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Thermodynamicestimationof liquidussolidus Ae3temperaturesand phasecompositions forlovv alloymuIticomponentsteels

A A B SugdenH K D H Bhadeshia

Introduction

In an attempt to develop improved models for the prediction of microstructures insteel weld deposits established thermodynamic procedures have been used toestimate the liquidus solidus and Ae3 transformation temperatures formulticomponent steels together with partitioning coefficients and otherparameters The method has been tested against a large amount of published dataand there is found to be good agreement between experiment and theory

MSTj975

copy 1989 The 1nstitute of Metals Manuscript received 25 August 1988 infinalform14 February 1989 The authors are in the Department of Materials Science andMetallurgy University of Cambridge

where the amount of experimental data available as averification of theory is much greater

The majority of steel weld deposits solidify under highlynon-equilibrium cooling conditions A consequence of thisis the chemical segregation of substitutional alloyingelements during solidification a segregation that persists asthe weld cools to ambient temperature Solidificationinduced segregation of interstitials is usually not a problembecause of the ease with which they can diffuse andhomogenise during cooling The presence of substitutionalelement segregation can greatly influence the subsequenttransformation of austenite into ferrite with reactionkinetics in general being accelerated in the solute depletedregions The formation of ferrite in these regions causes aredistribution of carbon into the remaining austenite thehardenability of which is therefore increased It has beendemonstrated 1 that such effects can have a major influenceon the development of microstructure and any method foralloy design must take them into proper consideration

Weld metals typically solidify as b-ferrite and sub-sequently transform to austenite y and then to ferrite a Toobtain a general model for the prediction of the propertiesof a weld metal it will be necessary to be able to predict thechemical segregation behaviour during solidification Forlow alloy C-Mn steel weld deposits solidifying as b-ferritesolute enriched prior b-boundaries will finish up approx-imately within the centre of the austenite grains The effectof the segregation will be to increase the temperature atwhich allotriomorphic ferrite initially transforms and toincrease the temperature range over which a forms Hencethe ultimate volume fraction for a given set of coolingconditions will increase2 Conversely for solidification asaustenite since regions in the proximity of the austeniteboundaries would be solute enriched nucleation of a wouldbe expected to be more difficult1 To predict weld metalsegregation quantitatively will necessarily require a know-ledge of the solidification temperature solidification rangelevel of partitioning in the melt and partition coefficientsfor the carbon and solute elements in the steel The presentwork is an attempt at modelling the high temperatureregion of the phase diagram for multicomponent steelsusing the general thermodynamic procedures developed byKirkaldy and co-workers 34 To verify the consistency ofthe present calculations and of the thermodynamic dataused calculations were alsomiddotattempted for the ay equilibria

Method of analysis

One of the most important factors which must beconsidered in thermodynamic modelling of the Fe-C-Xmulticomponent system is that it ceases to retain thecharacteristics of infinite dilution for concentrations above~ 02 wt-C (Refs 5 6) In the analysis of Kirkaldy andBaganis3 which is used in the present work this problem iscircumvented by determining the temperature deviation ofa particular phase boundary from the correspondingboundary in the binary Fe-C system The change in carbonconcentration at a phase boundary due to the addition ofsubstitutional alloying elements is given by summing theeffects due to each individual element

In the following description iron is designated as 0carbon as 1 and the alloying elements Si Mn Ni Cr MoCu V Nb Co W as i( = 2-n) The mole fractions in eachphase are designated as Xi (i = O-n) A general temperaturecoordinate on a phase boundary in the pure Fe-C system isdesignated J The temperature deviation from J due tothis addition of substitutional elements ~ T is calculated forthe required range of 4 so that the phase boundaryTFe-C-Xi may be found This procedure follows theclassical depression of the freezing point relationshipderived by Vant Hoff (see Ref 5) In multicomponentalloys these temperature changes resulting from individualalloy additions are additive as long as solute-solute inter-actions are negligible The interactions between elements insolution are represented by empirical coefficients known asthe Wagner interaction parameters and the above assump-tion of additive ~ T values is the same as saying that theinteraction between elements i and k Gik(i=1=k i and k gt 1)= O In fact this is not strictly correct 7 and silicon especi-ally can interact with other solute elements8 HoweverKirkaldy and co-workers34 found that this assumption isvalid as long as the total alloying element content is lessthan ~ 6 wt- and the silicon content is lt 1 wt-

To calculate the temperature deviation at a phaseboundary ~ T Kirkaldy and Baganis3 started with therelationship for the equality of the chemical potentials in

Materials Science and Technology October 1989 Vol 5 977

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978 Sugden and Bhadeshia Liquidus solidus Ae3 temperatures and phase compositions for low alloy steels

Location of the octahedral interstices () in bcccrystal (After Ref 16)

the two phases which are in equilibrium For example forthe austenite and liquidliquid phase boundary for iron

Prediction of Ae3 temperature

The overall intention of this and other current research is tobe able to predict the mechanical properties of multipasswelds This requires a detailed knowledge of the thermalhistory of the weld and necessarily of the transformationtemperatures of the steels In welding the Ae3 temperaturehas a considerable influence on inter alia the relativevolume fractions of the phases present in the as weldedmicrostructure and the size of the reaustenitised region inmultipass welds Therefore as an initial step a programwas written to allow the Ae3 temperature to be predictedusing the method described above A series of modificationswas incorporated into it as follows

1 The program had been used forMn Si Ni Cr Moand Cu additions3 In addition the elements for Nb Co Vand W were included using further data given by Kirkaldyet ai4

2 The Ae3 values for J were formulated into a sub-routine using accurate values derived from equationsfrom Bhadeshia and Edmonds10 giving values of J downto 200degC Extrapolating the Ae3 in this manner would bepotentially very useful allowing for example growth ratekinetics to be calculated at temperatures well below theeutectoid temperature 11

