Critical Evaluation and Optimization of the

Thermodynamic Properties and Phase Diagrams of

the CaO-AI2Oa, AI203-SiO2, and CaO-AI203-SiO2 Systems

GUNNAR ERIKSSON and ARTHUR D. PELTON

All available thermodynamic and phase diagram data have been critically assessed for all phases

in the CaO-A1203, A1203-SiO2, and CaO-A1203-SiO2 systems at 1 bar pressure from 298 K to

above the liquidus temperatures. All reliable data for the binary systems have been simulta-

neously optimized to obtain, for each system, one set of model equations for the Gibbs energy

of the liquid slag and all solid phases as functions of composition and temperature. The modified

quasichemical model was used for the slag. With these binary parameters and those from the

optimization of the CaO-SiO2 system reported previously, the quasichemical model was used

to predict the thermodynamic properties of the ternary slag. Two additional small ternary pa-

rameters were required to reproduce the ternary phase diagram and ternary activity data to within

experimental error limits. The calculated optimized phase diagram and thermodynamic prop-

erties are self-consistent and are the most reliable currently available estimates of the true values.

I. INTRODUCTION

a thermodynamic "optimization," all available

thermodynamic and phase equilibrium data for a system

are evaluated simultaneously in order to obtain one set

of model equations for the Gibbs energies of all phases

as functions of temperature and composition. From these

equations, all of the thermodynamic properties and the

phase diagram can be back-calculated. In this way, all

the data are rendered self-consistent and consistent with

thermodynamic principles. Thermodynamic property data,

such as activity data, can aid in the evaluation of the

phase diagram, and phase diagram measurements can be

used to deduce thermodynamic properties. Discrepancies

in the available data can often be resolved, and inter-

polations and extrapolations can be made in a thermo-

dynamically correct manner. A small set of model

parameters is obtained. This is ideal for computer stor-

age and calculation of properties and phase diagrams.

We are currently engaged in a systematic analysis of

oxide systems with a view to developing a comprehen-

sive database for molten and solid oxide phases for the

system SiOz-A1203-CaO-MgO-MnO-FeO-Na20-K20-

TiO2-Ti203-ZrO2-S. The first stage has been the opti-

mization of all binary subsystems and is now completed.

In a second stage, models are used to predict the thermo-

dynamic properties of ternary solutions from the opti-

mized model parameters of the constituent binaries.

Ternary phase diagrams can be calculated from these es-

timated properties. The predictions are compared with

measured ternary properties and phase diagrams, when

these are available, and when necessary, small opti-

mized ternary parameters are added. Finally, from the

optimized binary and temary parameters, thermo-

dynamic properties and phase diagrams of multi-

component systems can be predicted. The present article

GUNNAR ERIKSSON, Associate Researcher, and ARTHUR D.

PELTON, Co-Director, are with the Centre for Research in

Computational Thermochemistry, Ecole Polytechnique, Montreal, PQ,

Canada H3C 3A7.

Manuscript submitted October 5, 1992.

reports on the evaluation of the CaO-A1203 and A1203-

SiO2 binary systems and the CaO-A1/O3-SiO2 ternary

system. The optimization of the CaO-SiO2 system was

reported previously, m

For the molten slag phase, we have used our modified

quasichemical model, f2-131 Details of the model have been

given previously, t2'41 and the equations for binary sys-

tems have been summarized in a recent submission to

this journal, tl3] A brief outline of the model for a ternary

system is given below. This includes, for the first time,

a description of the inclusion of ternary terms. All tem-

peratures in this article have been corrected to the In-

ternational Temperature Scale of 1990.

II. THE MODIFIED

QUASICHEMICAL MODEL

In a molten slag AO~-BO,-CO~, we consider the for-

mation of second nearest-neighbor

(i-j)

bonds from

(i-i)

and

(j-j)

bonds:

(A- A)+ (B- B)=2(A-B) [11

(B-B) + (C-C)=2(B-C) [21

(C-C)+(A-A)= 2(C-A) [3]

The Gibbs energy changes for these reactions are rep-

resented by (WAB -- T/ABT), (W~C -- T/BcT) and (WCA --

T/cAT).

Let the mole fractions of the components be XA =

XAO x,

Xa = XBoy,

and Xc =

Xco,.

