to faster dissolution at higher

experimental temperature. The reduction in surface area of the lime sample

appeared to be the cause of slowing down of the of dissolution rate. The results

are also tabulated in Table 3.4. Results at 1550 °C and 1600 °C are tabulated in

Table 3.5 and Table 3.6 and illustrated in Figure 3.8 and Figure 3.9, respectively.

The time intervals for sampling of slag during the rotating of lime in slag at these

two temperatures were every two minutes for the first ten minutes of experiment,

where the dissolution rate is faster and the rest of the sampling performed at

every 10 minutes. At these two temperatures the curves reached plateau after the

first ten minutes of reaction. After 60 minutes and at the end of the experiment, it

was observed that the bottom of the crucible was totally dissolved in the slag at

1550 and 1600 ºC. It is likely that the disappearance of the bottom of CaO

crucible happened after 10 minutes of reaction time, when the slope of lime

dissolution curve just started to decrease, and then the dissolution continued from

the remaining wall of lime crucible with much smaller surface contact with the

molten slag. As the lime sample was attached to the alumina tubes with zirconia

paste, the complete dissolution of lower part of lime sample exposed the zirconia

paste to the melt and resulted in traces of zirconia in the chemical analysis of the

slag samples after 10 minutes of reaction time. As the calculation of the mass

transfer coefficient and diffusion coefficient was based on the complete geometry

of the crucible, i.e. disk and cylinder, so the CaO concentration data up to the

139

reaction time of ten minutes were used in the calculations. It can bee seen that at

1500 ºC as the crucible was not fully dissolved in the slag, during the reaction

time, the dissolution occurred from the whole surface of the sample. This lead to

higher concentration of CaO in slag compare to the 1550 ºC close to the end of

reaction time, but the rate of dissolution of lime at 1550 ºC was still higher than

at 1500 ºC. The dissolution rate at 1600 °C was found to be higher than the rate

at 1550 °C.

140


Table 3.4: The variation of CaO concentration in base slag by measurements from XRF analysis at 90 rpm and in air at 1500 °C


0 8.08 43.1 0.185 0.03 50.2 50.202 7.91 42.7 0.160 0.03 50.4 50.404 7.74 41.9 0.067 0.07 50.6 50.596 7.89 42.6 0.060 0.05 50.6 50.768 7.88 42.6 0.062 0.07 51.1 50.9110 7.82 42.4 0.059 0.07 51.1 51.0520 7.73 41.8 0.055 0.09 51.4 51.6330 7.74 41.5 0.079 0.14 52.2 52.0540 7.57 40.9 0.060 0.14 52.5 52.3950 7.58 40.6 0.052 0.18 52.5 52.6860 7.48 40.3 0.062 0.16 53.0 52.93

Reactiontime (min)

XRF analysis of bulk slag (wt%) CaO from curvefitting

141




0 8.1 43.1 0.22 < DL 50.2 50.192 7.93 42.7 0.143 < DL 50.6 50.554 7.80 42.0 0.089 0.06 50.7 50.846 7.82 42.1 0.077 0.08 51.0 51.088 7.77 41.8 0.077 0.09 51.4 51.2810 7.77 41.6 0.086 0.12 51.6 51.4420 7.68 41.3 0.066 0.11 51.8 51.9830 7.65 41.1 0.063 0.13 52.3 52.2640 7.5 40.3 0.08 0.1 53.4 52.4250 7.6 40.6 0.06 0.1 52.6 52.5160 7.54 40.5 0.066 0.14 52.5 52.56

Reactiontime (min)


142



SiO2 Al2O3 MgO CaO

0 8.1 42.4 < DL 49.4 49.37

2 8.1 42.3 < DL 50.6 50.86

4 7.7 41.3 0.1 51.7 51.37

6 7.7 41.1 < DL 51.8 51.64

8 7.8 41.1 0.1 51.8 51.82

10 7.9 41.1 0.0 51.7 51.94

20 7.6 40.6 0.1 52.2 52.29

30 7.4 40.1 < DL 52.6 52.50

40 7.3 39.4 0.2 52.7 52.67

50 7.2 39.4 0.2 52.8 52.83

60 7.2 38.9 0.2 52.2 52.97

Reactiontime (min)

XRF analysis of bulk slag (wt%) CaO from curve fitting

143

Figure 3.10: Comparison of CaO Concentrations dissolved in slag at 90 rpm and in air at 1430 – 1600 °C

Figure 3.10 shows the curve-fittde data on dissolution of CaO in calcium

aluminosilicate slag at various temperatures. It was found that by increasing the

temperature of the experiments, the amount of dissolution lime increased.

3.1.1.3 Effect of additives on the dissolution of CaO in slag

In order to investigate the effect of additives on the lime dissolution rate, 5 wt%

of CaF2, Fe2O3, TiO2, Mn2O3, ilmenite and SiO 2 were added to the master slag.

The experiments were conducted at temperatures ranging from 1430 to 1600 °C

and at constant rotating speed of 90 rpm. Fe2O3, TiO2, Mn2O3 and ilmenite were

expected to increase the diffusivity and ionic conductivity, while SiO 2 was

expected to have the opposite effect. The effect of additives on the concentration

of lime in the slag at each temperature is presented in Appendix A, while for

144

each additive the results at various temperatures are compared in the following

sections.

3.1.1.3.1 Effect of CaF2 addition on dissolution of CaO in slag at various temperatures

The influence of CaF2 on the dissolution of CaO in calcium aluminosilicate slag

was investigated by addition of 5 wt% CaF2 to the slag and carrying out

dissolution experiments at 1430, 1500, 1550 and 1600 °C. The experiments were

performed in air and a rotation speed of 90 rpm and for a reaction time of 20

minutes. The dissolution of lime in the slag was so fast specially at temperatures

higher than 1500 °C, that the bottom and lower half of crucible were dissolved

after 10~20 minutes of running experiments, which is shown in Figure 3.11, on

this basis, the reaction time was limited by 20 minutes. The results for

experiments with 5 wt% CaF2 content of slag and at 1430 °C are presented in

Appendix A.2. The dissolution of lime at 1430 ºC increased dramatically

compared to higher temperatures. By examining the lime specimen after

completion of experiments at 1430 ºC (Figure 3.11), deep grooves were found on

the surface of the crucible, which indicates that solid particles caused physical

erosion of lime from the specimen rather than dissolution of lime into the liquid

slag. The phase diagram for CaO-Al2O3-CaF2 system (Figure 3.12) shows the

possibility of formation of a compound 11CaO.7Al2O3.CaF2 during the reaction

of lime with slag at 1430 °C. As the melting point of this compound is 1577°C, it

was postulated that the solid phase formed was floating in melt causing the

erosion of lime crucible and chipped off lime pieces from the surface of lime.

This resulted an excessive CaO content of slag from XRF analysis of sampled

145

slags from the bath. By conducting experiments at 1500, 1550 and 1600 °C, the

dissolution rate was slower than at 1430 °C. By increasing the temperature, the

11CaO.7Al2O3.CaF2 solid phase becomes unstable and dissolves in the slag,

decreasing the possibility of erosion of lime specimen by solid phase, which is

also confirmed by static experiments in section (3.2.1.2). The results are shown

in Appendix A.2. The lime dissolution curves at 1500 and 1550 °C have a similar

pattern, but at 1600 °C, the dissolution of lime is higher than at 1500/1550 ºC.

The dissolution rate of lime increased considerably with addition of 5 wt% CaF2

as it was shown in Table 3.2. The curve fitted data on variation of CaO

dissolution for the temperature range of 1430, 1500, 1550 and 1600 °C for the

slag, which contains 5 wt% CaF2 at speed of 90 rpm is shown in Figure 3.13.

Figure 3.11: The lime specimen after dissolution in the slag with 5 wt% CaF2 at 90rpm and after reaction time of 20 minutes

1430 ºC

1600 ºC

1500 ºC

1550 ºC

146

Figure 3.12: CaO- Al2O3-CaF2 phase diagram according to Mills and Keene (1981)

147

Figure 3.13: Comparison of total CaO content in slag with 5 wt% CaF2 at 90 rpm and in air at 1430 – 1600 °C

3.1.1.3.2 Effect of Fe2O3 addition on dissolution of CaO in slag at various temperatures

Experiments on the effect of addition of 5 wt% Fe2O3 on dissolution of CaO

were carried out in air with a rotation speed of 90 rpm at temperatures 1430,

1500, 1550 and 1600 °C for a reaction time of 1 hour. The results are illustrated

in Appendix A.3. For all experiments with addition of 5 wt% Fe2O3 in the slag,

the bottom of lime crucible was dissolved after the 1 hour reaction and in

experiment at 1600 °C, the whole crucib le was dissolved in the slag. The lime

specimen after the experiments at 1430 and 1500 ºC are shown in Figure 3.14.

Therefore, the concentration data used in the calculations taken from the data up

to the reaction time of 8~10 minutes, when the slope of lime dissolution curve

148

has started to change considerably, reflecting a change in the shape of the lime

specimen.

Figure 3.14: The lime specimen after dissolution in the slag with 5 wt% Fe2O3 at 90 rpm and after reaction time of 20 minutes

The effect of addition of Fe2O3 on the dissolution of lime in the slag at various

temperatures is illustrated in Figure 3.15 (curve-fitted data). Increasing the

temperature increased the rate of lime dissolution in the slag.

1500°C 1430°C

149

Figure 3.15: Comparison of CaO concentrations dissolved in slag with 5 wt% Fe2O3 at 90 rpm and in air at 1430 – 1600 °C

3.1.1.3.3 Effect of TiO2 addition on dissolution of CaO in slag at various temperatures

The effect of 5 wt% TiO 2 content in slag on the dissolution rate of CaO in

calcium aluminosilicate slag was studied in air with speed of 90 rpm at

temperatures of 1430,1500,1550 and 1570°C. The results are presented in

Appendix A.4. After reaction time of 1 hour at 1430 °C, there was a substantial

reduction in diameter of crucible (Figure 3.16). In experiments at 1500, 1550 and

1600 °C, the bottom of the crucible was completely lost to the slag, which caused

change of dissolution rate of lime in the slag. Therefore the concentration data up

to 10 minutes of reaction time were used to calculate the rate of dissolution. The

curve-fitted concentration of CaO in the slag, which contains 5 wt% TiO 2 is

presented in Figure 3.17.

150

Figure 3.16: The lime specimen after dissolution in the slag with 5 wt% TiO2at 90 rpm and after 60 minutes of reaction.

Figure 3.17: Comparison of concentrations of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1430 – 1570°C for 1 hour

1600°C1500°C

151

3.1.1.3.4 Effect of ilmenite addition on dissolution of CaO in slag at various temperatures

The influence of addition of 5 wt% ilmenite on the dissolution of CaO in calcium

aluminosilicate slag was investigated at 1500, 1550, 1570 and 1600 °C. The

experiments were performed in air and a rotation speed of 90 rpm and for a

reaction time of 10 minutes. The reaction time was chosen on the basis of

considering the fact that during the dissolution experiments with addition of TiO 2

and Fe2O3, the shape of the cylindrical lime sample was changed after 10~20

minutes of rotation of lime in the melt. According to Figure 3.18, it was observed

that at 1550 and 1570 ºC, there was a substantial reduction in diameter of the

lime sample after the total reaction time of 10 minutes and at 1600 ºC, the bottom

of the lime crucible was lost after completion of the experiment.

The results for addition of 5 wt% ilmenite to the slag at 1500-1600 ºC are

presented in Appendix A.5. The dissolution of lime in the slag containing 5 wt%

ilmenite at 1500 ºC was increased linearly with time and generally was lower

probably due to formation of a solid layer. At 1550 and 1570 ºC, the dissolution

of lime was faster with a similar dissolution pattern, however at 1600 ºC, there

was a pronounced effect on the dissolution of lime compared to other

temperatures. The variation of CaO dissolution for the temperature range of 1500

to 1600 °C for the slag, which contains 5 wt% ilmenite at rotational speed of 90

rpm is shown in Figure 3.19 (curve-fitted data).

152

Figure 3.18: The lime specimen after dissolution in the slag with 5 wt%ilmenite at 90 rpm and after reaction time of 10 minutes

Figure 3.19: Comparison of concentrations of CaO dissolved in slag with 5 wt% ilmenite at 90 rpm and in air at 1500 – 1600 °C

b

1600ºC1570ºC

1550ºC1500ºC

153

3.1.1.3.5 Effect of Mn3O4 addition on dissolution of CaO in slag at various temperatures

Experiments were carried out with addition of 5 wt% Mn3O4 to the master slag in

air, at rotating speed of 90 rpm at temperatures 1430, 1500, 1550, 1600 ºC for a

reaction of time of 10 minutes. The results are presented in Appendix A.6. The

reaction time was selected as explained in previous sections. At temperatures

above 1430 ºC, the bottom of crucible was again dissolved in slag after

completion of the experiments (Figure 3.20). At 1600 ºC, there were substantial

grooves on the surface of the lime crucible; therefore the dissolution rate was

measured from the data up to 6 minutes where the rate of dissolution could be

considered linear and not affected by the complete dissolution of crucible

bottom. The curve-fitted concentration of lime in the slag with addition of Mn2O3

for various temperatures is illustrated in Figure 3.21.

154

Figure 3.20: The lime specimen after dissolution in the slag with 5 wt% Mn2O3 at 90 rpm and after reaction time of 20 minutes

Figure 3.21: Concentration of CaO dissolved in slag with 5 wt% Mn3O4at 90 rpm and in air at 1430 – 1600 ºC

1430 ºC 1500 ºC

1550 ºC 1600 ºC

155

3.1.1.3.6 Effect of SiO2 addition on dissolution of CaO in slag at various temperatures

After consulting CaO-Al2O3-SiO2 phase diagram in Slag Atlas (Eisenhuttenleute

(1995)), the experimental temperatures were chosen in a way in order to avoid

formation of solid phases, which would affect the dissolution behaviour of lime

in the slag. The effect of SiO 2 addition on dissolution of lime was investigated by

adding 5 wt% SiO 2 to the slag and carrying out dissolution experiments in air at a

rotating speed of 90 rpm at temperatures 1500 to 1600 ºC. The results are shown

in Appendix A.7. The variation of lime dissolution with changing temperature is

given in Figure 3.22 (curve-fitted data).

Figure 3.22: Comparison of concentrations of CaO dissolved in slag with additional 5 wt% SiO2 at 90 rpm in air at 1500 – 1600 °C for 1 hour

3.1.1.4 Effect of variables on the dissolution rate

The effects of temperature and additives (slag chemistry) on the dissolution rate

of lime is summarized in Table 3.2 and illustrated in Figure 3.23. The dissolution

156

rate was calculated according to section 3.1.1.1. The results show that addition of

5 wt% CaF2 increased the dissolution rate compared to the master slag by a

factor 4 at 1500 °C, a factor of 3 at 1550 °C and a factor of 2 at 1600 °C. The

addition of 5 wt% Fe2O3 to master slag at 1430, 1500, 1550 and 1600 °C

increased the dissolution rate of lime about a factor of 3.3, 3.6, 2.6 and 1.9,

respectively. With addition of 5 wt% TiO 2, the dissolution rate increased by a

factor of 1.5, 2, 1.5 in comparison with the values for master slag at temperatures

of 1430, 1500, 1550 °C, respectively and at 1570 °C the rate was about 1.3 times

the dissolution rate for master slag at 1600 ºC. When 5 wt% ilmenite was added

to the master slag, the dissolution rates at 1500, 1550 and 1600 ºC increased by

1.6, 2.3 and 2 times compared to the rate data for master slag. The dissolution

rate of slag containing ilmenite at 1570 ºC was 1.25 times higher than the rate for

slag containing 5 wt% TiO 2 at the same temperature. The addition of SiO 2

increased slightly the dissolution rate compared to the master slag at various

temperatures.

Increasing the temperature increased the lime dissolution rate in almost all slags

studied. The exception being when 5 wt% CaF2 was used, where an apparent

decrease in dissolution was observed at 1430 and 1500 ºC. This is likely to be

due to inhomogenity of slag at 1430 ºC, where the phase diagram for CaO –

Al2O3 – CaF2 indicates stability of solid phase at temperatures below 1550 ºC.

Given the fact that there is an error of about 15% in calculation of dissolution

rate, the general trend of effect of additives on the dissolution rate at various

157

temperatures shows that Ilmenite, MnOx and FeOx increased the dissolution rate

and have comparable effect in comparison with CaF2.

Figure 3.23: The rate of dissolution of lime (g/cm2.s) in the slag at various temperatures and with additives

3.1.1.5 Effect of basicity on the dissolution of lime at constant temperature

Experiments were carried out to study the effect of basicity (at a constant

temperature of 1500 ºC) on the dissolution rate of lime. Experiments were

performed in slag of CaO – 20.4 wt% Al2O3 – 41.4 % SiO2 (basicity = 0.9) at

various rotating speeds of 40, 60 and 90 to investigate if the dissolution processes

of lime into liquid are controlled by mass transfer step. The results for data)

variation of concentration of lime with time are shown in Figure 3.24 (curve-

fitted data). As it would be shown later (3.2.1.9) on the static reaction of this slag

158

with lime, two reaction layers were formed on the lime/slag interface. At 40 rpm,

these layers seem to be unstable, floating in the slag, eroding the lime sample

which results in excessive dissolution of lime in the slag.

Figure 3.24: The concentration of lime (wt%) in the slag (basicity of 0.9) at various rotation speed at 1500 ºC

The proportionality of dissolution rate with 0.5 and 0.75 –th power of rotation

speed are shown in Figure 3.25 and Figure 3.26, where a linear relationship

exists. As rotation speed of 90 is within the regime, where the dissolution is

controlled by diffusion in liquid slag so the dissolution rate at this speed can be

compared to the rest of dissolution rate data. The dissolution rate in slag of 0.9

basicity was found to be ( 51036.2 −× g CaO/cm2/s) which is a third of the master

slag with basicity of 6 ( 51037.6 −× g CaO/cm2/s).

159

Figure 3.25: The dissolution rate of CaO with speed 0.5 in slag with basicity of 0.9

Figure 3.26: The dissolution rate of CaO with speed 07.5 in slag with basicity of 0.9

160

3.1.2 Dissolution of MgO in calcium aluminate slag

Preliminary experiments were carried out to investigate the dissolution of MgO

in the CaO – Al2O3 slag in air at 1430 °C by rotating MgO samples at speeds in

the range of 30 to 150 rpm and reaction time of 1 hour. The initial slag

composition was 45 wt % CaO and 55 wt % Al2O3 as shown in Figure 3.27. The

purpose of these experiments was to test the experimental set up and evaluation

of the results before carrying out the experiments, which investigated lime

dissolution.

Figure 3.27: CaO-Al2O3-MgO system phase diagram according to Slag Atlas (Eisenhuttenleute (1995))

The MgO samples were in the form of crucibles, 20 mm in diameter and 30 mm

in height. A slag sample of 60 grams was used in each experiment. MgO

161

dissolved in the slag was determined by sampling of molten slag using a

platinum wire at the tip of a steel rod. The sampling was done at five minutes

intervals. The MgO concentration in the slag was analysed using XRF, the

estimated error being within ±0.2 – 0.3 wt% (absolute).

3.1.2.1 Effect of rotation speed on the rate of dissolution

Variation of the dissolution rate of MgO in molten calcium aluminate slag with

the rotation speed (60, 90, 120 and 150 rpm) was investigated at 1430 ºC in air

for a reaction time of one hour. The concentration of MgO in the slag increased

with increasing rotation speed of the MgO sample in the melt. The experimental

results are shown in Figure 3.28.

162

Figure 3.28: Concentration of MgO dissolved in slag at different rotation speed, in air at 1430 °C for 1 hour

The proportionality of dissolution rate with 0.5 and 0.75 -th power of rotation

speed as two boundary conditions for dissolution of disk and cylinder side of the

magnesia specimen in the speed range of 60 to 150 rpm, is presented in Figure

3.29 and Figure 3.30. The total dissolution rate is related to the rotation speed

according to Equation (3.9), on the basis of combination effect of cylinder and

disk and kinematic viscosity of slag (as explained in Section 3.1.1.1).