3 Although data were provided 12 for values for thestandard Gibbs free energy change accompanying the rtytransformation in pure iron L degGo-+ Y since a longterm aimwas to extrapolate the Ae3 to lower temperatures the datafrom Kaufman et ai13 which give values down to 0 K andwhich are known to be reliable over an entire temperaturerange of interest14 were used The function L degGo-+ Y wasrepresented by curve fitting values from Table 3 ofKaufman et ai13 and later corrected values forL degGo-+Y(T gt 1183 K) from Kaufman and Bernstein1s

4 Values for L degHo -+ Y were obtained from work carriedout by Kaufman et ai13

In applying equation (3) to the calculation of the Ae3

Kirkaldy and Baganis3 had taken e~ 1 as zero Theyargued that the error introduced is negligible since theinteraction parameter is multiplied only by the very lowconcentration of carbon in ferrite This assumption canbe assessed quantitatively Figure 1 shows the carbon sub-lattice in a crystal of (X-FeThe bcc unit cell contains twoiron atoms and six carbon sites (This ignores tetrahedralsites but the probability of their occupation is ratherlow) The maximum solubility of carbon inb-Fe is 0middot09 wt- = 0middot417 at- Therefore there are(9960417) = 239 iron atoms for every carbon atom orthere is one carbon atom for every 119 unit cells so thateven at saturation the probability of two carbon atomseven being in the same unit cell is only 0middot004 Thus the

and

AO = exp [(L degGnRJ)+ einXi]n 1+eInxi exp (L degGtfRJ)

where n = 1 or i (Ref4) and L degHo and L degH 1 are thestandard molar enthalpy changes corresponding to L degGoand L degG1 respectively

This was the relationship used for the determination ofthe Fe-C-Xi multicomponent equilibrium phase diagramThe solute elements for which the program has been writtenare those that might commonly be found in low alloy steels(Mn Si Ni Cr Mo andmiddot Cu) although if the relevant freeenergy changes per unit of solute dissolving L degG and theinteraction parameters e are known L T can in principle becalculated for any alloy

(3)

(2)

(1)

n

LT = RT2 AX~o LJ 1 1

i = 2

The Wagner-Taylor expansions for the activitycoefficients9 were then substituted into equations (1)and (2) Eventually this gave the temperature deviation inthe form

where X~ is the mole fraction of component i and where

A _ A-[1+Xf(1-Xf)(eii-eI1A~A)J exp Bi - [X f L degH 1A ~ + (1- X 1L)L degH 0] exp B

for which

B = L degGo _(XL)2 eeL -eY (AO)2]

RT~ 2 11 11 1

where Xo = 1- Li= 1 Xi is the mole fraction of iron Yo is theactivity coefficient for the iron and the superscripts Y and Ldenote the austenite and liquid phases respectively In thisequation L degGY -+ L = degGL - degGy or more generally thedifference between the Gibbs free energies of the purehigher and lower temperature phases T is the phaseboundary temperature and R is the universal gas constant

Similarly for carbon(n = 1) or component i

y y _ L L (L degGi -+ L)XiYi - Xi Yi exp RT

Materials Science and Technology October 1989 Vol 5

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Sugden and Bhadeshia Liquidus solidus Ae3 temperatures and phase compositions for low alloy steels 979

(6)

(4)~ degG~ Y = 25middot57T - 32640

Fe-NbA large deviation from the air phase boundary was foundbecause of an error in ~ degG~ Y Kirkaldy et al4 give

~ degG~ Y = 60middot0-5middot4 x 10-3T (5)

In fact this value was due to a mistake in the originalsource19 in applying the equation due to Andrews20relating the excess molar Gibbs free energy to the soluteconcentration in the two phases Recalculating with respectto niobium (rather than pure iron) gives

~ degGC -+ Y = -RT In IXampblNb X~b

At 1262 K Xampb = 6middot0 X 10-3 and X~b = 1middot1X 10-2(Ref21) At 1493 K Xampb = 1middot2 X 10-2 and X~b =1middot6X 10-2 (Ref 19) Therefore ~ degG~ Y may be expressedas

experimental results on the Fe-C-Mn system In theirwork ~ degG~ Y was calculated as a function of temperaturefrom a knowledge of the activity and molar concentrationsof manganese in austenite and ferrite at equilibrium to give

L degG is in J mol-1 and T is in K unless stated otherwise

70~00 750 800 850 900MEASURED Ae3 TEMPERATURE deg c

3 Comparison of predicted and measured values forAe3 temperature for various steels

~ degG~ Y = 2middot1596 X 104 -12middot073T (7)

With this recalculation the discrepancy disappearedFigures 2a and b show two examples from the Ae3

program and illustrate well the effect on the Ae3 tempera-ture of adding 0middot5 wt-Mn when the austenite phase fieldexpands and 0middot5 wt-Si when the Ae3 temperature isincreased as the austenite phase field contracts

Experimental data for high purity Fe-C-X alloystogether with data for a broad range of steels were used tocheck the accuracy of the program The conditions imposedwere that Lf=2Xj ~ 6 wt- as Kirkaldy and Baganis3advised so that solute-solute interactions could realisti-cally be assumed to be negligible and that the siliconcontent was restricted to less than 1 wt- because theWagner interaction coefficients efjand eli for silicon are verylarge compared with those for other alloying elementsFigure 3 uses data from Aaronson and Domain22 andSwinden and Woodhead23 who established Ae3 tempera-

05

05

04

04

03

03

02

02

CARBON wt - deg0

I

900

0 Ref22

Ref23

850udegW0gtI-laquo0 800waw -ןdeg0

M

t GJlaquo

05deg0 Mn pound) 750 wl-t)

0 line of idealityw0a

01700

00

1000(0)

