Thermodynamic Models and Databases for Molten Salts and Slags

Arthur PeltonCentre de Recherche en Calcul Thermochimique

École Polytechnique, Montréal, Canada

Model parameters obtained by simultaneous evaluation/optimization of thermodynamic and phase equilibrium data for 2-component and, if available, 3-component systems.

Model parameters stored in databases

Models used to predict properties of N-component salts and slags

When combined with databases for other phases (gas, metal, etc.) can be used to calculate complex multi-phase, multi-component equilibria using Gibbs energy minimization software.

Reciprocal molten salt system Li,K/F,Cl

Liquidus projection

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

0.2

0.20.

40.4

0.6

0.60.

80.8

LiF(848

o)

KF(857

o)

LiCl(610

o)

KCl(771

o)Mole fraction

50

0o

353o

492o

60

5o

345o

718o

478o

800

750

700650600

800750700

700 750

700

650

600

550

750700

650

600550

500

Section of the preceding phase diagramalong the LiF-KCl diagonal

A tendency to de-mixing (immiscibility) is evident. This is typical of reciprocal salt systems, many of which exhibit an actual

miscibility gap oriented along one diagonal.

Margheritis et alBerezina et al

771o

848o

718o

Gabcova et al

Liquid

LiF + KCl

LiF + Liquid

Mole fraction KCl

Tem

per

atu

re (

o C)

0 0.2 0.4 0.6 0.8 1.0650

700

750

800

850

900

Molecular Model

Random mixture of LiF, LiCl, KF and KCl molecules.

Exchange Reaction:LiCl + KF = LiF + KClGEXCHANGE < O

Therefore, along the LiF-KCl «stable diagonal», the model predicts an approximately ideal solution of mainly LiF and KCl molecules.

Poor agreement with the observed liquidus.

ln ln ln ln

o o o oLiCl LiCl LiF LiF KCl KCl KF KF

LiCl LiCl LiF LiF KCl KCl KF KF

E

G X G X G X G X G

RT X X X X X X X X

G

Random Ionic (Sublattice) Model

Random mixture of Li+ and K+ on cationic sublattice and of F- and Cl- on anionic sublattice.

Along the stable LiF-KCl diagonal, energetically unfavourable Li+- Cl- and K+- F- nearest-neighbour pairs are formed. This destabilizes the solution and results in a tedency to de-mixing (immiscibility) – that is, a tedency for the solution to separate into two phases: a LiF-rich liquid and a KCl-rich liquid.

This is qualitatively correct, but the model overestimates the tedency to de-mixing.

ln ln ln ln

o o o oLi Cl LiCl Li F LiF K Cl KCl K F KF

Li Li K K Cl Cl F F

E

G X X G X X G X X G X X G

RT X X X X RT X X X X

G

Ionic Sublattice Model with Short-Range-Ordering

Because Li+- F- and K+- Cl- nearest-neighbour are energetically favoured, the concentrations of these pairs in solution are greater than in a random mixture:

Number of Li+- F- pairs = (XLiXF + y)Number of K+- Cl- pairs = (XKXCl + y)

Number of Li+- Cl- pairs = (XLiXCl - y)Number of K+- F- pairs = (XKXF - y)

Exchange Reaction:LiCl + KF = LiF + KCl

This gives a much improved prediction.

expEXCHANGE

Li F K Cl

Li Cl K F

X X y X X y G

X X y X X y ZRT

For quantitative calculations we must also take account of deviations from ideality in the four binary solutions on the edges of the composition square.

For example, in the LiF-KF binary system, an excess Gibbs energy term , GE, arises because of second-nearest-neighbour interactions:

(Li-F-Li) + (K-F-K) = 2(Li-F-K)

(Generally, these GE terms are negative: .)

is modeled in the binary system by fitting binary data. In predicting the effect of within the reciprocal system, we must

calculate the probability of finding an (Li-F-K) second-nearest-neighbour configuration, taking account of the aformentioned clustering of Li+- F- and K+- Cl- pairs. Account should also be taken of second-nearest-neighbour short-range-ordering.

ELiF KFG

0ELiF KFG

ELiF KFG

ELiF KFG

Liquidus projection calculated from the quasichemical model in the quadruplet approximation (P. Chartrand and A. Pelton)

0.2

0.2

0.4

0.4

0.6

0.6

0.8

0.8

0.2

0.20.

40.4

0.6

0.60.

80.8

LiF(848

o)

KF(857

o)

LiCl(610

o)

KCl(771

o)Mole fraction

50

0o

353o

492o

60

5o

345o

718o

478o

800

750

700650600

800750700

700 750

700

650

600

550

750700

650

600550

500

Experimental (S.I. Berezina, A.G. Bergman and E.L. Bakumskaya) liquidus projection of the Li,K/F,Cl system

Phase diagram section along the LiF-KCl diagonal

The predictions are made solely from the GE expressions for the 4 binary

edge systems and from GEXCHANGE. No adjustable ternary model parameters

are used.

Margheritis et alBerezina et al

771o

848o

718o

Gabcova et al

Liquid

LiF + KCl

LiF + Liquid

Mole fraction KCl

Tem

per

atu

re (

o C)

0 0.2 0.4 0.6 0.8 1.0650

700

750

800

850

900

SILICATE SLAGS

The basic region (outlined in red) is similar to a reciprocal salt system, with Ca2+ and Mg2+ cations and, to a first approximation, O2- and (SiO4)4- anions.