75.05.0 026.0093.0 ωω +≈totalRate (3.9)

As it can be seen, the dissolution rate changes linearly with 0.5 and 0.75 -th

power of rotation speed in the speed range of 60 to 120 rpm. Also Figure 3.31

163

shows that the dissolution rate changes linearly with the correlation of rotation

speed expressed in Equation (3.9). The result at the speed of 150 rpm show

deviation from linear regression. The apparent sudden increase in dissolution rate

may be caused by erosion of polycrystalline manganese sample at such high

rotating speed. The measured data under static condition, i.e. zero rotation speed

should correspond to the rate of lime dissolution under condition of natural

convection as well as agitation caused by sampling the melts. The dependency of

rate of magnesia dissolution on the rotation speed of 60 – 120 rpm, suggests that

the measured dissolution rates were most likely controlled by mass transfer in the

liquid phase. Rotation speed of 90 rpm was chosen for subsequent experiments to

determine the effects of addition of Fe2O3 and (CaF2 + Fe2O3) to the slag. As it is

shown in appendix D, the error in the rate of dissolution is about 15 – 20%.

Figure 3.29: Dependence of rate of dissolution of MgO with 0.5 -th power of speed

164

Figure 3.30: Rate of dissolution of MgO with 0.75 -th power of speed

Figure 3.31: Variation of the dissolution rate of MgO versus 75.05.0 ωω BA +of rotation speed in air. A and B are defined at 1430 ºC

165

3.1.2.2 Effect of Fe2O3 addition on dissolution of MgO in slag

The influence of Fe2O3 on the dissolution of MgO was studied by adding 5 wt%

and 10 wt% Fe2O3 to the calcium aluminate slag. The experiments were carried

out in air at a rotation speed of 90 rpm at 1430 °C and the total reaction time of 1

hour. The results for these experiments are presented in Appendix A.7. The

comparison of magnesia concentration in the alumina silicate slag with addition

of 5 and 10% Fe2O3 at 1430 ºC is illustrated in Figure 3.32. The addition of 5

wt% Fe2O3 increased the dissolution rate by a factor of 3 and addition of 10 wt%

Fe2O3 increased the rate of dissolution by a factor of 5. The dissolution rate data

are tabulated in Table 3.7.

Figure 3.32: Concentration of MgO dissolved in slag with 5 and 10% Fe2O3at 90 rpm in air at 1430 °C for 1 hour

166

Table 3.7: The rate of dissolution of MgO in the slag at 1430 °C and with various additives

Slag samples Rate (g/cm2/s)

master slag 2.7E-05

slag + Fe2O3 5% 6.5E-05

slag + Fe2O3 10% 1.0E-04

slag + Fe2O3 5% + CaF2 5 % 2.9E-04

slag + Fe2O3 10% + CaF2 5% 2.1E-04

3.1.2.2.1 Effect of (Fe2O3 + CaF2) addition on dissolution of MgO in slag

An attempt was made to study the influence of CaF2 on the dissolution rate of

MgO in the slag but after addition of 5 wt% CaF2, the slag was not fully molten

at experimental temperature of 1430 °C. Therefore, 5 wt% CaF2 was added to

two types of slag; slag with 5 wt% Fe2O3 and slag with 10 wt% Fe2O3. The

experiments were conducted in air at rotational speed of 90 rpm. The results are

presented in Appendix A.8. The dissolution rate was very fast for the first five

minutes of rotation and then it became flat as it approaches the saturation limit of

magnesia in the slag after 10~20 minutes of rotation. Therefore, the calculations

were based on the results for the first 20 minutes of the experiment. The rate of

dissolution was increased with a factor of 10.7 for the slag which contained 5

wt% CaF2 + 5 wt% Fe2O3 and also the rate was increased with a factor of 7.7 for

the slag which contained 5 wt% CaF2 & 10 wt% Fe2O3. The results on the rate of

167

dissolution with these two types of additives are tabulated in Table 3.7. The

variation of MgO concentration in the slag with additives at 1430 ºC is presented

in Figure 3.33.

Figure 3.33: Concentration of MgO dissolved in slag with additives at 90 rpm and in air at 1430 °C for 1 hour

3.2 Static experiments

3.2.1 CaO experiments

In static experiments, lime was reacted with various slags at different

temperatures. The results on solubility of lime in the slags and formation of a

solid layer at lime/slag interface will be presented in the following sections. The

concentration of various elements in the slag phase was analysed quantitatively

168

with EPMA. Phase identifications and measurement of the thickness of a reaction

layer were done using SEM.

3.2.1.1 Solubility of lime in the master slag under various temperatures

The driving force for dissolution of lime can be defined as the difference

between the solute and the saturation concentration of lime in the molten slag.

Experiments were performed by placing a piece of dense lime with slag in a

platinum capsule, heating them up to a specific temperature in a muffle furnace

and holding for the required reaction period. The lime sample and slag were then

withdrawn from the furnace and quenched in air. The quenched samples were

sectioned vertically, mounted and polished.

Initially experiments were carried out in air at 1430 ºC with reaction times of 0.5,

1, 2, 4, 6, 12 and 24 hours to determine the time required for the dissolution of

CaO in calcium aluminosilicate slag to reach equilibrium. The concentrations of

CaO in the quenched bulk slags close to the lime/slag interface were analysed

using SEM – EDS. Samples from the rest of experiments with additives were

analysed with EPMA for higher accuracy. The results of the analysis are

presented in Figure 3.34 and tabulated in Table 3.8.

169

Figure 3.34: Variation of bulk slag composition (wt%) measured by SEM-EDS with the reaction time at 1430 ºC in air.

Table 3.8: SEM – EDS analysis of the bulk slag at1430 ºC in air

These results indicate that, within experimental scatter, a steady value of

concentration had been reached after half an hour. The reaction time of 3 hours

Ca Al Si O

0.5 36.63 22.07 4.02 37.7 51.281 36.73 21.66 4.1 37.6 51.422 35.34 22.51 3.25 39.05 49.484 36.66 21.85 4.1 37.66 51.326 35.43 22.06 4.07 38.33 49.6012 36.24 20.89 4.05 38.82 50.7424 35.91 21.25 3.89 38.67 50.27

Time (hr)Slag composition (wt %) CaO

(wt%)

170

was sufficient to reach equilibrium, which is enough for the experiments at

higher temperatures and with addition of additives, where the dissolution rate is

faster compared to the master slag.

In these experiments where the lime sample was reacted with master slag at 1430

ºC, a reaction layer was formed on the lime/slag interface, which is shown in

Figure 3.35. Growth rate of this layer will be measured and used for development

of a dissolution model detailed in the next chapter.

Figure 3.35: Interfacial region of CaO in contact with slag at 1430 ºC for the reaction time of 2 hours

Experiments were also carried out at, 1500, 1550 and 1600 ºC in air to determine

the dependency of lime solubility on temperature. The obtained results are

tabulated in Table 3.9.

CaOslag

Reaction layer

171

Table 3.9: EPMA analysis of the bulk slag close to the lime/master slag interface in air at different temperatures

Composition of slag (wt%)Temperature(ºC) O Mg Al Si Ca

CaO (wt%)

1430 35.79 0.12 16.68 3.16 43.08 60.66

1500 35.82 0.82 17.66 3.28 41.59 58.68

1550 35.59 0.81 17.45 3.21 41.33 58.54

1600 35.14 0.87 16.06 3.16 42.97 61.07

The measured solubility of lime at 1600 ºC could be compared with the results

from phase diagram (Figure 3.1), which is about 62 wt%. Considering the fact

that the error involved in the EPMA analysis for the Ca concentration was within

%2~1± , it shows a very good agreement.

3.2.1.2 Effect of addition of CaF2 on the solubility of lime in theslag

Experiments were performed to determine the solubility of lime in the slag with

addition of 5 wt% CaF2 at temperatures 1430, 1550 and 1600 ºC. The results are

presented in Table 3.10.

Table 3.10: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% CaF2 at various temperatures in air

Composition of slag (wt%)Temperature( ºC ) O F Mg Al Si Ca

CaO(wt%)

1430 35.29 0.98 0.56 16.41 3.39 41.51 57.63

1550 35.46 1.40 1.32 15.33 3.30 41.69 58.47

1600 34.11 1.59 1.06 15.65 3.21 42.68 58.34

172

Although the phase diagram in Figure 3.12, predicts the formation of a solid

phase (11 CaO.7Al2O3.CaF2), no phase was evident in the EDS-SEM analysis of

the sample (Figure 3.36). This might be due to the similarity between the

composition of glassy phase at 1430 ºC and the expected phase. Therefore the

BSE shows a similar contrast because of the similar density of atoms in liquid

slag and the expected phase. At higher temperatures no solid phase was also

detected, which is in accord with the expected behaviour from the phase diagram

for CaO – Al2O3 – CaF2 system.

Figure 3.36: Interfacial region of CaO in contact with slag containing 5 wt% CaF2 at 1430 ºC for the reaction time of 3 hours

3.2.1.3 Effect of addition of Fe2O3 on the solubility of lime in the slag

The solubility of CaO in slag with addition of 5 wt% Fe2O3 was determined in air

and at temperatures of 1430, 1500, 1550 and 1600 ºC. The results are tabulated in

Table 3.11.

CaO slag

173

Table 3.11: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% Fe2O3 at different temperatures in air

Composition of slag (wt%)Temperature(ºC) O Fe Mg Al Si Ca

CaO(wt%)

1430 35.17 2.87 0.60 16.48 2.90 39.81 56.441500 35.06 2.41 1.27 15.87 3.24 40.77 57.991550 34.46 2.43 0.82 15.78 2.81 41.49 58.701600 35.44 2.60 0.94 15.31 2.89 41.50 59.37

A solid phase was formed in the slag matrix when the experiment was conducted

at 1430 ºC. The oxide composition of the phase is given in Figure 3.37.

Figure 3.37: Interfacial region of CaO in contact with slag containing 5 wt% Fe2O3 at 1430 ºC for the reaction time of 3 hours

Phase:CaO: 61.35Al2O3: 35.19SiO2: 1.96FeOx: 1.125

CaO

174

3.2.1.4 Effect of addition of TiO2 on the Solubility of lime in the slag

Experiments were carried out to obtain the solubilities of lime in the slag

containing 5 wt%, TiO2 at temperatures 1430, 1500, and 1600 ºC in air. The

results are tabulated in Table 3.12.

Table 3.12: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% TiO2 at different temperatures in air

Composition of slag (wt%)Temperature( ºC ) O Ti Mg Al Si Ca

CaO(wt%)

1430 35.74 2.44 0.62 15.96 2.97 38.66 57.13

1500 36.67 2.12 1.07 15.15 3.03 39.81 59.04

1600 36.04 2.09 1.04 14.80 2.95 40.40 59.95

As it can be seen in Figure 3.38 a solid phase was formed on the CaO/slag

interface at 1430 ºC. The composition of the reaction layer is also given in Figure

3.38.

175

Figure 3.38: Interfacial region of CaO in contact with slag containing 5 wt% TiO2 at 1430 ºC for the reaction time of 3 hours

3.2.1.5 Effect of addition of ilmenite on the solubility of lime in the slag

Experiments on solubilities of lime in the slag with addition of 5 wt% ilmenite

were carried out by placing a piece of dense CaO in the molten slag for a period

of 3 hours in air. These experiments were performed at temperatures of 1430,

1500, 1550, 1600 ºC. The results are presented in Table 3.13. A reaction layer

was observed during the experiment at 1430 ºC, which is shown in Figure 3.39.

Table 3.13: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% ilmenite at different times in air

Composition of slag (wt%)Temperature(ºC) O Fe Ti Mg Al Si Ca

CaO(wt%)

1430 35.59 0.66 0.34 0.27 17.42 2.00 42.72 60.27

1500 36.69 1.19 1.26 1.00 15.34 3.05 40.39 58.52

1550 36.29 1.11 1.16 1.83 14.46 3.41 40.42 59.19

1600 35.41 1.12 1.23 0.89 14.78 2.85 42.09 60.30

Phase:CaO: 62.66Al2O3: 35.15SiO2: 2.16

CaO

176

Figure 3.39: Interfacial region of CaO in contact with slag containing 5 wt% ilmenite at 1430 ºC for the reaction time of 3 hours

3.2.1.6 Effect of addition of Mn3O4 on the solubility of lime in the slag

Experiments aimed at investigating the solubility of lime in the slag containing 5

wt% MnOx were performed at temperatures of 1430, 1550 and 1600 ºC in air.

The results are presented in Table 3.14. At 1430 ºC, a solid phase in the form of a

layer was formed in the slag, which is shown in Figure 3.40.

Table 3.14: EPMA analysis of the bulk slag close to the interface of lime/ slag containing 5 wt% MnOx at various temperatures in air

Composition of slag (wt%)Temperature(ºC) O Mn Mg Al Si Ca

CaO(wt%)

1430 36.04 2.34 0.60 15.83 2.94 41.00 59.56

1550 34.80 2.20 1.11 16.44 3.51 40.07 57.53

1600 36.42 2.31 1.36 15.87 3.12 39.51 57.66

Phase:CaO: 60.26Al2O3: 33.78SiO2: 4.38

CaO

177

Figure 3.40: Interfacial region of CaO in contact with slag containing 5 wt% Mn3O4 at 1430 ºC for the reaction time of 3 hours

3.2.1.7 Effect of addition of SiO2 on the solubility of lime in the slag

The experimental data on reaction of lime with base slag with addition of 5 wt%

SiO2 at 1500, 1550 and 1600 ºC are illustrated in Table 3.15.

As it is mentioned before, the rotating experiments were carried out at

temperatures at /above 1500 ºC as it was expected that at 1430 ºC a reaction layer

would be formed on the lime/slag interface. Indeed, in static experiment at 1430

ºC, a reaction layer was observed at the lime/slag interface (Figure 3.41), which

agrees with the CaO – Al2O3 – SiO2 phase diagram.

Phase:CaO: 62.23Al2O3: 34.15SiO2: 2.16

CaO

178

Table 3.15: EPMA analysis of the bulk slag close to the interface of lime/ slag containing additional 5% SiO2 at various temperatures in air

Composition of slag (wt%)Temperature(ºC) O Mg Al Si Ca

CaO(wt%)

1430 37.71 0.38 22.20 3.50 34.82 49.091500 34.82 0.46 15.46 4.04 43.45 60.871550 35.80 1.12 14.66 4.53 42.12 60.431600 34.88 0.99 14.35 4.48 43.50 61.62

Figure 3.41: Interfacial region of CaO in contact with slag containing 5 wt% SiO2 at 1430 ºC for the reaction time of 3 hours

It is clear from this table that there is little difference in solubility of CaO in the

slags with additives compare to the master slag.

3.2.1.8 FactSage thermodynamic modelling

Attempt was made to do thermodynamic modelling with FactSage developed by

Bale et al. (2003) to calculate the solubility of lime in base slag and slag with

CaO: 65.43 SiO2: 33.43Al2O3: 1.13CaO

179

addition of 5 wt% CaF2, Fe2O3, TiO2, Mn3O4, ilmenite and SiO 2. The

Equilibrium module of the package was used which identifies phases and their

compositions by the Gibbs free energy minimization.

Table 3.16: The solubility of lime in various slags at different temperatures by FactSage (Bale et al. (2003)) modelling

Solubility of lime in slag with addition of 5 wt% additivesTemperature

(ºC)Master

slagCaF2 Fe2O3 TiO2 ilmenite Mn3O4 SiO2

1430 57.84 57.69 57.43 57.86 57.84 55.368 59.35

1500 59.29 58.01 58.34 59.29 59.23 56.395 60.1341550 59.54 58.30 58.65 59.55 59.53 56.717 60.35

1600 59.84 58.64 59.01 59.87 59.78 57.087 60.62

There is a very good agreement between the results from static experiments

analysed by EPMA and solubility data from FactSage modelling. The data from

thermodynamic modelling confirm that with the exception of Mn3O4, the

additives have little effect on the equilibrium solubility of lime in the slags.

3.2.1.9 Formation of a reaction layer on the lime/base slag interface

Experiments were conducted to measure the growth rate of a solid layer formed

during the reaction of the calcium aluminosilicate slag with lime at 1430 ºC in

air. The lime specimen used in the experiment was taken from the same lime

crucibles used in the rotating experiment and it was reacted with slag in a

platinum capsule made from thin platinum foil. The reaction was followed by

quenching the platinum foil with its content at various time intervals and

180

examining them by the Scanning Electron Microscope. It was found that a solid

phase product layer was formed between the lime samples and the slag, which

was identified by EDS analysis as very close 3CaO.Al2O3. This observation is

consistent with the phase diagram.

The thickness of the reaction layer formed at the lime/slag interface was

measured from the backscatter image generated by SEM. It was seen that the

product layer thickness increased with time. The micrographs of the reaction

layer and its growth is illustrated in Figure 3.42 to Figure 3.48.

Figure 3.42: SEM micrograph of the CaO and slag interface for lime reacting 30 minutes with slag in air at 1430 °C

181

Figure 3.43: SEM micrograph of the CaO and slag interface for lime reacting 1 hour with slag in air at 1430°C

Figure 3.44: SEM micrograph of the CaO and slag interface for lime reacting 2 hours with slag in air at 1430°C

182



183



184

A plot of square layer thickness as a function of time in Figure 3.49 shows a

linear relationship and the equation corresponding to this line was calculated as:

tx 92 102 −×=Δ (3.10)

Where

=Δx thickness of the solid layer (mm)

=t time of reaction (s)

According to Zhang et al. (1994),the growth rate of a solid phase may be

expressed as:

( ) ⎥⎦

⎤⎢⎣

⎡−⎟⎟

⎠

⎞⎜⎜⎝

⎛Δ

=Δ

2/1tK

xK

dtxd df

(3.11)

Where Kf (mm2/s) is the parabolic rate constant for the formation of solid phase,

and Kd (mm/s1/2) is the rate constant for the dissolution of solid phase by

molecular diffusion. Integration of Equation (3.11) with the initial condition of

0=Δx at 0=t yields:

tKx 22)( =Δ (3.12)

Where { [ ] } 2/12/12 2)( fdd KKKK ++−= , which can be considered as an

effective parabolic rate constant for solid-solution growth. From Equation (3.10)

185

and (3.12), one can obtain 5104 −×=K mm/s1/2 under the mentioned

experimental condition.

Figure 3.49: Thickness of solid layer as a function of square root of time in slag in air at 1430ºC

186

3.2.1.9.1 Effect of basicity on the formation of reaction layer on the lime/slag interface

Experiments were performed to investigate the effect of basicity on the formation

of the reaction layer and dissolution of lime in the slag. Lime pieces were reacted

with slag of CaO – 20.4 wt% Al2O3 – 41.4 SiO2 (basicity = 0.9) for pre-

determined reaction times. Two incoherent phases of 2CaO. SiO 2 and 3CaO.SiO 2

were formed on the lime/slag interface, where 3CaO.SiO 2 was observed to be

between the lime and 2CaO. SiO 2 phase. As the formed phases were not in the

form of a continuos layer, the measurement of their thickness was not possible.

The results are presented in Figure 3.50 to Figure 3.55:

Figure 3.50: Interfacial region of CaO in contact with slag (basicity = 0.9) at 1500 ºC for the reaction time of 1 hour

3CaO.SiO 2

CaO

2CaO.SiO 2

slag

187

Figure 3.51: Interfacial region of CaO in contact with slag (basicity = 0.9) at 1500 ºC for the reaction time of 2 hours


CaO

CaO 3CaO.SiO 2

2CaO.SiO2

3CaO.SiO 2

2CaO.SiO 2

188



CaO

CaO

3CaO.SiO 2

2CaO.SiO 2

3CaO.SiO 2

2CaO.SiO 2

189


3.2.2 MgO experiments

The solubility of magnesia in the rotating experiments was determined by

examining a piece of slag attached to magnesia samples left after the completion

of the rotating experiments as the magnesia samples did not fully dissolve in the

slag after the reaction time. The magnesia sample was mounted and polished for

EPMA analysis in an area close to the magnesia/slag interface. Figure 3.56

shows solid oxide/slag interface after on hour of the rotation of magnesia sample

at 90 rpm in the master slag. The magnesia concentration in the area close to the

magnesia/slag interface was considered as the saturation limit of magnesia in the

slag. The reaction time of 1 hour during the rotating experiments was assumed

enough for magnesia to reach to equilibrium.