Equivalent fractions are then

defined as:

YA = bAXA/(bAXA + bBX~ +

bcXc) [4]

and similarly for Ya and Yc, where

b A,

bB, and bc are

constants. Letting

be the fractions of each type of

bond in solution, equilibrium constants are obtained for

Reactions [1] through [3]:

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--807

X~ [ (wo--~7~jT) ] [5]

KiJ - x~xjj = 4 exp

-2

zRT

Three mass balance equations may be written as

2YA

= 2XAA ~- XAB ~- XCA [6]

2YB = 2XBB + XBc + XAB [7]

2Yc = 2Xcc + XCA + XBc [8]

The molar enthalpy, nonconfigurational eptropy, and

configurational entropy of mixing are given by

: (bAXA -'}-

bBXB +

bcXc)

9 (XAB O)AB -}- XBCOJBC -]- XCAtOCA)/2 [9]

AS nC

-- (bAXA q-

bBXB +

bcXc)

9 (XAB'I~AB + XBC'I'~B C "~- XCAr/CA)/2

[10]

AS c

= -- R(X A

In XA + XB In XB + Xc In

Xc)

-- -- (bAX A -C

bBX B -+-

b~c)

XA A XBB XCC

9

XAA In

,-7S- + X~u In ~ + X~ In --

Y), Y~ Yc

XAB XBc

+ XAB In -- + XBc in --

2YAYB 2YBYc

XCA ]

+ XCA In 2YcYAJ [11]

where, as explained previously, 12,41 the appropriate val-

ues of the constants z and

are z = 2, bsio = 1.3774,

bca o = bsioJ2,

and bAj %

5 = 3bsi~ 4"

Equations for the

partial mol~ar properties can also-be written, t2,41 Equa-

tions for any binary subsystem are obtained by simply

setting one component mole fraction to zero in Eqs. [4]

through [ 1 1 ].

Given a composition and values of the energies (~oq -

"%T), Eqs. [41 through [8] can be solved to give the bond

fractions

Xo,

which can then be substituted into Eqs. [9]

through [1 1] to give the thermodynamic properties. The

solution of Eqs. [4] through [8] is very similar to a com-

plex gas-phase equilibrium calculation involving diatom-

ic molecules, and can be performed by similar numerical

algorithms9

When (tOAB -- T/ABT) is negative, Reaction [1] is shifted

to the right and the solution is structurally ordered, with

A-B pairs predominating over A-A and B-B pairs. When

(tOAa -- ~TAaT) is positive, clustering occurs. When all

(o9~ - "riot )

are set to zero, the solution is ideal. The

relationship of the modified quasichemical model, when

applied to molten slags, to other models of molten sili-

cates, such as cell models tl4,151 and to the Toop and Samis

model, I16~ has been discussed previously. I~,a,41

In each binary system, (t% - r/,~T) is expanded as a

polynomial in the equivalent fractions. For example, in

the A-B binary system,

OAB = W0<Am + <Ol(AmY~ + ~O2<AmY~

+ O)3<AB,Y 3 q-

[12]

T]AB = ~0(AB) ~- "01(AB)YB at- TI2(AB) Y2 q- T/3(AB~Y 3 +

[13]

The coefficients

OJk(AB )

and ~Tk<aA) are the binary model

parameters which are obtained by optimization of the bi-

nary data. Nonlinear least-squares optimization software

has been written for this purpose. I6,~71

In order to estimate the thermodynamic properties of

the ternary slag from the optimized binary parameters,

it is necessary to approximate oJij and ~70 in the ternary

solution from their values in the binaries. For ternary

silicate slags, AOx-BO/SiO2 (abbreviated A-B-C), very

good results have been obtained by letting

WBC

and WCA

(and ~c and r/CA) be constant along lines of constant

SiO2 content, Yc, while WAB and r/AB are assumed con-

stant along lines of constant

YA/YB"

For basic slags, this

approximation has been shown 131 to be consistent with

Conformal Ionic Solution Theory. When AO~ and BOy

are both basic oxides (CaO, MgO, MnO, FeO, Na20,

K20), quantitative or nearly quantitative predictions of

measured ternary thermodynamic properties and phase

diagrams have been obtained 14'5'7-9'11'121 with no addi-

tional ternary terms. For the CaO-AI203-SiO2 system,

two additional small ternary parameters were required,

as discussed subsequently in Section VII.

III. PURE COMPONENT PROPERTIES

The thermodynamic properties of SiO2, A1203, and CaO

used in the evaluations are given in Table I. For SiO2,

enthalpy, entropy, and heat capacity expressions for all

solid phases were taken from Berman

et al. t~sj

The melt-

ing point and values of A/~},,, and A~,, at the melting

point were taken from the JANAF Tables. 1191 An expres-

sion for Cp(1) was obtained from the tabulated values, tlgl

Below the melting point, Cp(1) was set equal to Cp of

high cristobalite. For A1203, properties of the solid were

taken from Berman

et al. tlsi

The melting temperature, as

well as AH~f,s and A~,, at the melting point, was taken

from Barin

et al.,t2~

while Cp(l) was obtained from the

tabulated values of Barin9 I21] Below the melting point,

Cp(1) was obtained by adding to Cp(s) the expression for

ACp(fus) from Barin

et alJ 2~

For CaO, all data ior the

solid were taken from Berman

et al. ~I81

For reasons dis-

cussed previously, I~l we prefer the melting temperature

of 2572 ~ found in the older literature t221 to the higher

values given in the more recent literature. The enthalpy

of fusion at the melting point was taken from Kubas-

chewski

et al. I231

An expression for Cp(1) was obtained

from the tabulated data of Barin. t2~/ Below the melting

point, Cp(1) was set equal to Cp(S).