The CaO-MgO-SiO2 phase diagram.

Exchange Reaction:

Mg2(SiO4) + 2 CaO = Ca2(SiO4) + 2 MgO

GEXCHANGE < O

Therefore there is a tedency to immiscibility along the MgO-Ca2(SiO4) join as is evident from the widely-spaced isotherms.

Associate Models Model the MgO-SiO2 binary liquid assuming MgO, SiO2 and Mg2SiO4

«molecules»

2 4

2

2 2 4

2

2 ;

exp

o

oMg SiO

MgO SiO

MgO SiO Mg SiO G

X GK

X X RT

With the model parameter G°< 0, one can reproduce the Gibbs energy of the binary liquid reasonably well:

Gibbs energy of liquid MgO-SiO2 solutions

Mole fraction SiO2

G(k

ilo

jou

les

/mo

l)

0 0.2 0.4 0.6 0.8 1.0-40

-30

-20

-10

0

The CaO-SiO2 binary is modeled similarly.

Since GEXCHANGE < 0, the solution along the MgO-Ca2SiO4 join is modeled as consisting mainly of MgO and Ca2SiO4 «molecules».

Hence the tendency to immiscibility is not predicted.

Reciprocal Ionic Liquid Model

(M. Hillert, B. Jansson, B. Sundman, J. Agren)

Ca2+ and Mg2+ randomly distributed on cationic sublattice

O2-, (SiO4)4- and neutral SiO2 species randomly distributed on anionic sublattice

An equilibrium is established:

(Very similar to: O0 + O2- = 2 O-)

In basic melts mainly Ca2+, Mg2+, O2-, (SiO4)4- randomly distributed on two sublattices.

Therefore the tendency to immiscibility is predicted but is overestimated because short-range-ordering is neglected.

0 2 42 4

0

2

0

SiO O SiO

G

The effect of a limited degree of short-range-ordering can be approximated by adding ternary parameters such as:

Very acid solutions of MO in SiO2 are modeled as

mixtures of (SiO2)0 and (SiO4)4-

Model has been used with success to develop a large database for multicomponent slags.

4 4, : ,Ca Mg O SiO Ca Mg O SiOX X X X L

Modified Quasichemical Model

A. Pelton and M. Blander «Quasichemical» reaction among second-nearest-neighbour pairs:

(Mg-Mg)pair + (Si-Si)pair = 2(Mg-Si)pair

G° < 0

(Very similar to: O0 + O2- = 2 O-)

In basic melts:– Mainly (Mg-Mg) and (Mg-Si) pairs (because G° < 0).

– That is, most Si atoms have only Mg ions in their second coordination shell.

– This configuration is equivalent to (SiO4)4- anions.

– In very basic (MgO-SiO2) melts, the model is essentially equivalent to a

sublattice model of Mg2+, Ca2+, O2-, (SiO4)4- ions.

However, for the «quasichemical exchange reaction»:

(Ca-Ca) + (Mg-Si) = (Mg-Mg) + (Ca-Si)

GEXCHANGE < 0

Hence, clustering (short-range-ordering) of Ca2+-(SiO4)4-

and Mg2+-O2- pairs is taken into account by the model without the requirement of ternary parameters.

At higher SiO2 contents, more (Si-Si) pairs are formed, thereby modeling polymerization.

Model has been used to develop a large database for multicomponent systems.

The Cell Model

M.L. Kapoor, G.M. Frohberg, H. Gaye and J. Welfringer

Slag considered to consist of «cells» which mix essentially ideally, with equilibria among the cells:

[Mg-O-Mg] + [Si-O-Si] = 2 [Mg-O-Si]

G° < 0

Quite similar to Modified Quasichemical Model Accounts for ionic nature of slags and short-range-

ordering. Has been applied with success to develop databases for

multicomponent systems.

Liquidus projection of the CaO-MgO-SiO2-Al2O3 system at 15 wt % Al2O3, calculated from the Modified Quasichemical Model

(SiO2)

weight fraction

1600

1500

1500

1400

1400

1350

weight fractionweight fractionweight fraction

1300

weight fractionweight fractionweight fractionweight fractionweight fractionweight fraction

1250

1300

weight fraction

1270

weight fractionweight fractionweight fractionweight fraction

CaSiO3

Anor

1300

weight fractionweight fractionweight fractionweight fractionweight fractionweight fraction

1550

weight fraction

1600

MeliliteSpinel

Olivine

Ca2SiO4

Clino-py

Clino-py

1253 1253

1254

1264

1259

weight fractionweight fractionweight fractionweight fractionweight fraction

1300

1450

1600

1600

1330

1262

1265

weight fractionweight fraction

1800

weight fractionweight fractionweight fraction

2200

weight fraction

2400

weight fraction

2600

MgO(Mono)

CaO(mono)

1490

1440

1235

Cristo

16451676

1444

1275

1272

1256

1465

1536

Tridy

1662

1560Mull

1465

(CaO) (MgO)

2000

1500

5

10

15

20

25

30

35

40

45

50

55

60

65

70

75

80

80 75 70 65 60 55 50 45 40 35 30 25 20 15 10 5

80

75

70

65

60

55

50

45

40

35

30

25

20

15

10

5

Liquidus projection of the CaO-MgO-SiO2-Al2O3 system at 15 wt % Al2O3, as reported by E. Osborn, R.C. DeVries, K.H. Gee and H.M. Kramer