CaO

3CaO.SiO 2

2CaO.SiO 2

190

Figure 3.56: SEM micrograph of the magnesia / slag interface from the samples left from the rotation experiments at 90 rpm and 1430ºC

This was confirmed by reacting a piece of dense magnesia with base slags in the

platinum capsule in air and at 1430 ºC with reaction times of 0.5, 1, 2, 4, 8 hours

to determine the time required for MgO to reach equilibrium in calcium-

aluminate base slag. The results are tabulated in Table 3.17. These results show

that, after 0.5 hour of reaction time, the slag reached to equilibrium, according to

the phase diagram in Figure 3.27.

Table 3.17: SEM – EDS analysis of the bulk slag at1430 ºC in air

Composition of Slag (wt%)Time(hour) Al Si Ca Mg

MgO(wt%)

0.5 25.7 1.3 31.2 3.2 5.3

1.0 25.9 0.9 32.2 3.5 5.8

2.0 26.3 0.8 32.1 3.0 4.9

4.0 26.6 1.1 30.5 3.6 6.0

8.0 25.5 1.1 31.9 3.3 5.5

191

The results of solubility of magnesia in the slags with additives are presented in

Table 3.18. It can bee seen that the addition of additives in the slag changes the

solubility of MgO within 20 wt%.

Table 3.18: SEM – The solubility of magnesia in various slags

Slag samples MgO (wt%)

Master slag 4.32

slag + FeOx 5% 4.39

slag + FeOx 10% 4.50

slag + FeOx 5% + CaF2 5 % 5.60

slag + FeOx 10% + CaF2 5% 5.60

192

CHAPTER 4. Discussion

This chapter provides discussions of effects of temperature and additives on the

diffusivity of lime and magnesia in slags.

The first section covers derivation of diffusivity in slags from results of the

experiments using rotating disk/cylinder technique. The diffusivity of MgO in

the calcium aluminate slag and the effect of additives on the diffusivity will be

explained in second part of this chapter.

The diffusivity of lime in the slag and influence of temperature and additives on

the lime diffusivity will be also presented in the third section. The development

of a mix-controlled model where the dissolution of lime occurs in the presence of

a protective layer is detailed in the fourth section.

The fifth section deals with activation energy of diffusion and effects of various

additives on the activation energy. The relation of lime diffusivity with viscosity

of slag and validity of Eyring’s theory is discussed in the sixth part. The seventh

section discusses the relation between diffusivity and estimated ionic

conductivity in the slag. The last section summarizes the key findings in this

study.

193

4.1 Diffusivity of CaO / MgO in slag and effect of additives on the diffusivity

It was shown in the previous chapter that temperature and additive s have

significant effects on the dissolution rate of lime/magnesia in the slags studied.

As diffusivity plays a substantial role in the dissolution of solid oxides in the

slag, therefore the diffusivity of lime/magnesia in the slag will be calculated

using the dimensionless correlation of mass transfer under forced convection and

the dissolution rate data from the experimental results. The mass transfer from a

rotating crucible in liquid slag, which is used in the present study, consisted of

two partial fluxes from the disk surface and the cylindrical side of the specimen.

The mass transfer correlation used in each part will be detailed in the following

section and the derivation of diffusivity from the combined mass transfer will be

explained.

4.1.1 Mass transfer from the rotating disk

The fluid dynamics induced by rotating disk is well established. Cooper et al.

(1964) and more recently Sandhage et al. (1990) have shown that when rotating

disks are used, mass transfer is best described by Levich-Cochran equation for

rotating disk. The dependence of mass transfer coefficient on the angular velocity

of the disc and the physical properties of the liquid phase can be calculated using

the Levich-Cochran equation. Levich (1962) derived the following equation for

mass transfer from a rotating disk on the basis of the derivation of the mass

transfer from rotating disk, which is shown in Chapter 1.

194

2/13/1

61.1 ⎟⎠⎞⎜

⎝⎛⎟

⎠⎞⎜

⎝⎛=

ων

νδ D (4.1)

where, δ (cm) is the liquid boundary layer thickness, D (cm2/s) is the diffusion

coefficient ,ω (rad/s) is the angular velocity of rotating disk and ν is the

kinematic viscosity of melt. According to Sandhage et al. (1990), Equation (4.1)

is strictly valid for an infinitely large rotating disk in a semi- infinite slag bath.

The disk and the slag bath can be considered nearly infinite and semi- infinite,

respectively, if the thickness of the liquid boundary layer is several orders of

magnitude smaller than the disk radius. The liquid boundary thickness close to

the disk can be estimated using Equation (4.1). The estimated diffusivity in the

liquid slag on the basis of the results calculated in the next part of this section

was found to be in the order of magnitude of 10-5 cm2/s at 1500 °C. The density

(~2.8 g/cm3) and viscosity (~8 g/cm.s2) of slag were estimated using published

models, which will be explained later. By inserting these values into Equation

(4.1), the thickness of the liquid boundary layer could be derived at the given

rotation speed (90 rpm) for slag with and without additives. The thickness of

boundary layer ≈ 0.01 cm was 100~130 times smaller compared to the diameter

of the rotating crucible (2 cm) and depth of the slag bath (about 1cm). Therefore,

Equation (4.1) could be used for the present study.

For Equation (4.1) to be valid, the fluid has to be Newtonian and the flow must

be laminar. Molten silicates have been found to be Newtonian (viscosity is

independent of sheer strain) over a range of applied sheer stress according to

Michel and Mitchell (1975). In some cases, the presence of solid particles in the

195

slag could cause an apparent non-Newtonian behaviour as investigated by

Wright, Zhang, Sun and Jahanshahi (2000) & (2001). Laminar flow near a

rotating disk may be assumed if the Reynolds number is less than ~105. The

Reynolds number ( νω /Re 2r= , where r is the disk radius in cm) was calculated

and ranged from about 2~7 for the present work. So the flow in this study could

be assumed to be laminar. Use of Equation (4.1) also requires that the fluid have

a relatively large Schmidt number )1/( >>= DSc ν . The Schmidt numbers of the

melts in this study were calculated to be >104.

Noyes-Nernst Equation (4.2) was used to calculate the dissolution rate of solid

oxide from the disk side of the crucible to the liquid boundary layer, where the

mass transfer is diffusion controlled.

δbS

diskCC

Dj−

= (4.2)

Where diskj (g/cm2.s) is the mass flux, sC and bC (g/cm3) are the saturation and

bulk concentration, respectively and D (cm2/s) is the diffusion coefficient.

Equation (4.2) can be written as:

)( bSdiskdisk CCkj −= (4.3)

Where diskK is the mass transfer coefficient in liquid on the disk side of

specimen and is defined as:

196

δDk disk = (4.4)

Therefore on the basis of Equation (4.1), the mass transfer from the disk side of

crucible can be written as:

6/12/13/2621.0 −= νωDk disk (4.5)

Combining Equations (4.3) and (4.5) leads to the Equation (4.6), which describes

direct dissolution under conditions where mass transfer through a concentration

boundary layer in the melt is controlling the rate.

)(61.0 2/16/13/2 CbCsDj disk −= − ων (4.6)

According to the Equation (4.6), if dissolution is controlled by mass transfer

through the liquid boundary layer, the dissolution rate should be proportional to

the square root of rotation speed. This was investigated in Chapter 3 and it was

shown that a linear relationship between the rate of solid oxide dissolution and

square root of rotation speed (30 to 120 rpm) exists.

4.1.2 Mass transfer from the rotating cylinder

Generalized relationships of mass-transfer coefficient have been obtained

experimentally for many specific geometries. These were shown in Chapter 1.

Eisenberg et al. (1955) developed the following correlation for mass transfer

197

from a cylinder rotating in a stationary concentric crucible from studies of the

dissolution of benzoic and cinnamic solids into water-glycerol solutions:

3.0644.0 Re0791.0 −== ScV

kj cylinder

cylinder (4.7)

Where;

=j mass-transfer j factor from the cylinder side of the crucible

=V peripheral velocity of rotating disk

=Sc Schmidt number

=cylinderk mass transfer coefficient of the cylinder


Kosaka, Machida and Hirai (1969) studied the mass transfer from a rotating

metal cylinder into liquid metal in a temperature range up to 1400 ºC. They

employed Steel-Al, Steel-Zn, Cu-Pb, Zn-Hg and Sn-Hg as the combination of

solid metal cylinder- liquid metal bath. They reported the following relationship:

25.0644.0 Re065.0 −== ScV

kj cylinder

cylinder (4.8)

Comparing the applicability of Equations (4.7) and (4.8), the Eisenberg et al.

(1955) correlation was derived from the room temperature data with solute

dissolving in water or water based solvent, while in the correlation developed by

198

Kosaka et al. (1966), the experimental temperature was up to 1400 ºC, which is

very close to the operating temperature in the present work and also the solvent

was liquid metal with more similarity with behaviour of molten slag compare to

the water. Umakoshi et al. (1981) measured the dissolution of MgO into molten

FeOx-CaO-SiO2 slags at temperatures from 1350 to 1425 ºC. They used the

correlation developed by Kosaka in their calculations to measure the mass

transfer coefficient. Therefore, the Kosaka et al. (1966) correlation (4.8) has been

used in this study for the mass transfer calculation from the cylinder side of the

lime crucible. The mass transfer coefficient in the liquid slag was calculated by

re-arranging Equation (4.8), which yields:

VDkcylinder3/23/225.0Re065.0 −−= ν (4.9)

4.1.3 Total mass transfer from the solid oxide specimen

The total mass transfer from the solid oxide sample to the liquid slag was

obtained by considering the combined effect of disk and cylinder part of the lime

specimen, which is expressed in Equation (4.10):

cylinderdisktotal jjJ += (4.10)

This can be written as:

199

CAkCAkCAK cylindercylinderdiskdisktotaltotal Δ⋅⋅+Δ⋅⋅=Δ⋅⋅ (4.11)

Where; CbCsC −=Δ .

The total area of the solid oxide crucible is consisted of:

cylinderdisktotal AAA += (4.12)

The area of disk and cylinder can be defined as:

2rAdisk ⋅= π (4.13)

hrAcylinder ⋅⋅⋅= π2 (4.14)

Where, r is the radius of the lime crucible and h is the length of the crucible

immersed in the melt. By inserting Equations (4.13) and (4.14) into Equation

(4.11), we obtain:

cylinderdisktotal khr

hkhr

rK ⋅+

+⋅+

=2

22

(4.15)

And by substituting the corresponding values of mass transfer coefficient from

Equations (4.5) and (4.9) into the Equation (4.15), we have:

200

The dissolution rate data were used to calculate the total mass transfer

coefficient, as in Equation (4.17):

( ) slagbstotal CC

rateK

ρ⋅−= (4.17)

A model developed by Urbain (1984) was used for estimation the viscosity of

slag and various additives in the slag, which is explained in detail in Appendix B.

The density of slag was also estimated by a model proposed by Mills and Keene

(1987), which is explained in Appendix C. By equating Equation (4.17) and

(4.16) and rearranging the resulting equation, the effective diffusivity of solid

oxide in the slag was obtained. Two sets of data will be presented in the next

section, the results for MgO and CaO diffusivities.

4.2 Diffusivity of MgO in calcium aluminate slags

As it was explained in previous chapter, a number of preliminary experiments

were performed with MgO to compare the diffusivity results to the data from the

literature in order to test the experimental set-up. The MgO crucibles were

rotated in the slag of CaO – 55wt% Al2O3 at 1430ºC. The diffusion coefficient

was obtained on the basis of the rate of dissolution and solubility from the

experimental results. The diffusivity of MgO in the master slag and slags with

VDhr

hDhr

rKtotal3/23/225.06/12/13/2 Re065.0

22621.0

2−−−

++

+= ννω (4.16)

201

additives is tabulated in Table 4.1. The error associated with calculation of

diffusivity is about 30%. (see Appendix D)

Table 4.1: The diffusivity of MgO in the CaO – 56 wt% Al2O3 at 1430ºC in air with additives (wt%)

Slag samples D (cm2/s) viscosity(poise)

Master slag 1.45×10-5 15.78

slag + FeOx 5% 2.5×10-5 13.63

slag + FeOx 10% 4×10-5 11.82

slag + FeOx 5% + CaF2 5 % 2×10-4 9.72

slag + FeOx 10% + CaF2 5% 3×10-4 8.7

The diffusivity of MgO in slag was increased by addition of FeOx and mixture of

FeOx and CaF2. As the slag is high in alumina, the diffusion of MgO might be

governed by the movement of alumina ions in the slag.

It has been investigated before by Zhang et al. (1998b) & (1998a) that bond

strength between ionic species should influence the structure and, hence,

viscosity of such melts. Thus, apart from the differences in bond strength

between cations (Ca2+, Mg2+ and Fe3+) and oxygen ions (O2-), the influence of

various cations on the bonding environment of the aluminate anions is different.

At given aluminate content, when small fraction of cations is replaced by another

in melts, the changes in the structure of aluminate anions are not expected to be

great. Therefore, the variation in viscosity and diffusivity caused by such

202

replacement may be attributed mainly to the difference in the strength of M2+ -

oxygen ion interaction, i.e., the stronger the interaction between the atoms in the

melt, the more difficult the movement of atoms and slower diffusion. Therefore,

higher viscosity and lower diffusivity values are expected for melts with stronger

M-O bond. One may consider the melting point of oxide of a particular cation as

an indication of the strength of the interaction between that cation and oxygen

ions. For the metal oxides, investigated in the present work, the order of melting

points are, (CaO, 2887ºC)>( (FeOx, 1565ºC). As it is seen form the results in

Table 4.1, that 5 and 10 wt% FeOx increased the diffusivity of MgO.

The effect of additives on the diffusivity and viscosity of slag could also be

explained on the basis of observation by Bills (1963), where the effect of MgO

and FeOx on the viscosity of silicate melts was claimed to be the difference in the

electrostatic binding forces which bind Fe2+ and Mg2+ cations to silicate anions.

Also in the case of addition of CaF2 to the slag, the F- ions with an ionic radii of

1.33°A replace the oxygen ions with a similar ionic radii of 1.32

°A , then the

existing Ca2+ cations and the ones introduced in the melt by addition of CaF2

have weaker bonding with F- compared to oxygen which makes the movement of

anions easier and resulted to the faster diffusion of MgO.

Ukyo et al. (1982) measured the inter-diffusivity of MgO in the FeO – 30 wt%

CaO – 45 % SiO2 and CaO- 40 wt% SiO2 – 20 % Al2O3 slag in the temperature

range of 1350-1450 ºC. The order of magnitude of diffusivity was 10-5 cm2/s for

both types of slags, which is in agreement with the result of the present work,

where Fe2O3 was added to slag.

203

Umakoshi et al. (1984a) measured the dissolution rate and mass transfer

coefficient of sintered magnesia in the CaO – FeOx – SiO2 slags of CaO/SiO 2 = 1

(FeOx = 20 to 65 wt%) in the range of 1350 to 1425 ºC They applied the rotating

cylinder technique, using the dimensionless correlations and estimated the

diffusion coefficient of MgO to be 5101 −× to 5103 −× cm2/s at 1400 ºC. The

results of this study are in a very good agreement with these data.

Zhang et al. (1994) measured the diffusivity of MgO in the stagnant CaO-FeO-

CaF2-SiO2 slag in the temperature range of 1300 – 1400 ºC by reacting magnesia

rods with stagnant slag and measuring the concentration profile of Mg in the

slag. The diffusion coefficient was found to be lower than the diffusivity of MgO

in the present study. This could be explained in terms of different experimental

techniques in both measurements.

4.3 Diffusivity of CaO in calcium aluminosilicate slags

The derived diffusivity values from CaO dissolution experiments are presented in

this section. The diffusivities were obtained on the basis of experimental data on

the rate of dissolution and solubility of lime in the slags and are presented in

Figure 4.1 and Table 4.2. The viscosity and density of the slag were calculated

using Urbain model and Mill model, respectively. The error in calculation of the

diffusivity data is described in Appendix D, which is about 30%.

204

Figure 4.1: Diffusivity of CaO in CaO – 42 wt% Al2O3 – 8 SiO2 slag with 5 wt% addition of CaF2, MnOx, FeOx, TiO2, SiO2 and ilmenite. The activation energy of diffusion calculated on the basis of the slope of these graphs are compared for the base slag (44 kcal/mol) versus the slag with addition of 5 wt% CaF2 (15kcal/mol).

205

Table 4.2:Results for the measured diffusivity of CaO in the slag and the calculated slag viscosity at various temperatures

Composition Temperature (ºC) Diffusivity (cm2/s) Viscosity (poise)

1430 9.20×10-6 13.24

1500 1.32×10-5 8.789

1550 1.93×10-5 5.95Master slag

1600 3.07×10-5 5.8

Temperature (ºC) Diffusivity (cm2/s) Viscosity (poise)

1500 7.29×10-5 6.28

1550 7.94×10-5 4.69Slag + CaF2 5%

1600 1.03×10-4 3.68


1430 3.54×10-5 12.67

1500 4.28×10-5 8.15

1550 5.01×10-5 5.94

Slag + MnOx 5%

1600 6.82×10-5 4.35


1550 4.73×10-5 5.15

1570 4.74×10-5 4.65Slag + Imenite 5%

1600 6.01×10-5 3.86


1430 3.83×10-5 11.19

1500 3.86×10-5 7.1

1550 4.13×10-5 5.26

Slag + FeO 5%

1600 4.68×10-5 3.96


1430 1.38×10-5 10.84

1500 2.37×10-5 6.72

1550 2.49×10-5 5.04

Slag + TiO2 5%

1570 3.72×10-5 4.42

Temperature (ºC) Diffusivity (cm2/s) Viscosity (poise)1500 8.77×10-6 9.241550 1.51×10-5 6.61

Slag + SiO2 5%

1600 2.02×10-5 4.96

206

The increase in temperature had a pronounced effect on the calculated diffusivity

of CaO. Also the addition of CaF2, Mn3O4, Fe2O3, TiO2 and ilmenite

significantly increased the effective diffusivity of lime in the slag, as the addition

of SiO2 slowed down the diffusivity of CaO in the slag.

As it is seen in Table 4.2, addition of CaF2 had the strongest effect and increased

the diffusivity by about 5, 4 and 3 times at 1500, 1550, and 1600 ºC,

respectively. Addition of Fe2O3 increased the diffusion coefficient of CaO

substantially compared to the master slag. The value of diffusion coefficient at

1430, 1500 and 1550 ºC were about 4, 3, 2 times the corresponding values for

master slag, while at 1600 ºC, the diffusivity was about 1.5 times the value for

master slag. By adding Mn2O3 to the slag, the diffusivity increased about 2 – 4

times in the temperature range of 1430 to 1600 ºC compared to the diffusivity

data in master slag. The influence of addition of TiO 2 to the melt was to increase

the diffusion coefficient about 1.2 – 1.8 times at 1430, 1500, 1550 and 1600 ºC

compared to master slag. The addition of ilmenite to the slag had stronger effect

than Fe2O3 and TiO2 in increasing the diffusivity of lime in the slag. The

diffusivity results obtained with addition of ilmenite at 1550 ºC are comparable

with the case of addition of CaF2.

The relationship between the structure of melts and their transport properties is a

key to the fundamental understanding the mechanism of diffusion in silicate

melts and effect of additives on the diffusivities. It has been investigated before

by Zhang et al. (1998b) & (1998a) that bond strength between ionic species

should influence the structure and, hence, viscosity of such melts. Thus, apart

from the differences in bond strength between cations (Ca2+, Ti2+ and Fe3+) and

207

oxygen ions (O2-), the influence of various cations on the bonding environment

of the silicate anions is different. At given silica content, when a small fraction of

cations is replaced by other cations in melts; the changes in the structure of

silicate anions are not expected to be great. Therefore, the variation in viscosity

and diffusivity caused by such replacement may be attributed mainly to the

difference in the strength of M2+ - oxygen ion interaction, i.e., the stronger the

interaction between the ions in the melt, the more difficult the movement of ions

and slower diffusion. Therefore, higher viscosity and lower diffusivity values are

expected for melts with stronger M-O bond. One may cons ider the melting point

of oxide of a particular cation as an indication of the strength of the interaction

between that cation and oxygen ions. For the metal oxides, investigated in the

present work, the order of melting points are, (CaO, 2887ºC)>( TiO 2, 1843ºC)>

(MnOx, 1842ºC)>( (FeOx, 1565ºC).

As it is seen from the results in Table 4.2, additions of 5 % MnOx, FeOx and 5%

TiO2 increased the diffusivity of CaO. However, the effect of a 5 wt% ilmenite

addition was greater than either of the individual oxide additions, particularly at

the lower temperatures. This indicates that there is a synergistic effect in the

combined addition of FeOx and TiO2 that is presumably associated with their

combined effect on bond strength between the ions and oxygen.