The thermodynamic properties of the other com-

pounds listed in Table I were obtained from the opti-

mizations, as discussed below. As a starting point, the

compilations of Berman

et al.

,t18.24.251

who have used lin-

ear programming to optimize thermodynamic and solid-

solid equilibrium data for a large number of oxides, were

invaluable.

IV. THE CaO-AI~O3 SYSTEM

The calculated optimized phase diagram is shown in

Figure 1. The first studies of this system 126271 indicated

the presence of four compounds: Ca3A1206, CasA16Ol4,

CaA120 4, and Ca3AlloO~8. Lagerqvist

et al., I2sl

in X-ray

808--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

Table 1. Thermodynamic Properties Relative to Elements at 298.15 K

H(J/mol

-') = A

CvdT

S(J/mol-' K-')

= B

(CJT)dt

98.15 298.15

Cp(J mol -i K -l) = a + b (10 -3) T + c (10S)T -2 +

dT -I/2 +

e(10S)T -3 + f(10-6)T 2 + g(10-9)T 3

A B a b c d e f g

896795.9 50.82911 83.51360 - 24.55360 - 374.6930 2.800722

- 926635.5 9.91714 85.77200

1596353.2 43.56903 179.36549 - 9.19225 4.090836

- 1693605.9 - 53.06981 192.46400

- 555594.0 65.69076 58.79117 1.029788

578234.8 41.16108 62.76000

- 910699.9 41.46000 80.01199 4.915684

910702.7 41.45142 80.01199 8.44002 4.915684

908626.8 44.20680 80.01199 4.915684

907045.1 45.52370 75.37267 9.582461

906377.2 46.02880 83.51360 2.800722

1675700.0 50.82000 155.01888 4.090836

635090.0 37.75000 58.79117 1.029788

2933326.3 167.79626 321.19000 0.975300

2306045.5 127.60999 209.68000 12.974800

2307009.1 123.63668 209.68000 52.05242 12.974800

2281886.7 143.24801 209.68000 12.974800

3942846.1 210.87364 339.91000 13.735900

1632579.4 81.81003 149.07266 4.843494

1628506.5 85.27880 141.15611 9.407350

3587266.9 204.17924 321.58000 6.612200

2324157.8 115.06001 227.04000 0.855400

- 3999688.9 177.82000 337.98000 15.106000

-10704185.8 388.91011 992.73500 37.470110

- 6819210.0 274.90000 634.81000 21.227400

- 4231594.1 200.18614 439.36938 - 3.170232

- 3985858.5 198.60000 373.08740 4.779118

- 3988652.1 189.21529 151.34740 369.50000 4.779118

210.06818 373.08740 4.779118

SiO2 (1) (298 to 1996 K)

SiO2 (1) (>1996 K)

AlzO 3 (1) (298 to 2327 K)

Al2Os (1) (>2327 K)

CaD (1) (2115 to 2845 K)

CaD (1) (>2845 K)

SiO2(Q) (298 to 373 K)

SiO2(Q) (373 to 848 K)

SiO2(Q) (848 to 1140 K)

SiO2(Tr) (390 to 1738 K)

SiO2(Cr) (535 to 1996 K) -

A1203 (s) (298 to 2327 K) -

CaD(s) (298 to 2845 K)

CasSiO5 (s) (298 to 2073 K) -

CazSiO4 (,8) (298 to 970 K) -

Ca2SiO4 (a') (970 to 1710 K) -

Ca2SiO4 (c0 (1710 to 2431 K) -

Ca3Si207 (/3) (298 to 1737 K) -

CaSiO3 (or) (298 to 1404 K) -

CaSiO3 (/3) (1404 to 1813 K) -

Ca3A1206 (298 to 1814 K) -

CaAI204 (298to 1877 K)

CaAI407 (298 to 2038 K)

CaAl12019 (298 to 2106 K)

A16Si20~3 (298 to 2163 K)

CaAl2Si2Os (298 to 1828 K)

Ca2AlzSiO7 (298 to 698 K)

Ca2A12SiO7 (698 to 1600 K)

Ca2A12SiO7 (1600 to 1868 K) - 3972868.8

9.75341 - 828.3870

llA7146 - 133.9040

- 35.46684 - 240.2760

59.58095

- 24.55360 - 374.6930

38.61363 - 828.3870

- 11.47146 - 133.9040

- 9.94800 -2450.2000

- 79.89400 - 701.9000

- 79.89400 701.9000

-106.61000 - 985.1000

- 36.59348 690.2950

- 58.57595 - 417.2320

- 57.81300 -1255.4000

5.60800 -1669.1000

-121.12600 -1022.2000

281.47800 5350.0300

-172.09900 -3373.5000

-3734. 1490

- 47.78466 -2276.7550

125.12814 -2276.7550

- 47,78466 -2276.7550

- 45.212700 60.550445

- 105.843347 53.805442

- 146.900000

<FmA~CIT>

2100

......... l ......... [ ......... I ..... ~"I

......... I ........ I ......... I ........ i ......... I .........