950

900

~w 8500gtI-laquo0w 800awI-

750

70000 011000

(b)

950

900

u

w 8500gtI-laquo0w 800a~wI-

750

Fe-MnAs Kirkaldy and Baganis3 also found a systematic discre-pancy was observed between experimental and calculatedvalues for the Fe-Mn system attributable to errors in~ degG~ Y Instead data were used from Gilmour et al18who calculated ~ degG~ Y between 700 and 850degC using

2 Vertical sections of Fe-C-X phase diagramsshowing effect on Ae3 temperature of adding0middot5 wt- of a manganese and b silicon to binaryFe-C

assumption made by Kirkaldy and Baganis seems justifiedand was adopted

Since all the thermodynamic functions used were depen-dent on temperature ~ T cannot be obtained from a singleapplication of equation (3) but must be deduced iterativelyFor this purpose a loop was included in the programInitiillly T was set as 4 and a trial value of ~ Twascalculated Then the program was rerun withT = (T +~T) This procedure was repeated until the valueof T changed by less than 0middot1 K in successive iterations(typically five times) Results for all the alloying elementswere determined and verified for correspondence withdata from Fe-X binary phase diagrams compiled byKubaschewski17 overall agreement was excellent Howeverdiscrepancies were observed with the Fe-Mn and Fe-Nbsystems and these are discussed below


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Table 1 Compositions of low alloy multicomponentsteels analysed wt-

800Steelno C Si Mn Cr Mo Ni Cu Nb V

~ 201 0middot11 0middot12 1middot25 0middot06 0middot07 0middot03 0middot07780 202 0middot12 0middot27 1middot53 0middot02 0middot03 0middot03 0middot05

w 203 0middot18 0middot44 1middot26 0middot01 0middot06 0middot02 0middot02 0middot03cgt 204 0middot19 0middot40 1middot42 0middot07 0middot02 0middot13 0middot08I-lt line of ideality 205 036 0middot27 0middot58 0middot08 0middot02 0middot05 0middot12~w

206 0middot69 0middot23 0middot72 0middot02 0middot01 0middot02 0middot03Il~ 760 207 1middot01 0middot25 0middot46 0middot02 0middot02 0middot03 0middot03wI- 209 0middot20 0middot25 0middot90 0middot81 0middot06 1middot05 0middot07 0middot02

ll 211 0middot29 0middot21 0middot62 1middot11 0middot21 0middot15 0middot04 0middot04tI

ltt 213 0middot35 0middot24 0middot67 092 019 0middot05 0middot07 0middot02CI 214 0middot52 0middot22 0middot85 1middot07 0middot07 0middot07 0middot04 0middot14w

216 1middot01 0middot23 0middot33 1middot55 0middot01 0middot02 0middot04 0middot04I- 740u0 1 0middot30 0middot10 0middot13 0middot30 0middot024 0middot05w~ 2 0middot48 0middot06 0middot04 0middot08 0middot016 0middot015Il

3 0middot66 0middot31 0middot04 0middot04 0middot007 0middot0154 0middot81 0middot41 0middot04 0middot03 0middot012 0middot02

720 5 0middot58 0middot99 lt 0middot02 0middot03 lt 0middot02 lt 0middot02720 740 760 780 800 6 0middot89 0middot43 lt 0middot02 0middot02 lt 0middot02 lt 0middot02

MEASURED Ae3 TEMPERATURE OC 7 1middot20 0middot53 lt 0middot02 lt 0middot02 lt 0middot02 0middot038 1middot48 0middot55 lt 0middot02 0middot02 lt 0middot02 0middot04

4 Experimental and calculated values for Ae3 25 0middot004 0middot11 0middot14 0middot03

temperature using experimental data from Ref 24 26 0middot001 0middot32 0middot02 0middot04 0middot005 0middot02

(9)

tures for a series of experimental steels containing Mn SiNi Cr Mo Cu and Co It can be seen that the generalagreement between predictions and measurements is verygood the standard error being less than plusmn 10K Data werealso taken from Grange24 consisting of an analysis of 19medium carbon low alloy steels of commercial purityGrange identified the Ae3 temperature as the temperatureat which the last trace of ferrite transformed to austenite onprolonged isothermal heating This work24 as with dilato-metry on heating would be liable to yield higher than trueequilibrium values This is in agreement with the resultsobtained in Figure 4 the mean apparent overshoot of theexperimental results obtained being slightly less than 10 K

Prediction of peritectic region

LIQUIDUS TEMPERATUREOver recent years it has become apparent2526 that themode of solidification is a determining factor in the sub-sequent development of the weld metal microstructureHowever to attempt to model the mode of solidificationwould require a knowledge of the steels solidificationbehaviour Although equation (3) had been applied widelyto the prediction of the Ae3 temperature the accuracy ofthe equation at predicting the liquidus and other peritectictemperatures of low alloy multicomponent steels does notseem to have been verified Kirkaldy and Baganis3 didcompute the peritectic part of the phase diagram for severalternary alloys but their calculations do not seem to havebeen compared against experimental data

Most of the data required were already found inKirkaldy et al4 However several phase boundaries on thebinary phase diagram were not included in that analysisthese were the ferrite and austenite solidi and the bib +y

The data in Kirkaldy et a14 contain the following errata1 L1 degG~ l = -26650+4269T-0017T2 cal mol-l not 0middot17T2

2 L1 degGl )= 430 - O305T cal mol-l not 6503 L1 degG~ 1= 3500-2308T cal mol-I not 31004 Table 3 should be headed L1degGl-gt L not L1Gf -gt L

5 L1 degHi -gt L = - 5360 cal mol-l not - 56306 Ta1-gt1+11 = 1185-1503 wt-C+216(0865 wt_C)426K not 1115

Equation 1 and in Appendix 1 equations 2 14 17 18 21 and 22 alsocontain typographical errors the reader is referred to the present text and toRef 3 In addition in Tables 1-3 the standard state superscripts are omitted