Given the fact that the slag considered in this study is very basic, the SiO 44-

anions are mostly in the form of non-chained anions and the CaF2 addition to the

slag does not have network breaking effect. By addition of CaF2 to the slag, the

F- ions replace the oxygen ions then the existing Ca2+ cations and the ones

introduced in the melt by addition of CaF2 have weaker bonding with F-

208

compared to oxygen which makes the movement of anions easier and resulted to

the faster diffusion of CaO as it is shown in Table 4.2.

The diffusivity of lime in the slag of lower basicity (0.9) at 1500 ºC was not

calculated since two non-coherent reaction layers were formed on the lime/slag

interface. The formation of these layers affects the diffusivity of lime in the slag,

as it is not clear when the diffusion happens in the liquid or solid phase. The

lower dissolution rate of lime in the slag of lower basicity compared to the

master slag indicates the effect of higher silicate anions on the dissolution.

4.3.1 Comparison of CaO diffusivity with literature data

In comparing the results of the present work with previously published

diffusivity data (Figure 4.2), it should be remembered that slag composition

obviously has a major effect on the diffusivity specially where the silicate

content of slag is high. Also the method of measurement will affect the

diffusivity data obtained. This is particularly the case where self-diffusion rather

than Chemical diffusion has been measured in the past. Generally, the values of

chemical diffusivity are higher than self-diffusivity. Self-diffusion is the

movement of various species present in the melt by random motions (Poirier and

Geiger (1998)). The movement of these species are monitored where a fraction

of one (or more) of the species is radioactive, which is called tracer diffusivity.

Chemical diffusion is the movement of a species in the melt in response to the

establishment of a chemical potential gradient resulting from either concentration

or temperature gradients in the melt and therefore has higher values compare to

self-diffusivity.

209

Figu

re4.

2: D

iffus

ivity

of c

alci

um a

ccor

ding

to th

e pu

blish

ed d

ata

and

the

dedu

ced

diffu

sivity

in th

e pr

esen

t wor

k fo

r bas

e sla

g –(

B:ba

sici

ty, C

: CaO

, Al:

Al2O

3, Fe

: FeO

, M:M

g)

210

The results of the present work are initially compared with data from Johnston et

al. (1974), who measured the self-diffusivity of Ca45 into three types of slags as

mentioned in the Chapter 1. Their results revealed that diffusivity of Ca45 is

higher in slag with no silica content, compared to slags containing silica. Based

on the previous viscosity measurements by Kozakevitch (1951), the authors

proposed that in the slag containing silica, there is a greater proportion of highly

polymerized aluminosilicate units which make the diffusivity slower. The

diffusivity in the slag of CaO – 50 wt% Al2O3 at 1500 ºC shows 5109.1 −× ,

which is in good accord with result of diffusivity in the present study in the

master slag at 1500 ºC ( 5103.1 −× ). The presence of about 8 wt% silica in the

master slag is expected to affect the diffusivity in the present study compared to

the mentioned published data. At the same time, the diffusivity of calcium in the

base slag from the present work is higher than the other diffusivity data by

Johnston et al. (1974), where the basicity of slags were 0.3 and 0.9 respectively.

Again it appears that the slag silica content is a major factor, decreasing the

diffusivity, as it would explain later in this section. It was also shown by the

same authors that addition of CaF2 to the melt had a substantial effect on the

diffusivity of Ca45, which is in a very good agreement with the result of the

present study where CaF2 is added to the slag.

The diffusivity of lime in the iron containing slag can be compared to the data by

Hara et al. (1989) as they measured the self-diffusivity of Ca45 in FeO – SiO2 –

CaO slag at 1270 to 1450 ºC. The average diffusivity was reported to be in an

order of magnitude of 10-5, which is a very good agreement with the results in the

present work.

211

The data from measurements of Keller et al. (1979b) on the self-diffusivity of

Ca45 in the CaO – SiO2 melts in the temperature range of 1500 to 1700 ºC is

compared to the results from the present work. They showed that diffusivity of

calcium was decreased by increasing the silica content of the slag from (mole

fraction) 0.448 to 0.634. This is in agreement with the results in the present work,

where diffusivity decreases with increase in the silica content of the slag. Their

measured self-diffusivity data are lower compared to the present result. This

difference could be explained by substantial difference in the silica content of

slags, and methods of diffusivity measurements. As the slag considered in their

work had high silica content compared to the about 8 wt% silica in the present

work and also self diffusivity is lower than chemical diffusivity data.

The self-diffusivity of calcium in steelmaking slag of CaO – 27 wt% SiO 2 – 40

% FeOx from the measurements by Goto et al. (1977) at various oxygen

pressures and at 1360 to 1460 ºC compared to the results from the present work.

The diffusivity data in the present study, where F2O3 is added to the slag show

the same order of magnitude and is in a good agreement with their data.

The self-diffusivity of Ca45 measured by Towers et al. (1957) and later Saito et

al. (1958) show lower values compare to the results from the present work. Apart

from slag chemistry where the silica content of slag was higher in the works by

these authors, the method of measurements could be another reason for such a

difference. The low diffusivity data by Saito et al. (1958) in comparison with

other calcium diffusivity measurements have been also addressed by Keller et al.

(1979b) and Johnston et al. (1974).

212

The effect of iron oxide on the dissolution rate of lime in the CaO-SiO2-Al2O3

and FeO-CaO-SiO2 slag was reported by Matsushima et al. (1977) using rotating

cylinder method, which has been reviewed in Chapter 1. The authors calculated

the mass transfer of CaO in slags from the rate of dissolution data, thus the

diffusivity data have been derived in the present work on the basis of their mass

transfer data. The deduced diffusivity data as well as the original mass transfer

data form their experiments are tabulated in Table 4.3. It is apparent from their

results that diffusivity of lime at 1500 ºC is about twice the diffusivity of lime

obtained through the present work. At the same time, addition of FeOx to the slag

increased the diffusivity of lime by a factor of two, which is in good agreement

with present results.

Table 4.3: Values for mass transfer coefficient, thickness of boundary layer and deduced effective diffusivity of lime in the slag according to Matsushima et al. (1977)

Slag Temperature( ºC )

Speed (rpm)

K(cm/s)

D*

(cm2/s)

1500 200 2.90×10-4 2.63×10-5CaO - 40 wt% SiO2 - 20

% Al2O3 1500 400 5.30×10-4 2.98×10-5

1400 200 9.70×10-4 5.19×10-5CaO - 40 wt% SiO2 - 20

% FeO 1400 400 1.71×10-3 5.57×10-5

D*: calculated by the present author

The diffusivity of lime in the present work could be compared with the

diffusivity data of similar oxides using the same experimental technique.

Umakoshi et al. (1981) measured the dissolution rate of MgO into molten slag

213

CaO – SiO2 – FetO slags at temperatures from 1350 to 1425 ºC using rotating

cylinder method. They used non-dimensional correlation and estimated the

apparent diffusion coefficients with the order of magnitude of 510− cm2/s at 1400

ºC. The apparent diffusivity data in the present work, where Fe2O3 is added to the

slag are within the same order of magnitude and are in good accord with these

data.

The effect of transition metals on increasing the diffusivity of oxides in the slag

in the present work can also be compared to the work done by Lee et al. (2001).

They measured the apparent diffusivity of alumina in the calcium aluminosilicate

melt of (30 wt% Al2O3 – 53 % CaO – 5 % MgO – 12 % SiO2) using a rotating

disk method. As shown in Figure 4.3, addition of FeOx and MnOx increased the

effective diffusivity of slag substantially. It was reported that addition of 5 and

10 wt% FeOx increased the diffusivity by about 2 and 2.5 times and addition of 5

and 10 wt % MnOx showed more profound effect and increased the diffusivity by

about 4 to 6 times. The results of diffusivity of lime in the present work in the

slag with FeOx and MnOx show a very good agreement, with the same order of

magnitude. In both results addition of FeOx and MnOx into the slag increased the

rate of dissolution and diffusivity of oxides in the slag.

214

Figure 4.3: Influence of addition of FeOx and MnOx on the apparent diffusivity of alumina at 1560-1590ºC according to Lee et al. (2001)

The effect of addition of iron oxide to the slag in the present work can be

compared to the difference in tracer diffusivity of Fe59 and Ca45 in silica

saturated melts of the FeO – CaO – SiO2 system at 1600 ºC which was

investigated by Keller et al. (1986). The Fe59 showed a higher diffusivity 5101 −×

compared to 6102 −× cm2/s for silica and the higher concentration of iron oxide

resulted in higher diffusivity of Fe59 in slag. The authors postulated that the

higher diffusivity of iron was possibly due to the different bonding by oxygen,

which caused a transition state in the jump of Fe2+ ions from one site to the next.

The increase in the diffusivity of CaO in the slag in the presence of FeOx in the

present work, is in accord with Keller’s findings, where the present results are

explained by the effect of additives on the bonding environment of silica melts.

215

The tracer diffusivity of Ca45 in their work shows lower values compare to the

chemical diffusivity in the present study.

The effect of addition of 5 wt% SiO2 to the slag in the present work could be

compared to the data by Keller et al. (1979a), who measured the tracer diffusivity

of Si31 in CaO-SiO2 melts (Mole fraction of silica NSiO2 = 0.484 – 0.634) at a1600

ºC. They reported that diffusivity of Si31 decreases with increasing silica content

of the slag and the values of Si31 diffusivity were found to be lower than that of

Ca45 by approximately one order of magnitude in the silica rich melt. The

difference decreased with decreasing silica content. The authors argued that the

Si31 in the CaO – SiO2 melts is normally assumed to bounded to large complex

silicate anions, which move slower than the cations but as the diffusivity of

oxygen is much higher than silica, they suggested silica ions would rotate during

time intervals in the melt and harbour the tracer atoms, which is easier than

translation of silicon ions in the molten liquid. The lower values of diffusivity of

silica compared to Ca and Fe reflect the bonding between these ions and oxygen

in the melt. In the present work, the order of diffusion of Ca in the melt with

additives is slag + FeOx > master slag > slag + additional SiO 2, which follows the

same trend as the mentioned published data.

The effect of additives on the diffusivity of CaO in slag in the present work can

be compared to results by Ukyo et al. (1982) on quasi- inter-diffusivities of

several solute oxides in CaO – SiO2 – Al2O3 and Fe2O3 – CaO – SiO2 slags.

Comparison of diffusivity values of FeOx, MnOx, P2O5, TiO2 reveals that the

oxides diffused in the order of; MgO>FeOx>MnO>P2O5>TiO2 in the CaO – SiO2

– Al2O3 slag. As the order of diffusivity for the oxides in FeOx – CaO – SiO2 slag

216

was: MgO>MnO>NiO>P2O5>TiO2. The substantial increase in the diffusivity of

CaO in the slag in the present study by addition of MnOx and FeOx, is in accord

with the findings by Ukyo et al. (1982).

4.4 Diffusion in a Mix – controlled regime

It was shown in Chapter 3 that when lime sample was rotated in the calcium

aluminio-silicate melt at 1430°C, the CaO concentration dissolved in the slag

increased approximately linearly with reaction time, but after about 10 minutes

of reaction, the CaO dissolution curve reached a plateau at a level of less than 52

wt%, which is far less than the saturation level of 59 wt%, given that the rotating

lime sample was not fully dissolved at the end of one hour reaction time. These

results can be explained in terms of CaO – Al2O3 – SiO2 phase diagram (Figure

4.4) where formation of a solid layer on the surface of lime occurred and

consequently the dissolution of lime was slowed down.

217

Figure 4.4: CaO-Al2O3-SiO2 phase diagram

To investigate this further, experiments were carried out in which the lime was

reacted with base slag at 1430ºC under static condition. These experiments were

aimed at obtaining evidence of the formation of a solid layer and measuring

growth rate of the layer at the lime/slag interface. The SEM examination of

solidified samples confirmed the presence of a 3CaO.Al2O3 layer and the

thickness of the layer was observed to increase with increasing reaction time,

which was demonstrated in Chapter 3. The growth rate of the 3CaO.Al2O3 layer

218

was found to be linear and correlated to reaction time according to Equation

(4.18):

tx 92 102 −×=Δ (4.18)

Where xΔ is the change in thickness in millimiters and t is reaction period in

seconds.

The diffusion of lime in the solid layer was then estimated according to the

following Equation:

( )txD

2Δ≅ (4.19)

The value of diffusivity in the solid layer was deduced from the slope of the 2xΔ

versus time, where there is a linear relationship between ( )2xΔ and time, as

shown in Figure 4.5.

219

Figure 4.5: Estimation of CaO diffusion through a solid layer

According to Figure 4.5, the 3CaO.Al2O3 (C3A) solid layer grows linearly with

time. It is postulated that once a complete layer of C3A covers the surface of a

lime specimen, it increases in thickness by formation of C3A layer at the

lime/C3A interface and, the rate of formation of C3A is much faster than the rate

of dissociation. The linear behaviour of growth rate suggesting that dissolution

process is controlled predominately by the diffsion of lime in the reaction layer.

The diffusion coefficient of lime in the 3CaO.Al2O3 solid layer is estimated on

the basis of Equation (4.19) to be 9102 −× cm2/s at 1430 ºC.

Comparison could be made between the diffusion of CaO in the 3CaO. Al2O3

layer and growth rate of this layer with the previously published data. Zhang et

al. (1994) studied the dissolution of MgO in the CaO – FeO – CaF2 – SiO2 slags

220

in the temperature range of 1573-1673 ºC. They observed a layer of

magnesiowustite at the MgO/slag interface and measured its thickness versus

time. The authors also estimated the inter-diffusivity of MgO in the solid layer by

applying the cylindrical coordinate diffusion equation and it was found to be

8107 −× cm2/s. The average diffusivity was also estimated by applying Appel’s

equation, which is the solution to Fick’s second law with variable diffusivity in

multiphase system and the result was 8103 −× cm2/s. Attempt was made in the

present work to deduce the diffusion coefficient by the slope of the line in the

plot of (thickness)2 versus time as it is shown in Figure 4.6. The diffusion

coefficient value was found to be 8103 −× cm2/s, which shows that the

assumption made in Equation (4.19) is in a very good agreement with the result

given by analytical solution. The diffusivity of CaO in the present work is an

order of magnitude lower than the diffusivity of MgO in the Zhang’s work.

221

Figure 4.6: variation (Thickness2) of magnesiowustite layer as a function of time on the basis of work done by Zhang et al. (1994)

Allen, Sun and Jahanshahi (1995) measured the thickness of the reaction layers

of spinel and wustite when MgO was reacted with slag of 80 wt% FeOx and 20

wt% CaO. Using their results, an attempt was made in this work to estimate the

diffusivity of MgO in the wustite layers at various temperatures by plotting

square of thickness versus time according to Figure 4.7. The diffusion coefficient

for Wustite is between 9103 −× to 7101 −× cm2/s depending on the temperature. In

the case of spinel the diffusion coefficient at 1300 ºC is estimated as 9102 −×

(cm2/s) according to Figure 4.8. The results show that the estimation of

diffusivity in the 3CaO.Al2O3 layer in the present work is in the range of

published data on growth rate and diffusivity of oxides in the solid layer.

222

Figure 4.7: Variation of (thickness2) of wustite layer with time deduced from data according to Allen et al. (1995)

Figure 4.8: Variation of the (thickness2) of the spinel layer with time deduced from data according to Allen et al. (1995)

223

Blank and Pask (1969) investigated the inter-diffusion in the MgO – FexO

system, which exhibits complete solid solution under low oxygen pressure. In the

MgO phase the value of Mg diffusion was found to be 91024.1 −× cm2/s and the

ferrite phase, diffusion for Fe was with an average value of 81058.5 −× cm2/s.

Thus, we can conclude that the assumption made in the present work to deduce

the value of diffusivity in solid, results in diffusivity data, which is within the

values of diffusivity in solid layer and can be accepted as a reasonable

assumption.

Therefore, the “mass transfer coefficient” of lime in the solid layer was estimated

according to the following Equation:

xDKsolid Δ

= (4.20)

As it was mentioned earlier, mass transfer of lime in the liquid phase could be

estimated by Equation (4.16). The dissolution of lime into the master slag at

1430ºC initially started from the diffusion of lime in the liquid slag. On

formation of the 3CaO.Al2O3 protective layer on the lime/slag interface, the

diffusion of lime occurs through a mix-controlled regime, i.e. diffusion in the

solid layer and the diffusion in liquid slag. The newly formed solid layer is very

thin at early stages of dissolution, at this stage the mass transfer in the solid layer

is higher than the corresponding value for the liquid phase due to the thickness of

the product layer so the overall diffusion is predominately controlled by the

diffusion in the liquid slag. On increasing the reaction time, the solid layer on the

224

lime surface grew and the “mass transfer coefficient” in solid became smaller

compared to the mass transfer in the liquid phase, and the diffusion becomes

predominantly controlled in the solid layer. This would lead to slow diffusion of

CaO in the solid layer, which eventually controls and slows down the dissolution

process.

A mixed-control model was developed on the basis of diffusion in the solid and

liquid phases. The dissolution data obtained from the developed model was

compared with experimental results.

As the concentration of CaO in the 3CaO.Al2O3 layer was constant, Fick’s First

law, which according to Equation (4.21) states that the magnitude of the mass

flux is proportional to the concentration gradient at that point, could not be used;

xCDji ∂

∂= . (4.21)

Where, iJ is mass flux of i species (g/cm2.s), D is the diffusion coefficient

(cm2/s), and concentration C is expressed in g/cm3.

It was assumed in this work that the diffusion rate is proportional to the gradient

of its activity in both solid layer and liquid melt according to the Equation (4.22):

225

yaDCj

∂∂−= (4.22)

Where, D is the diffusion coefficient (m2.s-1) and y is the distance in the

direction of diffusion. For steady-state transfer, the rate at which CaO diffuses

through the 3CaO.Al2O3 layer is equal to the rate at which it diffuses into the

bulk liquid slag. Therefore, if lk and sk are the local mass transfer coefficients

in the solid layer and liquid phase respectively, then the flux of CaO could be

expressed as;

( ) ( )lillisss aaCkaaCkj −=−= (4.23)

Where:

=sk mass transfer coefficient of CaO in solid phase

=lk mass transfer coefficient of CaO in liquid phase

=sC concentration of CaO in solid phase

=lC concentration of CaO in liquid phase

=sa activity of CaO in solid phase

=la activity of CaO in liquid phase

=ia activity of CaO in the product layer/slag interface

226

At equilibrium, ia , activity of CaO is the same at the interface of the solid layer

and liquid slag adjacent to the liquid/slag interface ; therefore, it was eliminated

from both sides of Equation (4.23), and it becomes in Equation (4.24):

( )lstotalsl aaKCCj −= (4.24)

Where the total mass transfer totalK according to Equation (4.23) is expressed as:

llss

sltotal CkCk

kkK

+= (4.25)

sk , was found according to Equation (4.20) and lk on the basis of Equation

(4.16). The activity of CaO in lime specimen is equal to 1 and the activity of CaO

in bulk slag was calculated by the MPE model developed by Zhang, Jahanshahi,

Sun, Chen, Borke, Wright and Somerville (2002).

The concentration of CaO dissolved in the slag was estimated using the mix-

controlled model by integrating the rate Equation (4.24) and the results for two

lowest and highest rotation speeds were compared with experimental data. The

results are shown in Figure 4.9 to Figure 4.13. There is a good agreement

between the results from modelling and the experimental data. At a rotation

speed of 60 rpm, the data from modelling deviated slightly from the experimental

data after about 20 minutes. This could be due to disintegration of the lime

crucible after about 20 minutes due to the physical characteristics of the

227

particular lime sample used in that experiment, as the CaO concentration reached

to a plateau in compararison with the experiments at other rotation speeds.

Figure 4.9: The CaO concentration predicted by mix-controlled model and the experimental data at30 rpm & 1430 ºC

228

Figure 4.10: The CaO concentration predicted by mix-controlled model and the experimental data at 60 rpm & 1430 ºC


229


Figure 4.13: The CaO concentration predicted by mix-controlled model and the experimental data at150 rpm & 1430 ºC

230

4.5 Activation energy

The activation energy for diffusion (Q) in the slags studied has been calculated

using the Arrhenius equation:

⎟⎠⎞⎜

⎝⎛−=

RTQ

DD exp0 (4.26)

Where

=0D constant for a given solute; independent of temperature

=D diffusivity (cm2/s)

=Q activation energy for the diffusion process (cal/mole)

9872.1=R is the universal gas constant (cal.mol-1.K-1)

A plot of Ln (diffusivity) versus 1/temperature was constructed and the slope of

the lines were used for calculation of the activation energy which is presented in

Figure 4.14 and Table 4.4.