~, 2054o___>

2000

~o ~

LIQUID

0.87

IBO0

17650

0.82

~8o4 o

18oo

15410 0.45

1400

13620

1300

...... I ......... I ......... I ....

0.0

0.1 0.2 0.3 0.4 0,5 0.6 0.7 0,8 09 t.0

CaO Mole

fraction AI01. 5

AIOI. 5

Fig. 1--Optimized CaO-AI203 phase diagram. Compositions in terms

of components CaO-A10~ ~.

studies, identified

CasA16014 as Ca12Al14033

and

Ca3Al10Ot8

as CaAI407, and reported the compound Ca3A132OsI. By

a microscopic study of rapidly chilled samples, this latter

compound was identified as CaAl120~9 by Filonenko and

Lavrov. t29j Its composition has been confirmed. 130.3u The

high-alumina portion of the phase diagram has been

studied several times 13~ with a considerable spread

in the results, which is probably related to whether the

experiments were performed in air or in moisture-free

argon atmospheres.

Nurse

et al.P41

used high-temperature microscopy under

controlled atmospheres to conclude that the compound

Ca12Al14033

is actually a hydrate, Ca12Al14032 (OH)2, and

is not present in the binary CaO-A1203 system. The same

controlled atmospheres were used in the study of the

complete system by Nurse

a/. pSI In this work, all four

compounds were reported to melt incongruently: Ca3A1206

at 1541 ~ to a liquid of 45.1 mol pct A1OIs; CaA1204

at 1604 ~ to a liquid of 66 mol pct A101.5; CaA1407 at

1765 ~ to a liquid of 80 mol pct A101.5; and CaAll2019

at 1833 ~ to a liquid of 85 mol pct AIO~.5. A deep

eutectic at 1362 ~ and 53.0 tool pct A1Oi.5 was found.

This eutectic temperature and composition have been

confirmed. 136]

Rolin and Pham p31 reported congruent melting of

CaA1204 at 1602 ~ Wisnyi t3~ reported congruent melt-

ing of

CaAl407

at 1748 ~ Eutectics were reported at

1599 ~ and 1725 ~ by Wisnyi and at 1592 ~ and

1778 ~ by Rolin and Pham. CaAl120~9 was reported to

melt incongruently at 1823 ~ by Wisnyi, while Rolin

and Pham reported incongruent melting at 1906 ~ and

an allotropic transformation at 1836 ~ The possible

nonstoichiometry of the compounds has apparently not

been investigated.

CaD activities in the liquid at 1500 ~ were obtained

from gas/slag equilibration studies of melts saturated with

CaS, pT1 and CaD and A1203 activities in the liquid were

obtained at 1787 ~ by Knudsen cell-mass spectrometry

measurements, pS~ Results were reported relative to the

solid standard state in both studies. Points plotted on

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--809

Figure 2 were changed to the liquid standard state with

the Gibbs energies of fusion used in the present analysis.

The

values for all four compounds were taken from

Berman and Brown. p4,251 In the case of CaA1p_O19, the

values were calculated from the approximation formula

of these authors. The values of A/4~298 for

Ca3A1206

and

CaA1204 were reported by Coughlin. I391 These were

changed in the optimization by 356 and 2071 J/mol, re-

spectively. The value of AH~298 of CaAI4OT, reported by

Kubaschewski and Alcock, t4~ was changed by -599

J/mol. The values of S~98 for Ca3A1206, CaA1204, and

CaAI407 were reported by King. tnu Those of Ca3A1206

and CaAI204 were changed by -1.255 and 0.837 J/tool

K, respectively. The value of ~98 of

CaA1407 was

not

changed. All of these changes of A/-/~298 and AS298 are

within the stated uncertainties. No values of M-/~298 and

~98 for CaAll2Ow have been reported, although esti-

mates are available, t421

Allibert

et al. pSI

and Kumar and Kay, 1431 using gal-

vanic cells with solid electrolytes, have measured the

Gibbs energies of the four compounds relative to CaO

and A1203 in the temperature ranges of 650 ~ to

950 ~

and 800 ~ to 1200 ~ (Values for

Ca3A1206

were reported only by Kumar and Kay). For CaAl~2Otg,

the difference between the present optimized values and

those of Allibert

et al.

is less than 0.75 kJ/mol, while

the values of Kumar and Kay lie 3 kJ/mol lower at

900 ~ For CaAl407 and CaA1204, the optimized values

are lower than those of Allibert

et al.

by 9 and 1 1 kJ/

mol, respectively, and lower than those of Kumar and

Kay by 1.4 and 5 kJ/mol, respectively. For Ca3A1206,

the optimized values are 9 kJ/mol lower than those of

Kumar and Kay.