Data for steels 201-216 taken from Ref 29 and for steels 1-26 fromRef 30

line Also the equation given in Kirkaldy et al4 for 7for the austenite liquidus as a function of carbon due toBenz and Elliott27 did not seem to match publishedASM data28 and a new curve was calculated From the Fe-Cequilibrium phase diagram the lines were calculatedrespectively to be

7(j- (j+L = 1809- 2013(wt-C) - 2949(wt-C) (8a)

7y- y+L = 1793-1467(wt-C) -1674(wt-C)2 (8b)7y+(j -gt (j = 1666+ 1122(wt-C) (8c)

7y+L -gt L = 1783-1640(wt-C) - 7869(wt-C)2 (8d)

To discover if any data values were suspect the carboncontent X~ was set to zero so that dilute binary phasediagrams were generated for each element In this mannerthe value of ~ T for each solute element could be verifiedAlthough general agreement was excellent a systematicdiscrepancy was found for the Fe-Mn system and in thepresent work ~ degGM L has been estimated from values for~ degGM (j and ~ degGlt L Kirkaldy et al4 give

~ degGlt -gt (j = 2middot72 X 103 -128T~oGltL=120x104-850T

These two functions are then combined to give

~ degGM L = ~ degG~ y + ~degGltL

= 9middot25 x 103 -722T (10)As with the Ae3 program a temperature loop was includedin the program to increase the accuracy of the final result

To assess the overall accuracy of the program experi-mental data were taken from Jernkontoret29 in whichvalues for the liquidi solidi and solidification ranges of awide range of steels have been measured by differentialthermal analysis at a variety of cooling rates In additionnewly published experimental data from Howe30 giving theliquidus temperatures of a wide range of steels were usedThe compositions of the steels for which L=2Xi ~ 6 wt-are given in Table 1 For this analysis data from Ref 29obtained at the lowest cooling rates (01 K S-l) were usedsince these are expected to be closest to equilibriumExperimental and calculated values for the liquidustemperatures of the steels given in Table 1 are listed inTable 2 and plotted in Fig 5 It can be seen that agreement

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Table 2 Measured and predicted values for liquidustemperatures of 22 low alloy steels

Steel Primary Measured liquidus Predicted liquidusno solidification mode temperature degC temperature degC

201 Ferritic 1515 1523202 Ferritic 1514 1520203 Ferritic 1507 1516204 Ferritic 1506 1514205 Ferritic 1501 1507206 Austenitic 1474 1479207 Austenitic 1459 1458209 Ferritic 1503 1505211 Ferritic 1503 1508213 Ferritic 1495 1504214 Austenitic 1483 1485216 Ferritic 1451 14541 Ferritic 1505 15162 Ferritic 1470 15003 Austenitic 1476 14824 Austenitic 1464 14705 Austenitic 1472 14776 Austenitic 1456 14657 Austenitic 1437 14418 Austenitic 1408 141925 Ferritic 1529 153426 Ferritic 1530 1532

16001526 degC

U 1400w0gt-lt 12000w02w 1000-

800 5 10 15 20FeCARBON at -deg10

-- stable boundaries- - - boundaries of austenite-cementite equilibria

6 Fe-C equilibria of austenite with graphite andcementite (After Ref 17) yaustenite L liquid phase

is excellent and actually better than that achieved forthe Ae3 the slight overestimation for the liquidus beingattributable perhaps to the measurements being made undercontinuous cooling conditions

SOLIDIFICATION AS PRIMARY AUSTENITEThe small differences in Gibbs free energy between variousequilibria in the Fe-C system means that metastable equi-libria should also be considered since metastable phasesmay be kinetically favoured Depending upon the composi-tion and cooling conditions steels may solidify directly asaustenite or ferrite and in general the close proximity ofthe liquidus surfaces of these two phases means th~t m~ta-stable formation of one phase may occur when eqUlhbnumdata indicate3132 that the other phase is the stable oneOne particular advantage of using therm~chemi~alcalculations is that the yy +L phase boundary IS readIlycalculable High cooling rates can obviate nucleation

of the b-phase above the peritectic temperature so thatsolidification then proceeds according to the austenite-cementite system Since solute elements have differentsolubilities and diffusion rates in ferrite and in austenitesegregation is directly influenced by the form of the primaryprecipitation Specifically the diffusion rate of substitutionalelements in ferrite is two orders of magnitude greater thanin austenite and consequently segregation during a ferriticsolidiqcation process is much less than during an austeniticprocess33 This behaviour has profound significance inwelding since solidification as austenite will result not onlyin differences in solute segregation but also in thedistribution of the inclusions in the weld with respect tothe phases that subsequently form

Figure 6 shows the austenite-graphite and austenite-cementite phase diagram where the stable boundaries areindicated by full lines and the boundaries of the austenite-cementite equilibria by dashed lines This metastablesystem has been constructed in the program by extrapo-lating the austenite solidus and austenite liquidus It can beseen that the melting point of y-Fe is only rv 10 K lowerthan the melting point of b-Fe

PREDICTION OF SOLIDIFICATION RANGESSolidification of an alloy with a finite freezing range canallow the formation of an inhomogeneous solid and theamount of eventual segregation may be directly related tothe solidification range of the alloy Therefore it was crucialto verify the accuracy of the program at predicting thesolidus temperatures and solidification ranges of the steels

Table 3 Calculated and measured solidi andsolidification ranges for steels analysed

Solidus temperature degC Solidification range degCSteelno Measured Predicted Measured Predicted