231

Figure 4.14: Arrhenius plots for calculation of the activation energy for diffusion of CaO in the master slag and slags with additives

Table 4.4: Activation energy for master slag and slag with additives

SlagComposition

Activation Energy (kcal/mole)

Master slag 43.18

slag + CaF2 5% 17.24

slag + FeOx 5% 8.46

slag + MnOx 23.54

slag + ilmenite 5% 28.38

slag + TiO2 5% 30.02

slag + SiO2 5% 79.24

232

The activation energy decreased markedly with addition of 5 wt% of Fe2O3,

CaF2, Mn3O4, ilmenite and TiO2 but increased with addition of 5 wt% SiO 2 in the

slag. The activation energy (Q) is generally regarded as the energy required for a

species to diffuse in the melt. In the master slag, the energy barrier for the

diffusion of CaO is the movement of silica anions. By addition of metallic oxides

and CaF2, the bonding environment of the melt becomes weaker, the silicate

anions can move easier and the energy barrier for diffusion of CaO becomes

lower to the master slag. By addition of SiO 2, the silicate anions become

restricted and their movement is slow thus the energy barrier for diffusion would

increase.

Attempt was made to deduce the activation energy diffusivity of CaO and other

oxides in the slag from the published data using Equation (4.26).

The results form data published by Johnston et al. (1974) show a decrease in the

activation energy of Ca diffusion in the CaO – 20 wt% Al2O3 – 42 % SiO2 slag

when CaF2 was added to the slag which is shown in Figure 4.15. The activation

energy reduced from 30 kcal/mole to 16 kcal/mole, which is in accord with the

result of the present work.

233

Figure 4.15: Arrhenius plot for the diffusion of Ca2+ in the CaO – 20 wt% Al2O3 – 42% SiO2, used in the calculation of activation energy on the basis of data from Johnston et al. (1974)

Also by comparing the activation energy of diffusion for Ca, F and Fe in the

same CaO – Al2O3 – SiO2 slag, deduced from the work by Johnston et al. (1974),

the activation energy for diffusion of fluorine(16 kcal/mole) shows the lowest

value while this value for iron (20.4 kcal/mole) shows less activation energy in

comparison with activation energy for diffusion of Ca (30 kcal/mole). These

values show the level of bonding of each element with the silica in the slag. This

is in good agreement with the present results, where addition of CaF2 and Fe2O3

lowered the activation energy of diffusion significantly.

234

Figure 4.16: Arrehnius plot for the diffusion of Ca2+, F-1 and Fe2+ in the CaO – 20 wt% Al2O3 – 42% SiO2 slag, used in the calculation of activation energy according to data from Johnston et al. (1974)

Saito et al. (1958) measured the activation energy of diffusion of calcium in the

binary and ternary systems. The measured activation energy by the authors is

shown in Table 4.5. The activation energy calculated in the present work is

within the same range.

235

Table 4.5: The activation energy for binary and ternary slags according to Saito et al. (1958)

Slag system Activation energy (kcal/mole)

CaO – SiO2 2050 ±

CaO – Al2O3 60

CaO – SiO2 – Al2O3 (CaO/SiO2 = 0.73), Al2O3 = 10% 2060 ±

CaO – SiO2 – Al2O3 (CaO/SiO2 = 1.33), Al2O3 = 20% 2050 ±

CaO – SiO2 – Al2O3 – MgO (MgO :3~10%) 2050 ±

The effect of addition of silica on the activation energy of diffusion can be shown

by studying the diffusion data measured by Keller et al. (1979b). On deducing

the activation energy from the diffusivity data of calc ium in the molten CaO-

SiO2 over a range of temperatures, it can be seen that by increasing the silica

content of slag, the activation energy increased from 28 to 35 kcal/mole. The

result of the present work follows the same trend as the addition of SiO 2

increased the activation energy of diffusion.

236

Figure 4.17: Arrhenius plot for diffusion of Ca in the CaO – SiO2 slags according to diffusivity data from Keller et al. (1979b)

As it is mentioned before, Ukyo et al. (1982) measured the diffusivity of several

solute oxides in liquid CaO – 40 wt% SiO2 – 20% Al2O3 in a temperature range

of 1350 to 1450 ºC. The activation energy from their diffusivity data was

deduced by the present author and illustrated in Table 4.6.

Table 4.6: Activation energy for diffusion of various oxides in CaO- 40 wt% SiO2- 20 % Al2O3 slag according to Ukyo et al. (1982)

Oxides MgO TiO2 MnO Fe2O3 P2O5

Activationenergy

(kcal/mole)22.11 53.46 54.52 63.2 68.11

237

The results show that activation energy for diffusion of MgO is the lowest with

TiO2 and MnO also having lower activation energies than Fe2O3 and P2O5. These

results show that the movement of MgO, Fe2O3 and MnO in the melt are faster

than others. The lower activation energy of diffusion of lime in the slag

containing MnOx and FeOx in the present study is in accord with these data.

The activation energy of single elements in the slag of CaO – 40 wt % SiO2 –

20% Al2O3 were deduced from the diffusivity data reviewed by Nagata et al.

(1982). The results are tabulated in Table 4.7, where Fe and Ti show lower

activation energies compared to the Ca and Si. This is in accord with the results

of the present work where transition metal decreased the activation energy of

CaO in the slag.

Table 4.7: Activation energy from diffusivity data of various ions in liquid CaO- 40 wt% SiO2- 20 % Al2O3 slag according to Nagata et al. (1982)

Oxide Mg Fe Ti Al Mn Ca Si P

Activationenergy

(kcal/mole)26.1 31.3 50.2 55.2 58.2 67 68.1 76.3

4.6 Relationship of diffusivity with viscosity

The Eyring’s theory of diffusion (Glasstone et al. (1941)) has been explained in

Chapter 1, where a model was presented for liquid diffusion based upon their

theory of absolute reaction rates and using the concept that the liquid structure

238

contains a number of holes or void spaces. This theory was used by Yu et al.

(1997) to investigate the mechanism of dissolution in the molten slag . The slope

of the line in plot of )(TDLn versus )(ηLn was considered as the basis for

judgment as according to the Eyring relation this slope is expected to be –1,

whether the diffusing molecules are big or small. Their diffusivity data matches

in this correlation well and the effective diffusivity of alumina in the CaO –

Al2O3 – SiO2 melts was shown to be very close to the self-diffusivity of Si4+

measured by Cooper et al. (1964), thus it was proposed that alumina diffusion

was controlled by the mobility of silicate ions.

In the present work, attempt was made to apply the Eyring’s correlation to the

master slag and slags with different additives, so the plot of )(TDLn versus

)(ηLn was established in Figure 4.18. It is shown that master slag and slag with

addition of SiO 2 follow the Eyring relation as the slope of the lines are close to –

1. However, additions of CaF2, Fe2O3, Mn3O4, TiO2 and ilmenite have a different

effect on the mechanism of diffusion so the results show a deviation from Eyring

relation. This could be explained by the argument mentioned above, i.e.; the

movement of species in the melt is governed by the movement of silica anions in

the melt. In the case where SiO2 was added to the melt, silica anions lock the

silica anions together and consequently the diffusion of calcium cations

decreases, again the diffusivity data shows agreement with the Eyring’s theory.

However addition of other additives, like Fe2O3, TiO2, Mn3O4, ilmenite and

CaF2, makes the bonding environment between the cations and silica anions

weaker therefore, the movement of silica anions becomes easier where the Ca2+

239

cations can move and diffuse faster. So there is a deviation from the Eyring’s

correlation, as the movement of CaO is not controlled by the movement of silica

anions. With additions and the consequent weaker bonding environment in the

silica melt, there is more deviation from the Eyring’s correlation.

Figure 4.18: Investigation of applying Eyring theory in diffusion of CaO in the slag

4.7 Ionic conductivity

The ionic conductivity of the master slag and slags with additives was calculated

in order to investigate whether the transport of ionic species in the melt has the

same mechanism to electrical conduction. It should be noted that relationship

between conductivity and diffusivity is complex as different driving forces

(chemical potentials and electrical charge) affect the effective concentration of

240

charge carriers and transfer numbers. At the present work, the ionic conductivity

is computed from the diffusivity data assuming that the conduction is solely by

motion of Ca2+ ions and that the Nerst-Einstein equation is valid. The following

Equation (4.27) applies for estimation of ionic conductance:

RTCZDF 22

=λ (4.27)

Where:

=λ ionic conductivity ( 11 −−Ω cm )

=D diffusivity (cm2/s) of Ca2+, which is assumed to be equal to the diffusivity

of CaO in the melt.

2=CaZ is the charge of the Ca2+ ion,

=CaC Ca2+ concentration in moles.cm-3

96485.3415=F C.mol-1 is the Faraday constant

=T absolute temperature (K)

3144.8=R J.mol-1.K-1 is the universal gas constant

The ionic conductivity is tabulated in Table 4.8. The results followed the same

trend as the variation of diffusivity, which decreased by addition of 5 wt% SiO 2

and increased by temperature and also addition of 5% wt CaF2, Fe2O3, TiO2,

Mn3O4 and ilmenite.

241

Table 4.8: Estimated Ionic conductivity ( 11 −−Ω cm ) of CaO-Al2O3-SiO2slag and slags with 5 wt% additives at various temperatures

According to Richardson (1974), the conductance of silicate melts is always

raised by the addition of metal oxides and the conduction mechanism is primarily

ionic. In cases where the metal oxide is an electronic conductor such as FeOx,

which conduct by virtue of the presence of cations of variable valency,

conduction becomes more electronic.

The validity of Equation (4.27) in estimation of conductivity has been

investigated by Keller et al. (1979b). They measured the electrical conductivity

of Ca45 in CaO-SiO2 melts, using the four-point method and compared

experimental data with calculated data using Equation (4.27). Although the

computed values are lower than experimental data (Figure 4.19), they are quite

comparable. The difference is low at low SiO 2 content. The experimental

conductivity value at 1600 ºC and for a silica mole fraction of about 0.44 shows a

value of 0.5 11 −−Ω cm . The estimated conductivity in the present work for the

base slag shows a higher value (1.84 11 −−Ω cm ), which can be explained by slag

chemistry where the silica content is much less and also the fact that the

conductivity data in the present study in on the basis of chemical diffusivity

which is higher than tracer diffusivity.

Master slag CaF2 Mn3O4 Ilmenite Fe3O4 TiO2 SiO2

1430 0.61 - 2.24 - 2.42 1.02 -1500 0.84 4.33 2.60 2.58 2.35 1.37 0.531550 1.08 4.64 2.95 2.65 2.44 1.35 0.881600 1.84 5.33 3.92 3.08 2.69 2.15 1.15

Conductivity in slag with addition of 5 wt% additivesTemperature(C)

242

Figure 4.19: Electrical conductivity of CaO – SiO2 slag, measured experimentally calculated as a function of mole fraction of silica at 1600 ºC after Keller et al. (1979b)

The temperature dependence of the electrical conductivity is usually expressed

by the Arrhenius relationship in Equation (4.28):

⎟⎠⎞⎜

⎝⎛ −

=RTE

A λλλ exp (4.28)

Where; λA is the constant, λE the activation energy, R the gas constant and T the

thermodynamic temperature. The activation energy of conductance can be

calculated on the basis of plot of Ln (conductivity) versus (1/temperature).

Attempt was made in the present work to compare the activation energy of

conductivity and activation energy of diffusivity. Firstly the activation of

243

conductivity for various slag compositions are deduced in the present work on

the basis of the data in the literature and compared with the published data on

activation energy of diffusivity of Ca in the slags of similar composition. This

would justify the validity of the comparison between these two quantities. Sarkar

and Sen (1978) & Sarkar (1989) measured the conductivity in the slag of CaO –

26 wt% Al2O3 – 35% SiO2 – 4% MgO in the temperature range of 1500 – 1600

ºC. The activation energy of conductivity (38 kcal/mole) deduced according to

their data shows a good agreement with the activation energy of diffusivity of Ca

( 2050 ± kcal/mole) calculated by Saito et al. (1958) in the slag system of CaO –

SiO2 – Al2O3 (CaO/SiO2 = 1.33), Al2O3 = 20 wt%. Nesterenko and Khomenko

(1985) measured the conductivity of slags with composition of CaO – (34 – 49

wt%) SiO2 – 5% Al2O3 at temperatures of 1500 – 1600 ºC and the deduced data

of activation energy are in the range of 20 – 48 kcal/mole. These results are

compared with the deduced value of activation energy of Ca diffusivity

according to Keller et al. (1979b), where they studied the CaO – SiO2 system

(SiO2 = 0.448 – 0.634 mole fraction). As the activation energy of diffusion is in

the range of 28.16 – 35.19 kcal/mole, a good agreement exists between these two

activation energies of conductivity and diffusivity. Winterhager, Greiner and

Kammel (1966) measured the electrical conductivity of CaO – 19 wt% Al2O3 –

40% SiO2 – 5% MgO in the temperature range of 1350 – 1550 ºC. The activation

energy of conductivity of 42.71 kcal/mole is deduced in the present work on the

base of their data and is in a good agreement with the activation energy of

diffusivity ( 2050 ± kcal/mole) calculated by Saito et al. (1958) for the slag of

similar chemistry. Thus suggesting the validity of Equation (4.27) and hence its

244

application to predicting diffusivity of slags from a knowledge of the electrical

conductivity of slags.

Therefore, it can be seen that the activation energies of conductivity, which are

presented in Table 4.9 can be compared with those for activation energy of

diffusion in Table 4.4.

Table 4.9: Estimated activation energy of conductivity for master slag and slags with 5 wt% additives

SlagComposition

Activation Energy (kcal/mole)

Master slag 39.66

slag + CaF2 5% 13.68

slag + TiO2 5% 26.52

slag + FeOx 5% 3.61

slag + ilmenite 5% 24.70

Slag + MnOx 5% 19.97

slag + SiO2 5% 51.28

It can be seen that the presence of CaF2, FeOx, TiO2, MnOx and ilmenite in the

slag decreased the activation energy and addition of SiO 2 increased the activation

energy of conductivity. Although the activation energy of diffusion is higher than

conduction, they both follow the same trend, supporting the theory that ionic

conductance and chemical diffusion are controlled by the same processes

245

involving the same energy barriers, which is movement of the large anions.

Addition of metallic oxides, ilmenite and CaF2 makes the movement of silicate

anions easier in the melt due to the weaker bonding environment, which

decreases the energy barrier for conduction of Ca2+ cations. Addition of SiO 2

increases the bonding of silica anions, which leads to the higher energy barrier

and slower conductivity of Ca2+ cation. It should be mentioned that as the

concentration of additives to the slag, (such as FeOx, MnOx and TiOx) is low, the

conduction is predominantly ionic but at high levels of additives it becomes

electronic.

4.8 Summary of key findings

The diffusivity of MgO in the CaO - 46 wt % Al2O3 slag was measured with

rotating disk/cylinder technique, at 1430ºC. It was observed that addition of FeOx

and combination of FeOx and CaF2 increased significantly the diffusivity of MgO

in the slag.

The diffusivity of CaO in the CaO – 42 wt % Al2O3 – 8% SiO2 slag was

measured in the temperature range of 1430 – 1600 ºC, using rotating

disk/cylinder technique. The effect of temperature and addition of additives

(CaF2, FeOx, TiO2, ilmenite, MnOx and SiO2) on the diffusivity were

investigated. By increasing the temperature and addition of 5 wt% CaF2, FeOx,

TiO2, ilmenite and MnOx, the diffusivity of lime in the slag was increased while

addition of 5 wt% SiO 2 reduced the diffusivity.

246

The activation energy of diffusion was calculated on the basis of changes of lime

diffusivity in various slags with respect to temperature. It was shown that

additives could be categorized in two groups, those that increased and those that

decreased activation energy. The effect of additives on the activation energy

could explain the mechanism of diffusion of lime in the slags with various

additives.

The relationship between diffusivity and viscosity was demonstrated with Eyring

theory, where the mechanism of diffusion in the melt was expressed according

the validity of Eyring correlation for various slags.

The ionic conductivity of lime in the slags was calculated and it was shown that

there is a direct relationship between the diffusivity and ionic conductivity of

lime in the slag.

The results show that FeOx, ilmenite and MnOx are comparable with CaF2 with

respect to increasing the diffusivity of lime in the slag and can be used instead of

CaF2 for effective dissolution of lime in the slag.

247

CHAPTER 5. Conclusion

5.1 Dissolution rate of MgO in calcium aluminate slag and lime in the calcium aluminosilicate slags

The dissolution rate of MgO in CaO – 55 wt% Al2O3 base slag has been

determined at 1430 ºC and in air, using the rotating disk/cylinder technique. The

results showed the increase in the magnesia content of slag as function of period

of rotation of magnesia sample in the melt. The effect of varying the rotation

speed on the dissolution rate was investigated. It was shown that there is a linear

relationship between the rate of dissolution with 1/2 and 3/4 -th power of rotation

speed (ω ) and 4/32/1 ωω BA + over the rotation speeds of 60 to 120 rpm. The

dependence of the rate of magnesia dissolution on the rotation speed suggests

that the measured dissolution of MgO is most likely controlled by diffusion in

the liquid boundary layer. The effect of addition of Fe2O3 and (Fe2O3+CaF2) on

the rate of dissolution was studied at a constant rotation speed of 90 rpm and at a

constant temperature of 1430 ºC. It was shown that while the average dissolution

rate of magnesia in the base slag was about 5107.2 −× g/cm2.s, additions of 5 and

10 wt% Fe2O3 increased the dissolution rate by a factor of 2 and 4, respectively.

It was also found that addition of a mixture of (CaF2 5 wt% + Fe2O3 5 wt%) and

(CaF2 5 wt% + Fe2O3 10 wt%) increased the dissolution rate considerably by a

factor of 11 and 8, respectively.

The dissolution rate of CaO in CaO – 42 wt% Al2O3 – 8% SiO2 base slag in a

temperature range of 1430 – 1600 ºC and in air was studied by using the rotating

248

disk/cylinder technique At a given temperature, the results revealed the increase

in the lime concentration versus the period of rotation of lime cylinders in slag.

The effect of rotation speed on the rate of dissolution was studied by conducting

experiments in a range of rotation speed of 30 to 150 rpm. As there was a linear

dependency of dissolution rate with the 1/2 and 3/4 –th power of rotation speed

( )ω and 4/32/1 ωω BA + , it was concluded that liquid slag mass transfer played a

significant role in controlling the dissolution. The dissolution rate also increased

with temperature at constant rotation speed. At constant rotation speed of 90 rpm,

the effect of 5 wt% additives, such as CaF2, FeOx, TiO2, MnOx, ilmenite and

SiO2 in the slag were quantified at various temperatures. The average dissolution

rate (g/cm2.s) of lime in the base slag over a temperature range of 1430 – 1550

ºC, was of the order of magnitude of 10-5 (g/cm2.s) and at 1600 ºC, the

dissolution rate was an order of magnitude higher. While CaF2 had the highest

effect, increasing the rate of dissolution by about a factor of 3, addition of FeOx,

MnOx and ilmenite increased the rate of dissolution (about a factor of 2) and

proved to be comparable with CaF2. The effect of basicity on the dissolution of

lime at constant temperature of 1500 ºC was investigated, where it was shown

that dissolution rate was about a third of the rate data for the slag with basicity of

6. During static reaction of lime with slag with basicity of 0.9, the formation of

two non-coherent phases of 2CaO.SiO 2 and 3CaO.SiO 2 on the lime/slag interface

was observed, where the measurement of thickness of these phases and

consequently the diffusivity measurements were not possible.

During the dissolution of lime in calcium aluminosilicate base slag at 1430 ºC, a

layer of 3CaO.Al2O3 was formed on the lime/slag interface, which slowed down

249

the dissolution rate and subsequently the diffusivity of lime in the slag. This

suggested that dissolution of lime in the slag occurred in a mix-controlled

regime. By conducting static experiments, it was found that the thickness of the

solid layer increased with reaction time and the growth rate the layer was

measured to be about ( 5104 −× mm/s). A Mix-Controlled model has been

developed on the basis of the assumption that the dissolution rate is proportional

to the gradient of its activity in both solid layer and liquid melt. The model

predicts the concentration of lime in the slag during the course of dissolution of

lime while the solid reaction layer grows on the lime/slag interface. The result of

modelling was compared to the experimental data and very good agreement was

found, confirming the dissolution of lime in a mix-controlled regime at 1430 ºC.