The optimized quasichemical parameters for the liquid

phase are:

w = - 121164 - 353674YA4,O,, J/mol [14]

r/= -27.196 - 115.060y41o, 5 J/mol.K [15]

The large negative excess entropy, Eq. [15], is required

in order to reproduce the very

low [35'361

eutectic temper-

ature of 1362 ~

The thermodynamic analysis supports the congruent

melting of CaA1204 and CaA1407. The calculated activ-

ities in Figure 2 agree with the measured values within

experimental uncertainties.

The probable maximum inaccuracy in the assessed

diagram is estimated as -+25 ~ or -+2 mol pct.

V. THE A1203-SiO2 SYSTEM

The optimized A1203-SIO2 phase diagram is shown in

Figure 3. At 1 bar, the equilibrium diagram contains one

compound, mullite (A16Si2Ou). This phase was first

identified correctly by Bowen and Greig, ~44~ who re-

ported that it melts incongruently. An earlier study t26]

showed congruent melting at the sillimanite (A12SiOs)

composition. A number of earlier studies showed mullite

melting incongruently, L45-481 while others reported con-

gruent melting.t49'5~ Chaudhuri,1521 in a comprehensive

review, supports the results of Troemel

et al.,Is31

Davis

and Pask, 1541 and Aksay and Pask, t551 who showed that

either congruent or incongruent behavior can occur, de-

pending upon kinetic factors. Under equilibrium condi-

tions, it appears that incongruent melting is favored.

The present analysis is based upon the recent work of

Klug

et al.

,t561 who studied the region of the phase dia-

gram close to the melting point of mullite as well as the

non-stoichiometry of multite above 1600 ~ They an-

nealed their specimens in oxygen and analyzed the equi-

librium phase assemblages by optical microscopy, image

analysis, X-ray diffraction, and electron probe micro-

analysis. Selected experimental points are shown in

Figure 3. The range of homogeneity of mullite was found

to shift to higher alumina contents as the temperature

was raised. They reported a peritectic at 1890 ~ in-

volving mullite with a composition of 20.1 mol pct SiO2

(based on AlOe.5 and SiO2 as components).

At lower temperatures, the liquidus points of Aramaki

and Roy tS~ were chosen for the present optimization.

These were obtained in sealed noble metal containers to

0.7 ....

0.5

0,4

0.3

0.2 ~

0,t~

L-~

O0 ~

....

0 0

0.5 O.B 0.7 0.8

CBO

Mole

fraction

AIOI5

AIOI. 5

Fig. 2--Calculated activities of CaO at 1500 ~ (lower line) and at

1787 ~ (upper line) and of SiOz at 1787 ~ in liquid CaO-AI:O3

solutions. Experimental points: [] (Ref. 37) at 1500 ~ and O,

(Ref. 38) at 1787 ~

<F~A~C*T>

2100 ......... I ........ I ........ { ........ I ........ I ......... I ........ I ......... t ........ ~ .........

....

2054 e

2000 ~90 ~ LJOuIO

1400

S~ )

O _ O ~' 0.2 0 3 0 4 ,?,5 0.~- 07 0.8 09 I0

alO. a ~c. le eractlon S~O 2

SxO 2

Fig. 3--Optimized AI_,O3-SiO2 phase diagram. Compositions in terms

of components A10~.5-SiO> The metastable liquid miscibility gap and

spinodal curve are shown. Experimental points: [] (Ref. 50); and

O (Ref. 56).

810--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

prevent losses of silica by volatilization. At higher tem-

peratures, the liquidus of Aramaki and Roy is consistent

with the data of Klug

et al.

near the mullite melting point.

A eutectic at 1587 -+ 10 ~ and 93 mol pct SiOz (on the

scale of Figure 1) was reported by Schairer and Bowen. t571

Terminal solid solubilities were assumed to be negligible.

MacDowell and Beall ts8) used electron microscopic,

X-ray diffraction, thermal expansion, and density mea-

surements to study the metastable region of liquid im-

miscibility at compositions between mullite and silica.

They schematically illustrated the possible form of a gap

extending from approximately 30 to 85 tool pct SiO2 and

indicated as a rough estimate that the upper consolute

point is located around 1650 ~ From their flattened

mullite liquidus, Davis and Pask t541 predicted a meta-

stable liquid miscibility gap at subliquidus temperatures.