201 1455 1471 60 52202 1460 1460 54 60203 1460 1470 47 46204 1460 1467 46 47205 1440 1442 61 65206 1370 1383 104 96207 1340 1321 119 137209 1445 1459 58 46211 1450 1450 53 58213 1425 1440 70 64214 1400 1410 83 75216 1300 1318 151 136

oo

00

o Primary Ferritic Solidificationbull Primary Austenitic Solidification

1520

1540

u

w 1500agtI-lta w 1480a ~WI-

(f) 1460gtQgt0J 1440ClwI-oetJ 1420gtuJoetU

14f200 1420 1440 1460 1480 1500 1520 1540MEASURED LIQUIDUS TEMPERATURE I DC

5 Predicted and measured liquidus temperatures for 22low alloy steels for primary ferrite and primaryaustenite solidification data are taken from Refs 29and 30


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1500 1550

L

L

y

y

02 OA 0-6 0middot8

(0)

1400

1350o

1550

( b)

1500uo

1400

W0J~ 1450cwa~wI--

W0J~ 14500Wa~wI--

1350o 0-2 04 06 08 1-0 1middot2 4 1middot6 1middot8

CARBON wt - 00

9 Phase diagrams for a Fe-C-Mn and b Fe-C-Crdiagrams were constructed using points generatedby computer model (it should be noted that forsimplicity three phase peritectic region has beenmaintained as straight line)

1500

line of ideality

1300 1350 1400 1450

MEASURED SOLIDUS TEMPERATURE oe

7 Experimental and calculated values for solidustemperature of range of 12 low alloymulticomponent steels data are from Ref 29(017 wt-C corresponds to peritectic point onbinary Fe-C equilibrium phase diagram and thusindicates change in solidification mode for alloys)

bull C lt 017 wt o Cgt 017 wt

analysed For steels 201 and 202 which respectively contain0middot11 and 0middot12 wt-C and which solidify through the peri-tectic as b-ferrite the b-solidus was estimated to a firstapproximation by extrapolation of the b-solidus line Forthe other steels it was calculated from the austenite solidusTable 3 lists measured and predicted values of the solidustemperatures and solidification ranges for the Jernkontoretsteels These data are plotted in Figs 7 and 8 respectivelyAs with the liquidus it can be seen that the thermodynamicalgorithm is an excellent predictor of both the solidustemperature and the solidification range of the steels

Figures 9a and b show the entire peritectic region drawnusing the computer model The figures show two constantsections through the Fe-C-Mn and Fe-C-Cr phasediagram for 0 and lOMn and 0 and 20Cr (wt-)

1450~w~gt-ltEi 1400aEw-Vlgto~ 1350Vl

oWI-Uo~ 1300a

140

160

u

w 120~zlt~

line of ideality

respectively Although the exact composition of the phasesin microscopic equilibrium cannot be predicted from avertical section of the phase diagram it is possiblemiddot to do sofor trends in compositional change Depression of the peri-tectic and Ae3 temperatures can be seen Stabilisation of theaustenite phase field and a concomitant contraction of theb-phase field for manganese and the corresponding expan-sion of the b-field and contraction of the austenite fieldwhen chromium is present should also be noted

40 60 80 100 120 140 160

MEASURED SOLIDIFICATION RANGE 0 e8 Experimental and calculated values for solidification

range of 12 low alloy steels given in Table 1

60

40

Calculation of partition coefficients

The partition coefficient of a solute element is a character-istic value showing the level of microsegregation of anelement in an alloy system To determine the equilibriumpartition coefficients of solute elements for multicomponentsystems entails time consuming experiments Therefore theapplication of thermodynamic calculations to the deter-mination of partition coefficients is a logical step parti-cularly since for a dilute solution containing small amountsof alloying elements the contribution from the interactionamong the elements to the partition coefficient betweenb-ferrite or austenite and liquid iron is negligible7 Since thecooling rates encountered in welding are fairly high it can

80

z 100o~ltuLoJoVlow-Uow~a


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1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010

~ (b)zwU~b 08ouzoi=~ 06ltcgt~~ 04gtowQw~ 02-oJgtU-oJltU

0000 02 04 06 08 10

EXPERIMENTAL EQUILIBRIUM PARTITION COEFFICIENTS

10 Calculated and experimental values for theequilibrium partition coefficients of soluteelements for a ~-ferrite and liquid iron andb austenite and liquid iron

computer program has been written which accuratelydescribes the influence of low concentrations of alloyingelements on the Ae3 equilibrium temperature of low alloysteels containing up to 1middot8 wt-C Using the method ofKirkaldy and Baganis3 the phase boundary is calculatedusing empirical data to estimate the Gibbs free energy ofthe participating phases in the multicomponent system andthe resultant deviation of the phase boundary from that ofthe binary Fe-C system is then found New elements (VNb W Co) have been incorporated to the program andrevised values for ~ degGo ~ degHo and ~ have been used Inaddition discrepancies with the Fe-Mn Fe-Ni andFe-Nb systems have been resolved The program has beenshown to be valid for significant additions of Mn Si Ni CrMo Cu V Nb W and Co

The peritectic region of the phase diagram has beencalculated with each phase boundary being treated indivi-dually and for the first time its accuracy evaluated Resultsobtained by calculation have been compared with experi-mental data for the liquidi and solidi of a range of low alloymulticomponent steels and found to be in extremely goodagreement A good ability to predict the solidification

()-zwuLb 08ouzo~~ 06ltXCL

gtc~ 04gtowQw~ 02-Igtu-IltXU

Table 4 Prediction of liquidus equilibrium partitioncoefficients

(X~X~) (xrX~)

Measured Predicted Measured Predicted

Ref 340middot90 0middot78 0middot95 0middot770middot91 0middot72 0middot50 0middot820middot95 0middot84 0middot87 0middot690middot83 0middot50 0middot95 0middot620middot86 0middot50 0middot60 0middot360middot96 0middot77 0middot50 0middot280middot95 0middot780middot94 0middot88