5.2 Solubilities of MgO in calcium aluminate slag and CaO in calcium aluminosilicate slags

The solubility of MgO in the various slags was determined by analysing the

rotating magnesia samples after the completion of the experiments. The MgO

concentration in the slag attached to the magnesia samples close to the interface

was measured quantitatively. The solubility of MgO was shown to be about 4.3

wt% in the base slag and introduction of the additives i.e. 5 and 10 wt% FeO,

(CaF2 5 wt% + Fe2O3 5 wt%) and (CaF2 5 wt% + Fe2O3 10 wt%) to the slag,

increased the solubility slightly to about 5 – 5.6 wt%. It was found that within

experimental scatter, the existence of additives in the base slag, does not increase

the solubility MgO in the slag.

250

CaO solubility in CaO – 42 wt% Al2O3 – 8% SiO2 base slag over a temperature

range of 1430 – 1600 ºC and slags with additives has been investigated

quantitatively by reacting the CaO with the base slag and slags with additives, at

various temperatures in air and fast quenching of the reactants. It was shown that

within experimental scatter, by increasing the temperature and addition of CaF2,

FeOx, MnOx, TiO2, ilmenite and SiO 2 to the slag, the solubility of lime (about 60

wt%) remained almost constant.

5.3 Diffusivity of MgO / CaO in slags

The diffusivity of the studied solid oxides in the slags was quantified using the

dimensionless mass transfer correlations for rotating disk/cylinder in the melt.

The diffusivity values deduced using the data on dissolution rate and solubility,

of solid oxides in the slag. As the developed correlations for calculation of

diffusivity depend on the density and viscosity of slag, these quantities have been

estimated by Urbain’s model for viscosity and Mills model for density of melt.

The diffusivity of MgO in the calcium aluminate slag at 1430ºC was found to be

51045.1 −× cm2/s and addition of 5 and 10 wt% FeOx increased the diffusivity by

a factor ~ 2 to 3, respectively. However, with (CaF2 5 wt% + Fe2O3 5 wt%) and

(CaF2 5 wt% + Fe2O3 10 wt%) in the slag, the diffusivity was increased

considerably by a factor of about 14 and 20, respectively.

The diffusivity of CaO in calcium aluminosilicate was measured at a temperature

range of 1430 – 1600 ºC. The diffusivity was increased by temperature and

additives in the slag. At 1430ºC, the diffusivity was found to be 6102.9 −× cm2/s

251

and by increasing the temperature to 1600 ºC, the diffusivity was increased to

5107.3 −× cm2/s. Addition of CaF2 had the strongest effect and increased the

diffusivity by a factor of 3 to 5 in the temperature range of 1500 to 1600 ºC.

MnOx and FeOx had a comparable effect in increasing the diffusivity by a factor

of 2~4. Ilmenite and TiO 2 also increased the diffusivity by a factor of about 2.

However, addition of SiO 2 to the slag decreased the lime diffusivity. The

influence of additives in the lime diffusivity was expressed according to the

effect of various cations on the bonding environment of the silicate anions and

their movement in the melt. Therefore, the strength between the interaction of

cations and oxygen (from the anions) determines how freely the anions can move

in the melt, which affects the diffusion of other species like Ca2+ in the melt.

The effect of temperature on the diffusivity of lime in the base slag and slags

with additives were examined by calculation of activation energy of diffusion.

The activation energy for diffusion of calcium in the base slag was about 43

kcal/mole. Addition of SiO 2 to the melt increased the activation energy to about

80 kcal/mole; however, other additives in the slag decreased the activation

energy, with FeOx and CaF2 and MnOx had the strongest effects. This trend

confirmed the mechanism of diffusion as the energy barrier for diffusion in the

melt is the movement of silicate anions and any change in the activation energy

is an indication of bonding environment between the cations and silicate anions.

The validity of Eyring theory, where the rate-determining step in the diffusing

species is the movement of large species in the melt, has been investigated for all

slags at various temperatures. It was shown that in master slag and the slag with

252

added silica, the Eyring’s correlation is valid (plot of

Ln(Diffusivity/Temperature) versus. Ln (viscosity) having slope of –1), but when

CaF2 and other oxides are added to the slag, the correlation between diffusivity

and viscosity deviated from Eyring. These data showed the effect of additives on

the interaction between cations and oxygen in the silicate anions.

The ionic conductivity of slag was estimated using Nerst-Einstein correlation.

The changes in the ionic conductivity with temperature and additives follow the

same trend as diffusivity, confirming that the same mechanism controls two

quantities.

5.4 Recommendations for future work

The above findings show that although CaF2 had the strongest effect on the

dissolution rate and diffusivity of lime in the slag but MnOx, FeOx and ilmenite

in the slag increased the dissolution rate and diffusivity considerably. As these

candidates should not cause emission of toxic species to the environment; thus

the industry can consider these candidates as a substitute to fluorspar.

The present work recommends to steelmaking industry to reduce/eliminate the

use of fluorspar, applying alternative additives such as MnOx, FeOx and ilmenite.

It is also recommended to investigate the replacement ratio of ilmenite for the

ladle type slag.

In the present work, the diffusivity of lime in the ladle type slag was investigated

at various temperatures and with addition of additives. At 1430 ºC a solid phase

253

was formed as a coherent layer on the lime/slag interface. A mix-controlled

model was developed which confirmed the existence of this layer. However, the

effect of basicity on the diffusivity of lime in the slag was not studied. It was

shown that when lime was reacted with slag of lower basicity, two non-coherent

phases formed on the lime/slag interface where the diffusion in liquid and solid

was not clear. An experimental technique is desirable to measure the diffusivity

of lime in the slag systems with lower basicity.

Given diffusivity measurement is more difficult than electrical conductivity and

we already have good models of electrical conductivity, the linkage between

conductivity and diffusivity allows us to extend the application of conductivity

models to diffusivity.

254

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263

APPENDIX A. Solid oxides dissolution data

A.1 The effect of rotation speed on dissolution of CaO in calcium aluminosilicate slag at 1430 ºC

The effect of variation of rotation speed on the concentration of lime in the slag

with time is presented in this section. The experimental data analysed by XRF

along with fitted curve are presented in Figure A. 1 to Figure A. 4 and Table A. 1

to Table A. 4. There is an error of ± 0.2-0.3 wt% (absolute) from the XRF

analysis.

The Curve Fitting Toolbox in MATLAB uses the method of least squares when

fitting data. The fitting process requires a model that relates the response data to

the predictor data with one or more coefficients. The result of the fitting process

is an estimate of the “true” but unknown coefficients of the model. The

concentration versus time data for the first 10 minutes of experiment is given to

the Curve Fitting Toolbox, then the linear least squares method is applied to fit a

linear model to data.

264

Figure A. 1: Concentration of CaO dissolved in slag at 30 rpm and at 1430°C

Table A. 1: XRF analysis of the bulk slag when lime dissolves in slag in air at 30 rpm and 1430°C


0 8.03 41.9 0.315 0.09 48.5 49.605 7.90 41.9 0.211 0.08 49.2 50.2110 7.92 42.2 0.157 0.07 49.2 50.2715 7.81 41.6 0.293 0.06 48.7 49.7820 7.89 42.2 0.126 0.06 49.1 50.1625 7.87 41.8 0.203 0.05 49.6 50.6730 7.87 42.0 0.137 0.07 49.4 50.4535 7.84 41.7 0.137 0.06 49.3 50.3240 7.8 41.7 0.1 0.08 49.5 50.5045 7.84 41.7 0.131 0.08 49.6 50.6950 7.8 41.7 0.1 0.09 49.6 50.6255 7.79 41.6 0.133 0.09 49.5 50.5660 7.78 41.5 0.136 0.10 49.9 50.99

Reactiontime (min)


265




0 7.98 42.1 0.240 0.07 48.9 48.905 7.90 42.1 0.171 0.06 48.9 49.0610 7.95 42.2 0.143 0.06 49.2 49.1915 7.89 42.1 0.186 0.07 49.3 49.3120 7.82 41.6 0.160 0.07 49.4 49.4125 7.83 41.8 0.132 0.08 49.5 49.5030 7.85 42.0 0.133 0.08 49.6 49.5835 7.82 41.8 0.173 0.08 49.6 49.6540 7.82 41.5 0.168 0.08 49.6 49.7145 7.79 41.4 0.129 0.10 49.7 49.7750 7.77 41.3 0.156 0.10 49.8 49.8255 7.77 41.3 0.120 0.10 49.9 49.8760 7.71 41.2 0.130 0.12 49.9 49.91

Reactiontime (min)


266




0 8.06 42.0 0.310 0.09 49.8 49.835 7.91 41.9 0.178 0.08 50.5 50.3110 7.83 41.7 0.200 0.09 51.0 50.6515 7.83 41.6 0.152 0.10 51.1 50.9120 7.74 41.3 0.143 0.11 51.0 51.1125 7.77 41.3 0.152 0.12 51.3 51.2730 7.74 41.0 0.136 0.11 51.4 51.4035 7.74 41.1 0.121 0.10 51.6 51.5140 7.71 40.8 0.126 0.13 51.4 51.6045 7.80 41.2 0.149 0.14 51.6 51.6850 7.72 40.8 0.187 0.13 51.8 51.7555 7.70 40.6 0.128 0.14 51.7 51.8160 7.69 40.7 0.130 0.15 51.9 51.86

Reactiontime (min)


267




0 7.91 42.8 0.231 0.02 50.2 50.192 7.68 42.1 0.155 0.03 50.4 50.404 7.75 42.3 0.152 0.02 50.5 50.556 7.65 41.9 0.168 0.01 50.5 50.678 7.63 41.7 0.152 < DL 50.7 50.7610 7.66 42.0 0.143 0.04 51.0 50.8420 7.62 41.7 0.135 0.04 50.1 51.1430 7.57 41.3 0.132 0.05 51.2 51.3540 7.55 41.2 0.139 0.07 51.5 51.5350 7.53 41.2 0.129 0.08 51.8 51.6960 7.50 40.9 0.142 0.09 51.8 51.85

Reactiontime (min)


268

Figure A. 5: Concentration of CaO dissolved in slag at 150 rpm and in air at 1430°C



0 7.95 42.6 0.314 0.02 50.0 50.002 7.81 42.5 0.201 0.01 50.4 50.374 7.90 43.0 0.178 0.02 50.5 50.556 7.78 42.8 0.156 0.01 50.3 50.678 7.84 42.9 0.170 0.01 50.8 50.7710 7.83 43.0 0.167 0.03 51.1 50.8420 7.68 42.0 0.157 0.04 50.9 51.1530 7.58 41.4 0.172 0.05 51.3 51.4040 7.69 41.6 0.172 0.07 51.7 51.6450 7.61 41.5 0.156 0.07 52.0 51.8760 7.55 41.0 0.154 0.10 52.0 52.10


Reactiontime (min)

269

A.2 Effect of CaF2 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures

The effect of 5 wt% addition of CaF2 on the variation of concentration of lime in

the slag with time is presented in this section. The experimental data obtained by

XRF along with the fitted curve are presented in Figure A. 6 to Figure A. 9 and

Table A. 6 to Table A. 9. There is an error of ±0.2 – 0.3 wt% (absolute) from the

XRF analysis. The dissolution rate was obtained from the slope of the dissolution

curves, by fitting a straight line through the initial experimental concentration

data using MATLAB.

270

Figure A. 6: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1430°C

Table A. 6: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% CaF2 in air at 90 rpm and 1430°C

SiO2 Al2O3 MgO CaF2 CaO

0.00 8.09 39.8 0.05 4.82 47.8 47.78

1.33 7.76 38.0 0.06 4.13 50.7 50.86

2.67 7.27 37.1 0.22 4.23 52.1 51.92

4.00 7.07 36.8 0.30 4.33 52.3 52.46

5.33 6.91 36.4 0.49 4.31 53.0 52.77

6.67 6.94 36.1 0.33 4.45 52.9 52.97

8.00 7.05 36.2 0.33 4.56 53.0 53.11

9.33 6.97 35.7 0.36 4.45 53.4 53.20

10.66 7.16 36.1 0.31 4.97 52.6 53.27

20 6.85 35.2 0.36 4.50 53.5 53.43

XRF analysis of bulk slag (wt%)Reactiontime (min)

CaO from curve fitting

271

Figure A. 7: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1500 °C

Table A. 7: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% CaF2 in air at 90 rpm and 1500 °C


0.00 7.92 40.3 0.04 5.15 47.4 47.49

1.33 7.70 39.7 0.07 4.74 48.2 48.06

2.67 7.64 39.7 0.08 5.15 48.4 48.45

4.00 7.64 39.5 0.08 4.82 48.8 48.74

5.33 7.63 39.5 0.09 5.01 48.9 48.97

6.67 7.54 39.1 0.10 4.89 49.1 49.15

8.00 7.56 39.3 0.11 5.03 49.2 49.29

9.33 7.54 39.3 0.11 4.84 49.3 49.42

10.66 7.49 39.2 0.13 4.80 49.7 49.52

20 7.41 38.2 0.18 4.54 50.1 49.99

30 7.40 38.3 0.21 5.09 50.2 50.24

Reactiontime (min)


272

Figure A. 8: Concentration of CaO dissolved in slag with 5 wt% CaF2 at 90 rpm and in air at 1550 °C



0.00 7.97 40.3 0.06 5.07 47.4 47.451.33 7.81 39.6 0.04 4.99 48.1 48.102.67 7.70 39.7 0.07 4.72 48.6 48.534.00 7.58 39.4 0.04 5.23 48.4 48.825.33 7.46 38.8 0.13 4.91 48.9 49.036.67 7.57 39.1 0.13 4.84 49.2 49.188.00 7.56 39.0 0.11 4.91 49.2 49.309.33 7.52 39.0 0.13 4.95 49.2 49.40

10.66 7.54 38.9 0.11 4.91 49.2 49.4720 7.50 38.9 0.12 4.80 49.7 49.69

Reactiontime (min)


273

Figure A. 9: Concentration of CaO dissolved in slag with 5 wt% CaF2at 90 rpm and in air at 1600 °C for 1 hour



0.00 7.83 40.4 0.05 4.58 47.5 47.451.33 7.74 40.2 0.02 4.52 48.1 48.132.67 7.67 40.0 0.06 4.43 48.8 48.634.00 7.74 40.0 0.04 4.82 48.3 49.005.33 7.70 40.0 0.07 4.52 48.9 49.306.67 7.57 39.5 0.10 4.50 49.2 49.538.00 7.52 39.2 0.11 4.08 49.7 49.719.33 7.46 38.8 0.13 4.25 49.9 49.8610.66 7.47 38.8 0.13 4.25 49.9 49.99

20 7.39 38.5 0.19 4.35 50.4 50.42

Reactiontime (min)


274

A.3 Effect of Fe2O3 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures

The effect of 5 wt% addition of Fe2O3 on the variation of concentration of lime

in the slag with time is presented in this section. The experimental data analysed

by XRF along with the fitted curve are presented in Figure A. 10 to Figure A. 13

and Table A. 10 to Table A. 13. There is an error of ±0.2 – 0.3 wt% (absolute)

from the XRF analysis.

275

Figure A. 10: Concentration of CaO dissolved in slag with 5 wt% Fe2O390 rpm and in air at 1430°C for 1 hour

Table A. 10: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Fe2O3 in air at 90 rpm and 1430°C

SiO2 Al2O3 Fe2O3 MgO CaO0 7.52 40.3 5.09 0.03 47.3 47.202 7.43 40.3 5.01 0.06 47.9 47.904 7.37 40.2 5.00 0.04 48.2 48.246 7.39 40.0 5.00 0.04 48.5 48.478 7.30 39.8 4.91 0.06 48.3 48.63

10 7.34 40.0 4.98 0.06 48.8 48.7720 7.22 39.5 4.90 0.08 49.3 49.2930 7.21 39.0 4.86 0.12 49.8 49.7240 7.10 38.5 4.76 0.14 49.9 50.1250 7.10 38.4 4.77 0.17 50.6 50.5060 7.03 38.0 4.72 0.18 50.9 50.88

Reactiontime (min)


276

Figure A. 11: Concentration of CaO dissolved in slag with 5 wt% Fe2O3at 90 rpm and in air at 1500 °C for 1 hour

Table A. 11: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Fe2O3 in air at 90 rpm and 1500 °C

SiO2 Al2O3 Fe2O3 MgO CaO0 7.66 40.4 5.81 0.05 46.8 46.832 7.60 40.1 5.14 0.03 48.0 47.864 7.40 39.8 5.04 0.10 47.1 48.396 7.40 39.6 4.95 0.14 48.3 48.728 7.31 39.2 4.88 0.14 49.2 48.96

10 7.39 39.7 4.93 0.11 48.8 49.1420 7.17 38.5 4.79 0.19 50.0 49.7230 7.21 38.5 4.99 0.15 49.9 50.1040 7.19 38.3 4.92 0.20 50.4 50.4250 7.15 38.1 4.71 0.22 50.6 50.7160 7.28 37.3 4.62 0.29 51.1 50.98

Reactiontime (min)


277




0 7.61 40.65 5.13 0.05 47.2 47.26

2 7.39 39.47 4.95 0.14 49.0 48.09

4 7.42 39.65 4.92 0.12 49.0 48.65

6 7.46 40.27 5.05 0.03 48.5 49.04

8 7.39 39.48 4.94 0.11 48.9 49.34

10 7.34 39.33 4.92 0.15 49.6 49.57

20 7.23 38.83 4.83 0.15 50.3 50.21

30 7.31 39.05 4.84 0.15 49.9 50.50

40 7.07 37.68 4.73 0.16 50.7 50.65

50 7.00 37.15 4.57 0.25 50.8 50.74

60 6.98 36.93 4.54 0.28 50.7 50.79

Reactiontime (min)


278




0 7.82 40.7 5.35 0.02 47.2 47.33

2 7.53 40.1 5.21 0.01 48.3 48.08

4 7.43 39.8 5.02 0.10 48.6 48.66

6 7.33 39.4 4.97 0.13 49.2 49.13

8 7.24 39.0 4.94 0.15 49.5 49.52

10 7.21 38.7 4.89 0.19 50.4 49.85

20 7.10 38.0 4.95 0.22 50.7 51.04

30 6.92 36.8 4.66 0.29 51.9 51.85

40 6.87 36.5 4.66 0.26 52.8 52.51

50 6.73 35.7 4.51 0.35 53.2 53.08

60 6.73 35.7 4.51 0.36 53.4 53.61

Reactiontime (min)


279

A.4 Effect of TiO2 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures

The effect of 5 wt% addition of TiO 2 on the variation of concentration of lime in

the slag with time is presented in this section. The experimental data analysed by

XRF along with the fitted curve are presented in Figure A. 14 to Figure A. 17



280

Figure A. 14: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1430°C for 1 hour

Table A. 14: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1430°C

SiO2 Al2O3 TiO2 MgO CaO

0 7.76 40.3 4.93 0.05 47.5 47.55

2 7.66 39.8 4.89 0.06 48.0 47.69

4 7.68 40.0 4.92 0.01 47.7 47.83

6 7.63 39.9 4.86 0.07 48.3 47.97

8 7.64 39.9 4.90 0.03 47.9 48.10

10 7.60 39.7 4.86 0.04 48.3 48.23

20 7.61 39.5 4.84 0.10 48.9 48.84

30 7.51 39.0 4.81 0.09 49.4 49.40

40 7.39 38.4 4.75 0.16 49.7 49.91

50 7.28 37.8 4.67 0.20 50.5 50.37

Reactiontime (min)


281

Figure A. 15: Concentration of CaO dissolved in slag with 5 wt% TiO2at 90 rpm and in air at 1500 °C for 1 hour

Table A. 15: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1500 °C


0 7.81 40.1 4.99 < DL 47.4 47.39

1.5 7.64 39.9 5.03 0.08 48.1 48.14

3 7.60 39.6 4.90 0.08 48.5 48.48

4.5 7.51 39.0 4.84 0.08 49.4 48.70

6 7.39 38.3 4.69 0.14 49.0 48.86

7.5 7.48 38.7 4.80 0.10 49.3 48.99

9 7.45 39.0 4.79 0.09 49.0 49.11

10.5 7.36 38.4 4.74 0.16 49.6 49.21

20 7.36 38.1 4.70 0.16 50.0 49.73

30 7.34 38.4 4.72 0.14 49.8 50.26

40 7.30 37.7 4.60 0.21 50.4 50.77

50 7.14 36.7 4.51 0.24 51.2 51.19

60 7.14 36.7 4.51 0.26 51.7 51.68

Reactiontime (min)


282

Figure A. 16: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1550 °C for 1 hour

Table A. 16: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1550 °C


0.0 7.81 40.2 4.97 0.02 47.7 47.941.5 7.68 39.8 4.92 0.06 48.4 48.23

3.0 7.65 39.5 4.89 0.07 48.7 48.504.5 7.57 39.2 4.83 0.03 48.5 48.74

6.0 7.55 39.1 4.88 0.08 48.7 48.977.5 7.52 39.1 4.80 0.12 49.2 49.18

9.0 7.47 38.9 4.82 0.13 49.3 49.3710.5 7.45 38.6 4.74 0.09 49.5 49.55

20.0 7.32 37.8 4.64 0.17 50.3 50.4130.0 7.27 37.4 4.64 0.20 51.2 51.10

40.0 7.13 36.9 4.57 0.21 51.6 51.57

50.0 7.11 36.5 4.46 0.26 51.9 51.8760.0 7.04 36.1 4.43 0.29 52.1 52.14

Reactiontime (min)


283

Figure A. 17: Concentration of CaO dissolved in slag with 5 wt% TiO2 at 90 rpm and in air at 1570°C for 1 hour

Table A. 17: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% TiO2 in air at 90 rpm and 1570°C


0 7.80 40.4 4.93 0.06 47.4 47.52

2 7.58 39.4 4.86 0.10 48.6 48.33

4 7.60 39.4 4.92 0.06 48.6 48.92

6 7.45 38.7 4.76 0.12 49.3 49.37

8 7.47 38.8 4.80 0.12 49.3 49.73

10 7.43 38.5 4.77 0.13 49.9 50.04

20 7.39 38.3 4.69 0.16 50.0 51.08

30 7.20 37.1 4.58 0.23 51.7 51.77

40 7.05 36.1 4.47 0.26 52.6 52.34

50 6.93 35.7 4.36 0.34 52.8 52.83

60 6.82 35.1 4.26 0.41 53.2 53.29

Reactiontime (min)


284

A.5 Effect of ilmenite addition on dissolution of CaO in calcium auminosilicate slag at various temperatures

The effect of 5 wt% addition of ilmenite on the variation of concentration of lime

in the slag versus time is presented in this section. The experimental data

analysed by XRF along with the fitted curve are presented in Figure A. 18 to

Figure A. 21 and Table A. 18 to Table A. 21. There is an error of ±0.2 – 0.3 wt%

(absolute) from the XRF analysis.