In a more recent study, Jantzen

et al.

,t591 using ultrarapid

quenching from the melt and studying the kinetics of de-

mixing by small-angle neutron scattering, determined a

critical point at about 725 ~ and 56 mol pct SIO2.

The experimental difficulties in measuring liquid ac-

tivities are considerable due to the highly viscous melt.

Hence, the activity data obtained by Dhima

et al.lr~

were

not included in the optimization.

For stoichiometric mullite, heat capacities were taken

from Berman and Brown, I24"2sI while A/-/~298 and

S~298 were

taken from the JANAF tables, u~l No changes were made

to these values. The nonstoichiometry of mullite was de-

scribed by a general defect model similar to the Wagner-

Shottky model, t6~ The model was outlined previously. I11

In the present case, the energy parameters for the for-

mation of both majority defects were set to 121903 +

38.17T J/mol, with the constants /3~ = /32 = 1 (see

Reference 1).

For the liquid phase, the following optimized quasi-

chemical parameters were obtained:

to = 4800 + 100784y3io~

142068Y~io~ -

+ 78571y7io~ J/mol [16]

with r/ = 0. This gives small positive deviations in the

liquid, with a maximum integral excess Gibbs energy of

about 5 kJ/mol.

The calculated optimized diagram in Figure 3 repro-

duces the liquidus data well. The reported 1561 nonstoichi-

ometry of mullite is described very well. In the optimized

diagram, mullite containing 20.4 mol pct SiO2 melts

congruently at 1890 ~ The calculated eutectic is less

than 1 ~ lower at 19.4 mol pct SiO:. It was not pos-

sible, without producing an optimization that was judged

to be poorer overall, to make mullite melt incongruently.

In any case, the optimized diagram agrees with the data

of Klug

eta/. [561

within experimental uncertainties. Ac-

cording to the calculations, mullite is unstable with re-

spect to A1203 and SiO2 below 490 ~

The calculated metastable liquid miscibility gap and

spinodals are shown in Figure 3. The consolute point is

calculated at 1313 ~ at 61 mol pct SIO2. This temper-

ature is near the average of those reported, tsS,59j and the

composition is close to the reported t591 value of 56 mol

pct SiOz.

The probable maximum inaccuracy in the assessed

diagram is estimated as -+25 ~ for Xs~oz < 0.8 and -+10 ~

for Xs~o~ > 0.8.

VI. THE CaO-SiO2 SYSTEM

The optimization of this system was reported previ-

ously. I~l The calculated optimized phase diagram is re-

produced in Figure 4, and the optimized Gibbs energies

of formation of the compounds are listed in Table I.

Measurements of activities in the liquid were also con-

sidered in the optimization. The general defect model,

discussed in Section V, was used for the Ca2SiO4 phase.

The following optimized quasichemical parameters were

found:

w = -158218

37932Ysio2 - 90148Y~io2

439893y7io~ J/mol [17]

r/= -19.456 + 133.888yTiQ J/mol'K [18]

VII. THE CaO-AI203-SiO2 SYSTEM

The calculated optimized CaO-A1203-SiO2 phase dia-

gram is shown in Figure 5. A phase diagram was con-

structed by Osborn and Muan, t661 based upon critically

assessed data from several sources. This diagram is nearly

identical to the diagram in Figure 5 in regards to the

disposition of the primary phase fields, with the follow-

ing exceptions: a small primary field of CaL2A114033 was

shown on the diagram of Osborn and Muan, but, as ex-

plained in Section IV, this has now been shown to be a

hydrate; the phase field of Ca3SiO5 was shown as ex-

tending to the CaO-SiO2 binary, but consideration of the

most recent binary data indicates that this is not the

case; U/

a saddle point was shown between CaSiO3 and

Ca2AI2SiO7

which is not seen in Figure 5. A list of the temperatures

and compositions of all ternary invariant points, saddle

points, and congruent melting points from the assessed

diagram of Osborn and Muan is given in Table II. The

position of the (anorthite + corundum + CaAl120~9)

peritectic in Table II was taken from a later revision.t67~

Activities of SiO2 in the liquid slags were measured

by Rein and Chipman [68'69] at 1550 ~ and 1600 ~ by

equilibration with Fe-Si-C alloys in CO gas and by Kay

and Taylor I7~ at 1450 ~ 1500 ~ and 1550 ~ by mea-

surements of the equilibrium pressure in the reaction

<F~AWC*T>

2200

20600

2000

LIOUID 7

E ~ ~ o :

16oo

.... s,o o i

4 0 /4540 ~ 14650 C

I 47 1465 ~ Crist.->

&C?~-J 0'. 42

1 ~

Trld.-->

1400 ~ "

0.6J

1441 ~ S

,~oo~ % ~

t200

I I I

~... ~ ,, ......... t

......... I ......... I J

0.0 0.1 0.2 0.3 0.4 0.5 0.6 07 0,8 0.9 1.0

CoO Mole fraction SiO 2 SiQ 2

Fig. 4--Optimized CaO-SiO2 phase diagram, m Ex~nmental points:

9 (Ref, 62); & (Ref. 63); [] (Ref, ~); and ~ (Ref. 65).