Ref 350middot84 0middot780middot80 0middot720middot88 0middot840middot83 0middot500middot50 0middot50


Summary

be assumed that segregation occurring during solidificationis not influenced by subsequent diffusion during coolingfrom the liquidus1 By considering the steel at a tempera-ture at which both the ferrite and austenite are in equi-librium the proportions of these two phases and theircomposition (ie the partition of the alloy elements) canalso be calculated The partition coefficient of a given soluteelement is determined using the relationship given inequation (3) For example for the y-L transformation

Xi = XrAi (11)

where

Standard free energy changes and activity data for iron andits binary and ternary alloys have been used to evaluate thegeneral linear series (Wagner)middot expansion of the activitycoefficient and these have themselves been used to generatean accurate thermodynamic determination of equilibriummulticomponent Fe-C-X transformation temperatures A

(1 degGi L L)exp RTo

+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo

Values for the equilibrium partItIon coefficients of themajor alloying elements between b-Fe and liquid iron(xtXr) and between austenite and liquid iron (XUXr) havebeen calculated and are given in Table 4 together withexperimental data

Agreement for solidification as b-ferrite (Fig lOa) is fairThe reason for the poorer agreement for solidification asaustenite in (Fig lOb) is not obvious although even hereequation (11) describes qualitatively the relative effects ofthe various solute elements However in future work theuse of more detailed models 7 36 to describe partitioning inthe melt may be necessary


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range which strongly influences the amount of solute segre-gation was also obtained Finally an attempt has beenmade to estimate the amount of partitioning for alloyingelements between b- and liquid iron and between austeniteand liquid iron and agreement with observed results wasfair This model has been shown to predict accurately themodifications to the Fe-Fe3C phase diagram of any givenset of alloying elements in the following range (all wt-)C ~ 18 Mn lt 30 Ni lt 25 Cr lt 25 Co lt 2Mo lt 15 balance (including Si) ~ 10 This covers thelargest proportion of steels used in welding fabrication

The practical limitations of the program result from twosources ie the limitations of the theory itself in particularthe inability to account for solute-solute interactions sinceit is only strictly correct for infinitely dilute solutions andinadequate experimental data for the pure binary systemswith iron as one component It is anticipated that thesesource data will be refined as development of the programcontinues

Acknowledgments

The authors are grateful to the Science and EngineeringResearch Council and to ESAB AB Sweden for financialsupport and to Professor D Hull for the provision oflaboratory facilities at the University of Cambridge It iswith pleasure that the authors acknowledge helpfuldiscussions with members of the Phase TransformationsGroup at the University of Cambridge

References

1 B GRETOFT H K D H BHADESHIA and L-E SVENSSON ActaStereol 1986 5 (2) 365-371

2 M STRANGWOOD and H K D H BHADESHIA in Weldingmetallurgy of structural steels (Conf Proc) (ed J Y Koo)495-504 1987 Warrendale PA The Metallurgical Society ofAIME

3 J s KIRKALDY and E BAGANIS Metall Trans 1978 9A (4)495-501

4 J S KIRKALDY B A THOMSON and E A BAGANIS inHardenabi1ity concepts with applications to steel (ConfProc) (ed D V Doane and J S Kirka1dy) 82-125 1978Warrendale PA The Metallurgical Society of AIME

5 L S DARKEN and R w GURRY Physical chemistry of metals222-224 1953 Tokyo McGraw-Hill


6 E SCHURMANN J VON SCHWEINICHEN R VOLKER andH FISCHER Giessereiforschung 198739 (3) 97-103 and 104-113

7 A KAGAWA K IWATA A A NOFAL and T OKAMOTO MaterSci Technol 1985 1 (9) 678-683

8 P CRASKA and R B McLELLAN Acta Metall 1971 19 1219-1225

9 C WAGNER Thermodynamics of alloys 51-52 1952London Addison-Wesley

10 H K D H BHADESHIA and D V EDMONDS Acta Metall 198028 1265-1273

11 H K D H BHADESHIA Prog Mater Sci 1985 29 321-38612 H HARVIG Jernkontorets Ann 1978155 157-16113 L KAUFMAN E V CLOUGHERTY and R J WEISS Acta Metall

1963 11 (5) 323-33514 H K D H BHADESHIA Mater Sci Technol 1985 1 (7) 497-

50415 L KAUFMAN and H BERNSTEIN in Refractory materials

Vol 4 19 1970 New York Academic Press16 M COHEN Trans AIME 1962224638-65617 O KUBASCHEWSKI Iron-binary phase diagrams 1982 Berlin

Springer-Verlag18 J B GILMOUR G R PURDY and J s KIRKALDY Metall Trans

1972 3 1455-146419 R c HUDD A JONES and M N KALE J Iron Steel Inst 1971

209 (2) 121-12520 K W ANDREWS J Iron Steel Inst 1956 184 414-42721 M HANSEN The constitution of binary alloys 676 1958 New

York McGraw Hill22 H I AARONSON and H A DOMAIN Trans AIME 1966 236

781-79623 D J SWINDEN and J H WOODHEAD J Iron Steel Inst 1971

209 (11) 883-89924 R A GRANGE Met Progr 196179 (4)73-7525 K WATANABE Tetsu-to-Hagane (J Iron Steel Inst Jpn) 1975

61 3069-307626 R C COCHRANE Weld World 1983 21 16-2427 M G BENZ and J F ELLIOTT Trans AIME 1961221323-33128 T B MASSALSKI (ed) Binary alloy phase diagrams Vol 1

563 1986 Metals Park OH ASM29 A guide to the solidification of steels 155-156 1977

Stockholm Jernkontoret30 A A HOWE Ironmaking Steelmaking 1988 15 (3) 134-14231 H FREDRIKSSON and L HELLNER Scand J Metall 1974361-