285

Figure A. 18: Concentration of CaO dissolved in slag with 5 wt% ilmenite at 90 rpm and in air at 1500 °C

Table A. 18: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% ilmenite in air at 90 rpm and 1500 °C

XRF analysis of bulk slag (wt%)Reactiontime (min) SiO2 Al2O3 Fe2O3 TiO2 MgO CaO


0 8.01 40.0 2.16 2.82 < DL 47.3 47.29

1.333 7.82 40.0 2.13 2.81 0.04 47.3 47.48

2.666 7.74 40.1 2.13 2.80 0.05 47.6 47.67

3.999 7.75 39.8 2.12 2.79 0.07 47.9 47.86

5.332 7.72 39.8 2.10 2.77 0.08 48.1 48.05

6.665 7.65 39.4 2.09 2.75 0.08 48.0 48.24

7.998 7.67 39.6 2.10 2.76 0.09 48.4 48.43

9.331 7.58 39.1 2.07 2.73 0.12 48.9 48.62

286





0 7.94 39.85 2.13 2.82 0.04 47.3 47.18

1.333 7.73 39.84 2.12 2.81 0.04 47.5 47.83

2.666 7.66 39.31 2.09 2.77 0.08 48.2 48.24

3.999 7.56 38.81 2.07 2.73 0.13 48.9 48.52

5.332 7.61 39.27 2.09 2.76 0.09 48.4 48.73

6.665 7.58 39.00 2.08 2.74 0.1 48.6 48.89

7.998 7.56 38.80 2.07 2.75 0.12 49.0 49.02

9.331 7.57 39.04 2.08 2.75 0.12 48.9 49.12

10.664 7.55 38.81 2.08 2.74 0.1 49.1 49.20

287

Figure A. 20:Concentration of CaO dissolved in slag with 5 wt% ilmenite at 90 rpm and in air at 1570°C

Table A. 20: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% ilmenite in air at 90 rpm and 1570°C



0 7.95 40.0 2.22 2.81 0.04 47.3 47.29

1.333 7.84 40.0 2.15 2.81 0.04 47.7 47.74

2.666 7.73 39.9 2.12 2.80 0.06 48.2 48.15

3.999 7.68 39.6 2.11 2.78 0.08 48.5 48.52

5.332 7.60 39.1 2.08 2.77 0.10 48.8 48.85

6.665 7.58 38.9 2.07 2.75 0.13 49.2 49.15

7.998 7.47 38.4 2.05 2.72 0.15 49.8 49.40

9.331 7.63 39.0 2.08 2.75 0.13 49.2 49.62

10.664 7.47 38.3 2.04 2.70 0.16 49.8 49.80

288





0 7.87 40.1 2.14 2.83 0.05 47.4 47.40

1.333 7.74 39.4 2.14 2.77 0.12 48.3 48.11

2.666 7.68 39.4 2.12 2.76 0.10 48.7 48.59

3.999 7.65 39.2 2.09 2.75 0.11 48.9 48.99

5.332 7.60 38.8 2.07 2.74 0.14 49.0 49.33

6.665 7.54 38.7 2.07 2.72 0.14 49.6 49.62

7.998 7.55 38.6 2.07 2.72 0.15 49.7 49.87

9.331 7.44 38.2 2.04 2.69 0.18 50.0 50.09

10.664 7.35 37.8 2.02 2.66 0.21 50.5 50.28

289

A.6 Effect of Mn3O4 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures

The effect of 5 wt% addition of Mn3O4 on the variation of concentration of lime

in the slag versus time is presented in this section. The experimental data




290

Figure A. 22: Concentration of CaO dissolved in slag with 5 wt% Mn3O4 at 90 rpm and in air at 1430°C

Table A. 22: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Mn3O4 in air at 90 rpm and 1430°C

SiO2 Al2O3 MgO Mn3O4 CaO

0.0 7.76 40.4 0.05 4.76 47.6 47.661.3 7.65 39.8 0.06 4.81 47.7 47.83

2.7 7.70 40.0 0.08 4.82 48.1 48.004.0 7.60 39.6 0.10 4.77 48.4 48.185.3 7.56 39.4 0.10 4.74 48.4 48.35

6.7 7.57 39.3 0.10 4.73 48.5 48.538.0 7.60 38.5 0.1 4.65 48.4 48.70

9.3 7.52 39.0 0.14 4.70 49.1 48.8810.7 7.46 38.7 0.16 4.64 49.0 49.05

Reactiontime (min)


291

Figure A. 23: Concentration of CaO dissolved in slag with 5 wt% Mn3O4 at 90 rpm and in air at 1500 °C

Table A. 23: XRF analysis of the bulk slag when lime dissolves in slag with addition of 5 wt% Mn3O4 in air at 90 rpm and 1500 °C


0.0 7.91 40.1 0.100 4.46 47.4 47.481.3 7.70 40.0 0.080 4.57 47.9 47.67

2.7 7.68 40.0 0.070 4.57 47.9 47.864.0 7.67 40.1 0.080 4.59 48.3 48.05

5.3 7.62 39.9 0.080 4.54 48.1 48.246.7 7.67 39.9 0.080 4.54 48.3 48.43

8.0 7.65 40.1 0.090 4.57 48.5 48.61

9.3 7.61 39.7 0.110 4.53 48.8 48.8010.7 7.50 39.1 0.130 4.44 49.2 48.99

Reactiontime (min)


292

Figure A. 24: Concentration of CaO dissolved in slag with 5 wt% Mn3O4 at 90 rpm and in air at 1550 °C



0.0 7.84 40.3 0.05 4.60 47.6 47.581.3 7.72 40.2 0.07 4.59 47.9 47.96

2.7 7.73 40.1 0.08 4.57 48.3 48.284.0 7.59 39.6 0.10 4.52 48.7 48.565.3 7.58 39.7 0.11 4.51 48.7 48.79

6.7 7.58 39.5 0.11 4.52 48.9 49.008.0 7.58 39.4 0.14 4.49 49.3 49.18

9.3 7.52 39.2 0.15 4.46 49.3 49.3410.7 7.52 39.1 0.14 4.45 49.5 49.48

Reactiontime (min)


293

Figure A. 25: Concentration of CaO dissolved in slag with 5 wt% Mn3O4at 90 rpm and in air at 1600 °C



0.0 7.93 40.3 0.05 4.62 47.6 47.711.3 7.63 39.6 0.10 4.56 48.5 48.35

2.7 7.66 39.8 0.12 4.56 49.0 48.794.0 7.57 38.4 0.14 4.40 48.3 49.115.3 7.59 39.2 0.14 4.47 49.2 49.36

6.7 7.51 38.9 0.13 4.45 49.2 49.568.0 7.53 38.8 0.15 4.44 49.7 49.72

9.3 7.47 38.8 0.17 4.47 49.9 49.8510.7 7.40 38.3 0.20 4.38 50.2 49.96

Reactiontime (min)


294

A.7 Effect of SiO2 addition on dissolution of CaO in calcium aluminosilicate slag at various temperatures

The effect of 5 wt% addition of SiO 2 on the variation of concentration of lime in

the slag with time is presented in this section. The experimental data analysed by

XRF along with the fitted curve are presented in Figure A. 26 to Figure A. 28



295

Figure A. 26: Concentration of CaO dissolved in slag with additional 5 wt% SiO2 at 90 rpm and in air at 1500 °C for 1 hour

Table A. 26: XRF analysis of the bulk slag when lime dissolves in slag with additional 5 wt% SiO2 in air at 90 rpm and 1500 °C

SiO2 Al2O3 MgO CaO

0 12.8 40.2 < DL 47.4 47.43

2 12.6 39.9 0.03 48.3 47.74

4 12.7 40.1 0.02 48.0 48.00

6 12.6 39.9 0.07 48.4 48.22

8 12.3 38.8 0.12 49.3 48.41

10 12.6 39.6 0.08 48.4 48.58

20 12.3 38.9 0.07 49.8 49.21

30 12.2 38.7 0.14 49.5 49.65

40 12.3 38.8 0.14 49.6 50.00

50 12.2 38.3 0.16 50.4 50.30

60 12.0 37.8 0.19 50.5 50.57

Reactiontime (min)


296



SiO2 Al2O3 MgO CaO

0 12.9 40.3 < DL 47.7 47.64

2 12.5 39.6 0.04 48.0 48.15

4 12.4 39.3 0.10 48.8 48.48

6 12.3 39.0 0.10 48.7 48.73

8 12.3 38.7 < DL 49.9 48.92

10 12.3 39.0 0.08 49.3 49.08

20 12.4 39.2 0.04 49.4 49.66

30 12.3 38.7 0.12 49.4 50.10

40 12.1 38.4 0.11 50.2 50.50

50 11.9 37.6 0.22 51.0 50.87

60 11.7 36.8 0.25 51.3 51.24

Reactiontime (min)


297



SiO2 Al2O3 MgO CaO

0 13.1 41.4 0.03 47.4 47.37

1.33 12.6 39.8 < DL 48.0 48.20

2.66 12.5 39.4 0.15 48.9 48.60

4 12.3 39.2 < DL 48.9 48.85

5.33 12.3 39.1 0.11 49.3 49.03

6.66 12.5 39.8 0.07 48.3 49.17

8 12.4 39.3 0.10 49.1 49.29

9.33 12.4 39.0 0.09 48.9 49.39

10.66 12.3 38.7 0.12 49.4 49.48

20 12.4 39.3 0.12 49.4 49.99

30 11.9 37.6 0.20 50.5 50.48

40 11.6 37.0 0.21 51.1 50.93

50 11.5 36.7 0.26 51.2 51.31

Reactiontime (min)


298

A.8 Effect of Fe2O3 addition on dissolution of MgO in calcium aluminate slag

The effect of 5 and 10 wt% addition of Fe2O3 on the variation of concentration of

magnesia in the slag with time is presented in this section. The experimental data




299

Figure A. 29: Concentration of MgO dissolved in slag with 5 wt% Fe2O3 at 90 rpm in air at 1430°C for 1 hour

Table A. 29: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 5 wt% Fe2O3 in air at 90 rpm and 1430°C

Al2O3 CaO Fe2O3 MgO

0 48.7 42.0 9.65 0.00

10 47.9 41.8 9.69 1.34

20 47.3 41.5 9.61 1.83

30 47.6 41.4 9.37 2.16

40 46.9 41.5 9.67 2.47

50 47.3 41.4 9.31 2.58

60 47.1 41.4 9.39 2.63

Reaction time (min)

XRF analysis of bulk slag (wt%)

300

Figure A. 30: Concentration of MgO dissolved in slag with 10 wt% Fe2O3 at 90 rpm in air at 1430°C for 1 hour

Table A. 30: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 10 wt% Fe2O3 in air at 90 rpm and 1430°C

Al2O3 CaO Fe2O3 MgO

0 50.7 40.2 5.43 0.00

10 50.3 39.9 5.14 1.54

20 49.9 39.5 5.26 2.35

30 50.0 39.3 4.96 2.78

40 50.0 39.4 5.06 3.12

50 49.7 39.1 5.02 3.26

60 49.8 38.9 5.00 3.41

Reaction time (min)


301

A.9 Effect of (CaF2 + Fe2O3) addition on dissolution of MgO in calcium aluminate slag

The effect of (5 wt%CaF2 + 5 wt% Fe2O3) and (5 wt%CaF2 + 10 wt% Fe2O3)

addition on the variation of concentration of magnesia in the slag with time is

presented in this section. The experimental data analysed by XRF along with the

fitted curve are presented in Figure A. 31 to Figure A. 32 and Table A. 31 to

Table A. 32. There is an error of ±0.2 – 0.3 wt% (absolute) from the XRF

analysis.

302

Figure A. 31: Concentration of MgO dissolved in slag with addition of 5% CaF2 &5% Fe2O3 at 90 rpm in air at 1430°C for 1 hour

Table A. 31: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 5% CaF2 & 5% Fe2O3 in air at 90 rpm and 1430°C for 1hour

Al2O3 CaO Fe2O3 CaF2 MgO

0 49.0 41.54 5.26 3.57 0.00

10 46.4 38.96 6.17 2.93 4.62

20 46.1 38.84 6.04 2.83 5.15

30 46.1 39.09 6.02 2.68 5.39

40 45.4 38.85 6.07 2.00 5.10

50 45.8 38.64 5.51 2.93 5.30

60 46.5 39.04 5.58 2.90 5.27

Reaction time (min)


303

Figure A. 32: Concentration of MgO dissolved in slag with addition of 5% CaF2 &10% Fe2O3 at 90 rpm in air and at 1430°C for 1 hour

Table A. 32: XRF analysis of the bulk slag when MgO dissolves in slag with addition of 5% CaF2 & 10% Fe2O3 in air and at 90 rpm and 1430°C

Al2O3 CaO Fe2O3 CaF2 MgO

0 45.83 38.98 9.92 3.68 0.00

10 44.36 37.70 10.01 3.36 3.20

20 44.05 37.37 9.96 3.39 4.19

30 43.98 37.19 9.66 3.40 4.64

40 43.78 37.23 9.60 3.37 4.88

50 43.67 37.23 9.36 3.35 4.89

60 43.72 37.29 9.33 3.25 5.07

Reaction time (min)


304

Appendix B. Model for estimating the slag viscosity

A model developed by Urbain, Cambier, Deletter and Anseau (1981) was used in

the present study for estimation of viscosity of slags. The model uses the Frenkel

equation, as given in Equation (B. 1), where A and B are viscosity parameters, T

is the thermodynamic temperature K, and η is in poise;

)exp(TBAT=η (B. 1)

This model is based on the behaviour of CaO – Al2O3 – SiO2 system and the

parameters A and B are calculated by dividing the slag constituents into three

categories:

Glass formers:

522 OPSiOG XXX +=

Modifiers:

22222223 ZrOTiOMnOFeOCaFOKONaMgOCaOM XXXXXXXXXX ++++++++=

Amphoterics:

323232 OBOFeOAlA XXXX ++=

305

In the present work, Fe2O3 has been classified as a modifier and in the computer

program for the calculation of viscosity, where 32

5.1 OFex has been added to MX

and deduced from AX . “Normalized” values *GX , *

MX , and *AX are obtained by

dividing the mole fractions, GX , MX , and AX by the term

)5.021(225.12 ZrOTiOFeOCaF XXXX ++++ . Urbain et al. (1981) proposed that the

parameter B was influenced both by the ratio )( **

*

AM

M

XXX+

=α and by *GX . The

parameter B can be expressed in the form of Equation (B. 2), where B1, B2, and

B3 can be obtained by Equation (B. 3).

3*3

2*2

*10 )()( GGG XBXBXBBB +++= (B. 2)

2ααα iiii cbB ++= (B. 3)

B0, B1, B2, B3 can be calculated from the equations listed in Table B. 1 and these

parameters are then introduced into Equation (B. 2) to calculate B.

Table B. 1: Equations for B-parameters in Urbain model for viscosity2

0 049.449355.398.13 αα −+=B2

1 9978.1391505.117481.30 αα +−=B2

2 04.3000486.2349429.40 αα −+−=B2

3 1616.2119276.1537619.60 αα +−=B

The parameter A can be calculated from B by Equation (B. 4) and the viscosity of

the slag (in poise) can then be determined using Equation (B. 5).

306

6725.112693.0 +=− BLnA (B. 4)

⎥⎦

⎤⎢⎣

⎡= )

10exp(

3

TB

ATη (B. 5)

This model has been used to calculate the viscosities of slags with widely

varying compositions and it has been found that it gives values, which agree well

with experimental data. According to Slag Atlas (Eisenhuttenleute (1995)), the

discrepancies between the experimental values and the predicted values are of

the order of 25 – 30%, which are similar to the experimental uncertainties for the

viscosity measurements.

307

APPENDIX C. Model for estimating the slag density

An additive method for the estimation of densities in alloys and slags has been

widely used for some time. In this method, the molar volume V , can be obtained

from Equations (C. 1) and (C. 2) below, where M , x , and V are the molecular

weight, mole fraction, and the partial molar volume, respectively, and the

subscripts 1, 2, and 3 denote the various oxide constituents of the slag.

...332211

ρxMxMxM

V++

= (C. 1)

...332211 +++= VxVxVxV (C. 2)

Partial molar volume is usually assumed to be equal to the molar volume of the

pure component 0V but it has been pointed out by Lee and Gaskell (1974) and

Grau and Masson (1976) that the density of slag is also related to the structure.

Slags containing SiO 2, Al2O3, and P2O5 consist of chains, rings, and complexes,

which are independent upon the amount and nature of the cations present

according to Slag Atlas (Eisenhuttenleute (1995)). Thus it is necessary to make

the partial molar volumes dependant upon composition for oxides of this type.

According to Mills et al. (1987), the values for 2SiOV have been derived using the

experimental density data for the systems, FeO – SiO2, CaO – SiO2, MnO – SiO2,

308

Na2O – SiO2, K2O – SiO2, and CaO – FeO – SiO2. From these experimental

values the relation 22 966.755.19 SiOSiO xV += (cm3.mol-1) was derived.

Values for 32OAlV were also determined by Mills et al. (1987), using

experimental density data for the systems; Al2O3 – CaO, Al2O3 – CaF2, Al2O3 –

SiO2, Al2O3 – CaO – MgO, and Al2O3 – MnO – SiO2. The relation

323232245.313231.28 OAlOAlOAl xxV −+= was derived. The recommended values

for V for the various oxides at 1500 ºC by the same authors are given in Table C.

1.