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993-- 811

si%

(try)

f889 I~

f598

1689

f44f A

Ranklnlte

Ca3SI2l

Ca2SI04

(zl~) .

Ca3SlOs

li~

CaSlO z

(te~)

15411

A16512013

(la~)

154t ) ~,782 -1597

CaO

Ca3AI 20 s CaAI2 04

(~?2] J 06~)

Ca3AIzO s ~'-

Ca2 SIO 4

Weight %

Fig. 5--Optimized CaO-AI:O3-SiO: phase diagram. Temperature in ~

lr~ lass

AI20 3

CoAl407

CaA1120ig

(zes4)

0 rs6)

SiO2 + 3C = SiC + 2CO. Results of Rein and Chipman

at 1600 ~ and of Kay and Taylor at 1550 ~ are repro-

duced in Figures 6 and 7. The experiments of Rein and

Chipman were repeated for very low SiO2 activities by

Ozturk and Fruehan, [7~1 who obtained an isoactivity line

for asio2 = 10 4 at 1600 ~ at SiO2 contents about 3 wt

pct higher than the line shown in Figure 6. Activities of

CaO in the slag at 1500 ~ were measured by Kalyanram

et al. t721

by gas/slag equilibration. Their results are re-

produced in Figure 8.

Thermodynamic properties of anorthite (CaAI2Si208)

and gehlenite (CaA12SiOT) were taken from Berman and

Brown. [24,25j The values of 2~/~298 for these compounds

were subsequently adjusted by -2864 and +2299 J/tool

in the optimization.

In order to reproduce the data within experimental error

limits, two small ternary parameters were required in the

quasichemical equations for the liquid. These were found

by a nonlinear least-squares program written for that pur-

pose. itTl To the value of (.O(Ca_Si) in the binary system from

Eq. [17], the ternary term -88144

(YA~olJ(Ycao +

YAIO,.,)) 2 J/tool was added. To the value of W(A~-Si) in the

binary system from Eq. [16], the ternary term

-48668Ycao/(Yc,o +

YA~o,,) J/mol was added. No ter-

nary terms were required for

T~(Ca_Si), TI(AI_Si), (.O(Ca_AI),

T/(Ca Ai)-

A comparison of the calculated ternary invariant points,

Si02

,o,4 00, -;90

v v ~

CaO 90 80 70 60 50 40 30 20 10

A101.5

Mole %

Fig. 6--SiO_, Activities (solid standard state) in CaO-AI203-SiO2 slags

at 1600 ~ Compositions in mole pct of components CaO-A10] 5-

SiO,. -- Measured ~6~-~'~ and -- calculated.

812--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

Table II. Comparison of Calculated Ternary lnvariant Points, Saddle Points, and Congruent Melting Points

from the Optimized Phase Diagram with Points from the Composite Experimental Diagram of Osborn and Muan. r661

Temperature Liquid Composition (Wt Pct)