6832 H FREDRIKSSON Met Sci 1976 10 (3) 77-8633 T EDVARDSSON H FREDRIKSSON and I SVENSSON Met Sci

1976 10 (9) 298-30634 Z MORITA and T TANAKA Trans Iron Steel Inst Jpn 1983 23

(10) 824-83335 Z MORITA and T TANAKA Trans Iron Steel Inst Jpn 1984 24

(3) 206-21136 A KAGAWA and T OKAMOTO Mater Sci Technol 1986 2

(10) 997~1008

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Location of the octahedral interstices () in bcccrystal (After Ref 16)

the two phases which are in equilibrium For example forthe austenite and liquidliquid phase boundary for iron

Prediction of Ae3 temperature

The overall intention of this and other current research is tobe able to predict the mechanical properties of multipasswelds This requires a detailed knowledge of the thermalhistory of the weld and necessarily of the transformationtemperatures of the steels In welding the Ae3 temperaturehas a considerable influence on inter alia the relativevolume fractions of the phases present in the as weldedmicrostructure and the size of the reaustenitised region inmultipass welds Therefore as an initial step a programwas written to allow the Ae3 temperature to be predictedusing the method described above A series of modificationswas incorporated into it as follows

1 The program had been used forMn Si Ni Cr Moand Cu additions3 In addition the elements for Nb Co Vand W were included using further data given by Kirkaldyet ai4

2 The Ae3 values for J were formulated into a sub-routine using accurate values derived from equationsfrom Bhadeshia and Edmonds10 giving values of J downto 200degC Extrapolating the Ae3 in this manner would bepotentially very useful allowing for example growth ratekinetics to be calculated at temperatures well below theeutectoid temperature 11

3 Although data were provided 12 for values for thestandard Gibbs free energy change accompanying the rtytransformation in pure iron L degGo-+ Y since a longterm aimwas to extrapolate the Ae3 to lower temperatures the datafrom Kaufman et ai13 which give values down to 0 K andwhich are known to be reliable over an entire temperaturerange of interest14 were used The function L degGo-+ Y wasrepresented by curve fitting values from Table 3 ofKaufman et ai13 and later corrected values forL degGo-+Y(T gt 1183 K) from Kaufman and Bernstein1s

4 Values for L degHo -+ Y were obtained from work carriedout by Kaufman et ai13

In applying equation (3) to the calculation of the Ae3

Kirkaldy and Baganis3 had taken e~ 1 as zero Theyargued that the error introduced is negligible since theinteraction parameter is multiplied only by the very lowconcentration of carbon in ferrite This assumption canbe assessed quantitatively Figure 1 shows the carbon sub-lattice in a crystal of (X-FeThe bcc unit cell contains twoiron atoms and six carbon sites (This ignores tetrahedralsites but the probability of their occupation is ratherlow) The maximum solubility of carbon inb-Fe is 0middot09 wt- = 0middot417 at- Therefore there are(9960417) = 239 iron atoms for every carbon atom orthere is one carbon atom for every 119 unit cells so thateven at saturation the probability of two carbon atomseven being in the same unit cell is only 0middot004 Thus the

and

AO = exp [(L degGnRJ)+ einXi]n 1+eInxi exp (L degGtfRJ)

where n = 1 or i (Ref4) and L degHo and L degH 1 are thestandard molar enthalpy changes corresponding to L degGoand L degG1 respectively

This was the relationship used for the determination ofthe Fe-C-Xi multicomponent equilibrium phase diagramThe solute elements for which the program has been writtenare those that might commonly be found in low alloy steels(Mn Si Ni Cr Mo andmiddot Cu) although if the relevant freeenergy changes per unit of solute dissolving L degG and theinteraction parameters e are known L T can in principle becalculated for any alloy

(3)

(2)

(1)

n

LT = RT2 AX~o LJ 1 1

i = 2

The Wagner-Taylor expansions for the activitycoefficients9 were then substituted into equations (1)and (2) Eventually this gave the temperature deviation inthe form

where X~ is the mole fraction of component i and where

A _ A-[1+Xf(1-Xf)(eii-eI1A~A)J exp Bi - [X f L degH 1A ~ + (1- X 1L)L degH 0] exp B

for which

B = L degGo _(XL)2 eeL -eY (AO)2]

RT~ 2 11 11 1

where Xo = 1- Li= 1 Xi is the mole fraction of iron Yo is theactivity coefficient for the iron and the superscripts Y and Ldenote the austenite and liquid phases respectively In thisequation L degGY -+ L = degGL - degGy or more generally thedifference between the Gibbs free energies of the purehigher and lower temperature phases T is the phaseboundary temperature and R is the universal gas constant

Similarly for carbon(n = 1) or component i

y y _ L L (L degGi -+ L)XiYi - Xi Yi exp RT


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(6)

(4)~ degG~ Y = 25middot57T - 32640














05

05

04

04

03

03

02

02

CARBON wt - deg0

I

900

0 Ref22

Ref23


M

t GJlaquo



01700

00

1000(0)

950

900


750

70000 011000

(b)

950

900

u


750






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(9)












7(j- (j+L = 1809- 2013(wt-C) - 2949(wt-C) (8a)


7y+L -gt L = 1783-1640(wt-C) - 7869(wt-C)2 (8d)







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16001526 degC

U 1400w0gt-lt 12000w02w 1000-











201 1455 1471 60 52202 1460 1460 54 60203 1460 1470 47 46204 1460 1467 46 47205 1440 1442 61 65206 1370 1383 104 96207 1340 1321 119 137209 1445 1459 58 46211 1450 1450 53 58213 1425 1440 70 64214 1400 1410 83 75216 1300 1318 151 136

oo

00


1520

1540

u






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1500 1550

L

L

y

y

02 OA 0-6 0middot8

(0)

1400

1350o

1550

( b)