Table C. 1: Recommended values for partial molar volume V ofvarious slag constituents at 1500 ºC

Constituent V , cm3 mol-1Al2O3

3232

245.313231.28 OAlOAl xx −+CaF2 31.3CaO 20.7FeO 15.8

Fe2O3 38.4K2O 51.8MgO 16.1MnO 15.6Na2O 33P2O5 65.7SiO2

2966.755.19 SiOx+

TiO2 24

In order to provide a temperature coefficient, the temperature dependencies of

the molar volumes )/( dTdV of several slag systems were examined by Mills et

al. (1987) and a mean value of 0.01% K-1 was adopted.

309

The standard deviation of the data predicted by the model compare to the

experimental values( )

exp

exp

ρρρ −est was reported by Mills et al. (1987) to be

between 1 and 2%. The experimental uncertainties associated with density

measurements for slags is about %.32 −±

310

APPENDIX D. Error analysis

The errors on dissolution studies come from a number of sources, such as

uncertainties in XRF chemical analysis of dissolved solid oxide concentration in

the slag, fitting a linear curve through initial concentration data, slag weight and

the exact geometrical shape of samples in individual experiments.

In the estimation of errors and the way they propagate through calculations, three

general rules have been applied in the present work according to Taylor (1982)

as the followings:

Suppose that x,…, w are measured with uncertainties wx δδ ,..., and the measured

values used to compute is :

)...(... wuzxq ++−++= (D. 1)

If the uncertainties in x, …, w are known to be independent and random, then the

uncertainty in q is the quadratic sum as in Equation (D. 2):

2/12222 ])(...)()(...)[( wuzxq δδδδδ +++++= (D. 2)

If the same variables are measured, used to compute as :

311

wuzxq

××××=

......

(D. 3)

If the uncertainties in x, …, w are independent and random, then the fractional

uncertainty in q is the sum in quadrature of the original fractional uncertainties

as:

2/12222

......⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞⎜

⎝⎛++⎟

⎠⎞⎜

⎝⎛+⎟

⎠⎞⎜

⎝⎛++⎟

⎠⎞⎜

⎝⎛=

ww

uu

zz

xx

qq δδδδδ

(D. 4)

Also if x is measured with uncertainty of xδ and is used to calculate the power

nxq = (where n is a fixed, known number), then the fractional uncertainty in q

is:

xx

nqq δδ

= (D. 5)

To estimate the uncertainty of diffusivity measurements, the first step is to

estimate the error involved in calculation of initial rate of dissolution, which was

calculated from the slope of linear line fitted through the initial concentration

data, slag weight (w ) and immersed area ( A ) of the solid oxide sample in the

melt as in Equation (D. 6):

312

10060 ×××=

AwSlopeRate (D. 6)

The error involved is found out on the basis of Equation (D. 7) as:

AA

ww

slopeslope

raterate )()()()( δδδδ ++= (D. 7)

As the rate of dissolution was deduced from the slope of the linear line fitted

through the initial data on the concentration of solid oxides in the slag, a Curve

Fitting Toolbox in MATLAB software was used to perform the curve fitting. The

Curve Fitting Toolbox uses the linear least square method to fit a linear model to

data. The result of the fitting process is an estimate of the coefficients of a first-

degree polynomial mode. As these coefficients determine the slope of the fitted

line, the Toolbox also generates maximum and minimum prediction bounds for

each coefficient, thus the error involved can be calculated. Depending on various

experiments, the average uncertainty for the slope of fitted line slopeslope )(δ was

calculated to be 10%.

The initial interfacial reaction area in the lime/magnesia dissolution experiment

was well defined by the immersed area of solid oxide cylinder in the melt. It is

difficult to estimate the change in the shape and area of the solid oxide surface

during the rotation of lime sample in the melt but based on the observation of

dissolution data, it was concluded that the area of solid oxide sample does not

change radically during the first 10 minutes of reaction in the melt. This error is

313

calculated according to calculation of area of disk and cylinder immersed in the

melt as in Equation (D. 8):

rhrA ππ 22 += (D. 8)

Where r is the radius of the disk (cm) and h is the height (cm) of the immersed

sample. The error is found as:

hrrhrrA δπδπδπδ 222 ++= (D. 9)

The change in radius and height of the sample could be found on the basis of the

dissolution rate data. The change in weight of lime sample (dw) in the slag can be

calculated according to the volume change of the sample dv as in Equation (D.

10):

)2( 2dhrrhdrdvdw +×=×= πρρ (D. 10)

It is assumed here that the change in diameter (dr) and height (dh) are

approximately the same and it is called characteristic length, therefore when the

left side of the equation is divided by )2( 2rrh +π , it would be equivalent to the

rate of dissolution. As the average rate of dissolution is 4102 −× g/cm2.s for

various experiments, this value is divided by the density of slag (about 3 g/cm3)

to find out the changes of the characteristic length, which was calculated to be

5106 −× cm/s. By considering the changes of this length during 5 minutes of

rotation, the radius change dr is about 2102 −× cm. In the estimation of the error

314

involved in the hight of the immersed sample, it is also assumed that while the

sample is rotating, the melt could wet the sample within 1.0± cm of the assumed

height of immersion. This value is added to the characteristics length and results

in 0.12 cm error in the estimation immersion height dh . By inserting these

values into Equation (D. 9) and dividing it by total area of the sample, the error

from the calculation of immersed area in the melt is around 7 %.

The uncertainty of estimated slag weight during experiments is limited.

According to the concentration of solid oxide dissolved in the slag, the maximum

amount of lime dissolved in the slag during the first 10 minutes is about 1.2

grams. The mass of slag taken during sampling of the slag during 10 minutes, is

about 2.5 grams (7 times sampling, each 0.3~0.4 grams). The error due to

measurement of slag weight and loss of volatile component of slag at high

temperature is also included, where they totally result to 4 % error.

The estimation of error in calculation of rate of dissolution is found by inserting

the errors from the initial slope of dissolution curve, immersed area of the sample

and weight of molten slag into Equation (D. 7). The error is about 15%.

The next step is estimation of error from calculation of mass transfer coefficient.

This parameter was calculated from rate of dissolution, the driving force of the

solid oxide and density as in Equation (D. 11):

315

ρ×Δ×=

CrateK 100

(D. 11)

The error involved could be found as in Equation (D. 12):

ρδρδδδ +

Δ+=

CC

raterate

KK

(D. 12)

The error from the chemical analysis of the concentration of solid oxide in the

melt is about 0.2 grams. As the driving force between the original solid oxide

concentration is about 5-10%, then CCδ is about 2-4%. It is mentioned in the

literature that the error from the density calculation is about 2-3%. These errors

result in about 22% uncertainty in calculation of mass transfer coefficient.

In the calculation of diffusivity, the mass transfer coefficient calculated in

Equation (D. 11), was inserted in Equation (D. 13) in order to deduce the

diffusivity (D) in the right side of the Equation (D. 13):

Therefore, the error for diffusivity ddδ is calculated according to Equation (D.

14):

3/23/225.03/26/12/1 Re065.02

2621.02

VDhr

hDhr

rK −−−

++

+= ννω (D. 13)

316

)()(5.15.1

tcoefficientcoefficien

kk

dd δδδ += (D. 14)

Where the coefficient is defined as in Equation (D. 15):

In estimation of error;)()(

tcoefficientcoefficienδ , the random errors resulted from

hrr2+

andhr

h2

2+

are very small, also the rest of components, due to their magnitudes

have very small random errors, therefore the calculation of the error on

diffusivity data mainly depends on the error resulted from the mass transfer

coefficient in Equations (D. 12) and (D. 14). Thus the total error on diffusivity

calculations is about 33%.

Vhr

hhr

rtCoefficien 3/225.06/12/1 Re065.02

2621.02

−−−

++

+= ννω (D. 15)

317

Appendix E. Preliminary study of lime dissolution in static slag

Experiments were carried out to study static dissolution of CaO into a CaO – 45

wt% SiO2 – 10 %Al2O3 slag and effect of additives (10 wt%: Fluorspar,

Nepheline Syenite and ilmenite) on the dissolution of lime. The slag was packed

into dense CaO crucibles and heated to 1500 and1600 °C. After reaction period,

the crucible was air cooled and cross-sectioned. The formation of the Ca2SiO4

phase and concentration profiles of various cations across the reaction zone were

examined by Electron Probe Micro Analysis. At 1500 °C, a Ca2SiO4 layer was

found to form at the CaO/slag interface. No such layer was evident at 1600 °C,

however the formation of this layer was verified by conducting the experiments

with the same slag chemistry in platinum capsule. Ilmenite and nepheline syenite

were found to be effective in increasing CaO dissolution.

E.2 Experimental

Static dissolution of CaO into slag was studied by holding slag in a dense lime

crucible, varying holding reaction time, temperature and slag chemistry.

E.1.1 Materials

While acknowledging that in industry, the burnt lime is porous (more than 50 %

porosity for soft-burnt lime and about 25 % porosity for hard-burnt), it was

decided to manufacture and use a low porosity of 8.4 % lime to ensure a sharp

lime/slag boundary and consequently better control of experimental conditions,

318

under which the lime dissolution included two major processes, the chemical

reaction and CaO mass transfer in the slag phase.

Manufacturing of lime crucibles included the following operations. The

limestone powder with 50-70 microns average particle size was milled with

alumina balls, which resulted in 0.8-1 micron particles that were then calcined to

CaO and pressed in a mould and subsequently fired to provide the necessary

density and strength. This technique allowed a close control of bulk density and

apparent porosity by precisely varying compacting pressure, sintering

temperature, rate of heating and cooling and sintering time.

The experimental slags were prepared in a platinum crucible by melting a

mixture of slag components, quenching the melt and then re-melting to ensure

slags’ homogeneity. The master slag was a three component CaO-SiO2-Al2O3

system with 45 wt% CaO, 45 % SiO 2, and 10 % Al2O3. Flux additions were

made by adding 10 wt% of the chosen flux to the master slag. The flux

compositions used in the present work are presented in Table E. 1 and Table E. 2.

In the case of the CaF2 addition, subsequent analysis revealed that the CaF2

content of the resultant slag was only 5.7 wt% indicating a loss of fluorine. The

fluorine loss and oxidation of calcium of fluorspar was reported by Shimizu et al.

(1996).

E.1.2 Experimental Procedure

The dissolution of dense lime in molten slag was studied at 1500 and 1600 °C as

a function of time and slag composition. The concentration profiles of different

319

elements in the lime/slag interface were quantitatively measured by EPMA

mapping.

The CaO crucible was filled with slag and charged to the muffle furnace. A

sample was heated slowly at 100°C/hr up to 1250°C which is below the melting

point of slag studied in this work, in order to minimize the risk of thermal shock

in the crucible and then heated quickly at 600°C/hr up to 1500 or 1600 °C.

Reaction time was counted from the moment of reaching to 1500 or 1600 °C.

After the required reaction time, the crucible and slag were taken out of the

furnace and quickly quenched in air. The crucible was cut by a diamond saw

parallel to bottom of the crucible. The slice of the crucible with its contents was

mounted in resin.

Samples must be provided with a flat and well-polished surface, finished to (0-1)

micrometers for electron probe microanalysis (EPMA). Therefore, they were

polished initially with the Struers waterproof silicon carbide paper at consecutive

grits sizes of 320, 800 and 1200 μ using a Struers Labopol-5 grinding machine at

300 rpm. Since samples are very sensitive to moisture, Shell Macron oil was

used as the lubricating fluid. Diamond polishing of the specimen was done

initially with a Chemo-textile Cloth (Leco-PAN-W) using polycrystalline

diamond paste of 3 microns. The final mirror finish was obtained by using a Silk

type cloth (Kemet-MSF) with 1 micron polycrystalline diamond paste. A LECO

G25 Rotary Polisher was used for the final stage of polishing.

A CAMECA SX50 EPMA was used in quantitative analysis of the samples. It is

a fully automated instrument employing four wavelength dispersive

320

spectrometers in order to analyse various elements. These elements were

analysed with the TAP, PCO and PET crystals. All samples were examined using

an accelerating vo ltage of 15KV, a beam current of 20nA and a beam size of 1

micron. The instrument was operated with SAMx application software. X-ray

intensity distributions were acquired for the main constituents to produce

elemental analysis across the area of interest. A MATLAB script program was

developed to process the X-ray intensity distribution data. A JOEL 840 Scanning

Electron Microscope was used to obtain the backscattered electron images of

various phases in the samples operated at 20 KV.

Line scan analyses were carried out from the CaO region in the crucible into the

slag region. The step size for stage movement was 6 microns. Point analysis was

performed for each distinct phase identified using back-scattered electron mode.

The MATLAB program converted the concentration profile of each element in

the matrix to the mole percentage of various oxides and determined the phase

locations in the ternary phase diagram. The phase diagrams at different

temperatures were obtained from FactSage package developed by Bale et al.

(2003).

The elemental distribution in the slag adjacent to the slag/crucible layer was

mapped by 2-micron step size stage movement in an area of 512 by 512 microns

size and at a 256 by 256 image resolution. A MATLAB program was also

developed to analyse the results from mapping. This program incorporates a

Graphics User Interface media, which changes the concentration intensity of the

maps to the intensity images in order to illustrate the mole percentage of various

321

phases. The program also enabled the recognition of Ca2SiO4 and Ca3SiO5 phases

in the mapped area.

E.3 Experimental Results and Discussion

Electron Micrographs at 1500 °C (Figure E. 1) show formation of Ca2SiO4 layer,

which was also observed by Matsushima et al. (1977). However at 1600 °C

(Figure E. 2), no discrete layer of Ca2SiO4 was found. The appearance of

crystallites indicates that they were not present in the liquid phase but formed in

the process of crystallization. The Ca2SiO4 phase, identified by MATLAB

program on the basis of the EPMA analysis is shown in Figure E. 3 and Figure E.

4. Although a layer of Ca2SiO4 was not observed at 1600 oC, it does not mean

that it was not formed at this temperature.

Change in the slag chemical and phase composition in process of lime

dissolution at 1500 and 1600 oC is shown in the CaO-SiO2-Al2O3 phase diagrams

in Figure E. 5and Figure E. 6. After achieving 1500 oC (zero time), CaO

concentration in the slag increased from 45 wt% to 48 wt%, while at 1600 oC

(zero time) slag CaO content was 53 wt% and very close to the Ca2SiO4 line. At

1600 °C as reaction time increased to 30 and 60 minutes, change in slag CaO

content was small (54-55 wt%) indicating that dissolution of lime had slowed

dramatically. At this CaO content, the slag is saturated with di-calcium silicate,

however the proportion of the Ca2SiO4 phase is negligible.

At 1500 oC, CaO concentration increased to 52 wt% after 30-min reaction and

further to 54 wt% after 60 min. In the CaO-SiO2-Al2O3 phase diagram, these

322

compositions are within the liquid – Ca2SiO4 area (Figure E. 5) reflecting

microscopic observations of the Ca2SiO4 phase. Total content of CaO in the slag

was about the same at 1500 and 1600 °C after dissolution for 30 min (52-54

wt%) and 60 min (53-55 wt%). However, at 1600 °C all slag was presumably

liquid, while at 1500 °C, after reaction with lime crucible for 30 and 60 min, it

consisted of liquid phase and solid di-calcium silicate.

At 1500 °C, the growth rate of di-calcium layer was measured by line scan with

EPMA. The thickness of the layer is shown in Table E. 3. These measurement

shows that at time = 0, the Ca2SiO4 layer has already been formed with a

thickness of 164μm, so from the real time that the layer starts to form, the

dissolution of lime has been hindered. By increasing time to 30 minutes and one

hour, it seems that it is the Ca2SiO4 formed at the lime/slag interface which

dissolves and not the lime itself. Although, the experimental results show a net

growth of Ca2SiO4 layer but formation of layer seems greater than its dissolution.

At 1600 °C, we know that while heating from the melting point to 1600 °C, the

Ca2SiO4 was formed at 1500 °C with a thickness of 164μm. It takes 10 minutes

from 1500 to reach 1600 °C (heating ramp: 600°C/hour). It seems that during

this period of time, the net dissolution and formation of Ca2SiO4 left a layer,

which prevented the complete dissolution of lime. Since no Ca2SiO4 was

observed in the quenched samples, it is postulated that it was lost during

quenching/sample preparation, perhaps as a result of the large volume change

associated with the phase transformation of Ca2SiO4 at 860-780°C. This

behaviour has been observed by other researchers and is referred to as “dusting”.

323

The formation of the Ca2SiO4 layer was later verified by reacting a lime piece

and master slag in a platinum capsule and fast quenching in air. The result is

shown in Figure E. 7. It seems that the difference in the rate cooling in two

techniques would affect the stability and recovery of Ca2SiO4 layer.

On the other hand, the presence of the Ca2SiO4 layer in the experiments in the

lime crucibles is indicated by the fact that the amount of lime dissolved in the

slag at 1600 °C was not significantly higher than its corresponding values at

1500 °C and that dissolution stopped substantially at the Ca2SiO4 line at both

temperatures. The rate limiting stage could be diffusion of CaO through the

Ca2SiO4 layer. Future work may be defined to investigate further the formation

of Ca2SiO4 layer at 1500 –1600 °C with confocal scanning laser microscopy.

With the addition of the ilmenite and Nepheline Syenite fluxes to the slag, CaO

content of slag increased more rapidly with time (Table E. 4). Again no Ca2SiO4

layer was recovered in the experiments.

E.4 Key findings

The dissolution of dense lime in molten CaO-SiO2-Al2O3 slags was studied at

temperatures of 1500 and 1600 °C by reaction of slags with a static lime crucible.

The effects of different fluxing agents and time of reaction were investigated.

Ilmenite was the most effective flux and nepheline syenite was comparable to

fluorspar, increasing the lime dissolution. At 1500 °C a di-calcium silicate layer

was formed between the slag and CaO crucible and the growth rate was

measured. However at 1600 °C no di-calcium silicate layer was onberved. As the

324

formation of Ca2SiO4 layer was verified by a different experimental technique, it

would appear that at both temperatures rate of CaO dissolution is limited by the

formation of a Ca2SiO4 layer.

325

Figure E. 1: SEM of base slag at 1500 °C for time=0 with 1000 magnification.

Figure E. 2: SEM of base slag at 1600 °C for time=0 with 1000 magnification.

Phase: Ca2SiO4

50 100 150 200 250

50

100

150

200

250

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

phase: Ca2SiO4

50 100 150 200 250

50

100

150

200

250

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Figure E. 3: Identified Ca2SiO4phase by MATLAB program for base slag at 1500 °C for time=0 in a 512 by 512 microns area and 256 by 256 image resolution.

Figure E. 4: Identified Ca2SiO4phase by MATLAB program for base slag at 1600 °C for time=0 in a 512 by 512 microns area and 256 by 256 image resolution.

CaO

C2S

C2S

Slag

Slag

CaO

326

Figure E. 5: The composition of bulk slag at various reaction times in phase diagram for basic slag at 1500 °C

C2S: Ca2SiO4, C3S: Ca3SiO5, CA: Ca2Al2SiO7, C: CaO, L: Liquid Slag

327

Figure E. 6: The composition of bulk slag at various reaction times in phase diagram for basic slag at 1600 °C

C2S: Ca2SiO4, C3S: Ca3SiO5, C: CaO, L: Liquid Slag

328

Figure E. 7: Formation of Ca2SiO4 layer on reaction of lime with master slag at 1600 ºC in the platinum capsule

CaO

Ca2SiO4

Slag

329

Table E. 1: Chemical compositions of Nepheline Syenite

Oxides Wt%

SiO2 59.30

Al2O3 19.28

Fe2O3 2.25

CaO 0.91

MgO 0.09

Na2O 8.33

K2O 5.32

FeO 2.27

Table E. 2: Chemical compositions of ilmenite

Oxides Wt%

TiO2 55.3

Fe2O3 24.1

FeO 16

Al2O3 0.58

SiO2 0.93

MnO 1.48

P2O5 0.03

Cr2O3 0.045

330

Table E. 3: Growth of Ca2siO4 layer at 1500 °C

Temperature time = 0 time = 30 min. time =1 hr.1500 °C 164 μm 192 μm 321 μm

Table E. 4: Mass (grams) of CaO dissolved in the slags (per 100 grams of slag) at 1600 °C

Slags T=0 T=30 minutes T=1 hour

Master slag 17 19.5 19.9

Slag + CaF2 15 16 20

Slag + N.S 18.7 23.3 26.3

Slag + ilmenite 29.4 30.8 30

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