1500uo

1400

W0J~ 1450cwa~wI--

W0J~ 14500Wa~wI--


CARBON wt - 00


1500

line of ideality

1300 1350 1400 1450







oWI-Uo~ 1300a

140

160

u

w 120~zlt~

line of ideality


40 60 80 100 120 140 160



60

40



80



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1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010


0000 02 04 06 08 10








(X~X~) (xrX~)





Summary


Xi = XrAi (11)

where



+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo




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Acknowledgments


References





























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(6)

(4)~ degG~ Y = 25middot57T - 32640














05

05

04

04

03

03

02

02

CARBON wt - deg0

I

900

0 Ref22

Ref23


M

t GJlaquo



01700

00

1000(0)

950

900


750

70000 011000

(b)

950

900

u


750






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(9)












7(j- (j+L = 1809- 2013(wt-C) - 2949(wt-C) (8a)


7y+L -gt L = 1783-1640(wt-C) - 7869(wt-C)2 (8d)







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16001526 degC

U 1400w0gt-lt 12000w02w 1000-











201 1455 1471 60 52202 1460 1460 54 60203 1460 1470 47 46204 1460 1467 46 47205 1440 1442 61 65206 1370 1383 104 96207 1340 1321 119 137209 1445 1459 58 46211 1450 1450 53 58213 1425 1440 70 64214 1400 1410 83 75216 1300 1318 151 136

oo

00


1520

1540

u






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1500 1550

L

L

y

y

02 OA 0-6 0middot8

(0)

1400

1350o

1550

( b)

1500uo

1400

W0J~ 1450cwa~wI--

W0J~ 14500Wa~wI--


CARBON wt - 00


1500

line of ideality

1300 1350 1400 1450







oWI-Uo~ 1300a

140

160

u

w 120~zlt~

line of ideality


40 60 80 100 120 140 160



60

40



80



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1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010


0000 02 04 06 08 10








(X~X~) (xrX~)





Summary


Xi = XrAi (11)

where



+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo




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Acknowledgments


References





























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(9)












7(j- (j+L = 1809- 2013(wt-C) - 2949(wt-C) (8a)


7y+L -gt L = 1783-1640(wt-C) - 7869(wt-C)2 (8d)







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16001526 degC

U 1400w0gt-lt 12000w02w 1000-











201 1455 1471 60 52202 1460 1460 54 60203 1460 1470 47 46204 1460 1467 46 47205 1440 1442 61 65206 1370 1383 104 96207 1340 1321 119 137209 1445 1459 58 46211 1450 1450 53 58213 1425 1440 70 64214 1400 1410 83 75216 1300 1318 151 136

oo

00


1520

1540

u






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(c)

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1500 1550

L

L

y

y

02 OA 0-6 0middot8

(0)

1400

1350o

1550

( b)

1500uo

1400

W0J~ 1450cwa~wI--

W0J~ 14500Wa~wI--


CARBON wt - 00


1500

line of ideality

1300 1350 1400 1450







oWI-Uo~ 1300a

140

160

u

w 120~zlt~

line of ideality


40 60 80 100 120 140 160



60

40



80



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1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010


0000 02 04 06 08 10








(X~X~) (xrX~)





Summary


Xi = XrAi (11)

where



+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo




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Acknowledgments


References





























(10) 997~1008

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16001526 degC

U 1400w0gt-lt 12000w02w 1000-











201 1455 1471 60 52202 1460 1460 54 60203 1460 1470 47 46204 1460 1467 46 47205 1440 1442 61 65206 1370 1383 104 96207 1340 1321 119 137209 1445 1459 58 46211 1450 1450 53 58213 1425 1440 70 64214 1400 1410 83 75216 1300 1318 151 136

oo

00


1520

1540

u






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(c)

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1500 1550

L

L

y

y

02 OA 0-6 0middot8

(0)

1400

1350o

1550

( b)

1500uo

1400

W0J~ 1450cwa~wI--

W0J~ 14500Wa~wI--


CARBON wt - 00


1500

line of ideality

1300 1350 1400 1450







oWI-Uo~ 1300a

140

160

u

w 120~zlt~

line of ideality


40 60 80 100 120 140 160



60

40



80



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(c)

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1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010


0000 02 04 06 08 10








(X~X~) (xrX~)





Summary


Xi = XrAi (11)

where



+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo




Pub

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(c)

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mun

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Acknowledgments


References





























(10) 997~1008

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1500 1550

L

L

y

y

02 OA 0-6 0middot8

(0)

1400

1350o

1550

( b)

1500uo

1400

W0J~ 1450cwa~wI--

W0J~ 14500Wa~wI--


CARBON wt - 00


1500

line of ideality

1300 1350 1400 1450







oWI-Uo~ 1300a

140

160

u

w 120~zlt~

line of ideality


40 60 80 100 120 140 160



60

40



80



Pub

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(c)

IOM

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mun

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ions

Ltd


1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010


0000 02 04 06 08 10








(X~X~) (xrX~)





Summary


Xi = XrAi (11)

where



+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo




Pub

lishe

d by

Man

ey P

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hing

(c)

IOM

Com

mun

icat

ions

Ltd




Acknowledgments


References





























(10) 997~1008

Pub

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Man

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(c)

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Com

mun

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ions

Ltd


1008

bull Ref34

~ Ref35

o Ref 36

bull Ref34

o Ret36

0604

line of ideality

02

line of ideality

(a)10

000010


0000 02 04 06 08 10








(X~X~) (xrX~)





Summary


Xi = XrAi (11)

where



+ GliX 1

Ai= ------~-o-G-1+ GY XL exp __ I

11 1 RTo




Pub

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Man

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(c)

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mun

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ions

Ltd




Acknowledgments


References





























(10) 997~1008

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Ltd




Acknowledgments


References





























(10) 997~1008

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