Solid Phases Type of Point (~ CaO A1203 SiO2

expt congruent 1555

An calc congruent 1555

expt congruent 1595

Ge calc congruent 1595

expt eutectic 1347 9.9 20.0 70.1

An + Tr + Mu calc eutectic 1367 10.1 20.7 69.2

expt saddle 1370 10.8 19.7 69.5

An + Tr calc saddle 1369 10.9 19.9 69.1

expt eutectic 1172 23.1 15.0 61.9

An + Tr + Wo calc eutectic 1190 24.8 13.5 61.7

expt saddle 1309 33.9 19.0 47.1

An + Wo calc saddle 1301 35.6 16.6 47.9

expt eutectic 1267 37.9 20.1 42.0

An + Wo + Ge calc eutectic 1264 40.0 18.5 41.6

expt peritectic 1312 47.3 12.0 40.7

Wo + Ge + Ra calc peritectic 1282 43.7 15.8 40.5

expt peritectic 1317 48.9 11.8 39.3

Ca2SiO4 + Ge + Ra calc peritectic 1328 47.1 14.1 38.8

Wo + Ge expt saddle 1320 45.7 13.5 40.8

expt peritectic 1514 15.5 36.7 47.8

An + Co + Mu calc peritectic 1547 17.7 42.3 40.0

expt saddle 1549 19.2 39.7 41.1

An + Co calc saddle 1547 18.2 42.7 39.1

expt 1671 peritectic 1407 27.5 39.6 32.9

An + Co + CaAl12019 calc peritectic 1446 27.4 40.7 31.9

expt eutectic 1382 29.0 39.2 31.8

An + Ge + CaAl12019 calc eutectic 1392 30.7 37.1 32.1

expt peritectic 1472 31.2 44.6 24.2

CaAlaOv+CaAI12OI9 + Ge calc peritectic 1443 30.7 41.1 28.2

expt saddle 1387 30.0 37.1 32.9

An + Ge calc saddle 1392 30.8 36.9 32.3

expt saddle 1554 34.7 50.3 15.0

CaAI407 + Ge calc saddle 1572 34.6 50.6 14.8

expt eutectic 1502 37.5 53.1 9.4

CaA1204 + CaA1407 + Ge calc eutectic 1529 36.3 57.2 6.6

expt saddle 1514 37.7 52.9 9.4

Ge + CaAI204 calc saddle 1529 37.2 52.9 6.9

expt saddle 1547 49.7 23.8 26.5

Ca2SiO4 + Ge calc saddle 1548 50.3 23.8 26.9

expt peritectic 1382 48.0 42.3 9.7

Ca2SiO4 + CaA1204 + Ge calc peritectic 1461 49.3 37.0 13.6

Ca2SiO4 + CAA1204 +

"Ca12Al14033" expt eutectic 1337 51.8 41.8 6.4

CazSiO4 + CaAI204 + Ca3AlzO 6 calc eutectic 1335 51.7 45.6 2.7

expt peritectic 1472 59.6 32.9 7.5

CaO + Ca3SiO5 +

Ca3AlzO 6

calc peritectic 1445 60.1 30.0 9.9

expt peritectic 1457 59.5 33.0 8.5

CazSiO4 + Ca3SiO5 + Ca3A1206 calc peritectic 1438 59.6 31.0 9.4

CaO+CazSiO4 + Ca3SiO5 calc peritectic 1800 65.2 11.8 23.0

An = anorthite; Co = Corundum; Ge = gehlenite; Mu = mullite; Ra = rankinite; Tr = tridymite; Wo = pseudowollastonite.

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--813

sio2

,o o ! 5so

o_s

v v v v v v v v v-~ 0

CaO go 80 70 60 50 40 30 20 10 AI 2 03

Weight %

Fig. 7--SIO2 activities (solid standard state) in CaO-AI203-SiO2 Slags

at 1550 ~ -- measured I68,691 and --Calculated.

-I 5oo~

f'J

10 20 30 40

AI2

0 3

Weight %

Fig. 8--CaO Activities (solid standard state) in CaO-AI~O3-SiO, slags

at 1500 ~ -- Measured 1721 and -- Calculated.

saddle points, and congruent melting points from the op-

timized phase diagram with those from the composite

diagram of Osborn and Muan t661 is shown in Table II.

The largest differences occur in those regions where the

experimental measurements are sparse and where there

is the greatest disagreement among measurements. At all

points, the agreement is within experimental error limits.

Calculated silica activities are compared with the ex-

perimental data in Figures 6 and 7. Again, agreement is

within experimental error limits, the accord between the

experimental and calculated values being generally as good

as that between the two sets of measurements. For

SiO 2

activities below 0.01, the calculated values are higher

than the reported values in Figure 6 at higher A1OLs/

CaO ratios. It is difficult to see how the SiO2 activities

could be as low as the reported 168,69,7H values, since ex-

trapolation to the SiO2-A10~ 5 binary would then result

in very low SiO2-activities in this system, contrary to the

binary assessment discussed in Section V.

The activity data of Kalyanram

eta/. [72]

in Figure 8

were not included in the least-squares optimization, be-

cause their results in the CaO-SiO2 binary system do not

agree well with the optimized CaO-activities in this bi-

nary. However, CaO-activities calculated from the op-

timized parameters agree very well with the data of these

authors in the ternary system as can be seen in Figure 8.

The probable maximum inaccuracy in the assessed dia-

gram is estimated as _+35 ~ or _+3 mol pct.

VIII. CONCLUSIONS

Critical evaluations of all available reliable thermo-

dynamic and phase diagram data for the CaO-A1203 and

A1203-SIO2 binary systems have been conducted. Through

the technique of least-squares optimization, all data were

evaluated simultaneously to obtain one set of self-

consistent model coefficients for the Gibbs energies of

all phases as functions of temperature and composition.

The evaluations are valid from room temperature to above

the liquidus temperatures. For all compounds and the

liquid solutions, the present evaluations are considered

to give the most reliable currently available estimates of

the true values of the thermodynamic properties. The phase

diagrams, calculated thermodynamically from the same

optimized parameters, are considered to be the most re-

liable currently available estimates of the true phase dia-

grams. The modified quasichemical model was used to

represent the thermodynamic properties of the binary liq-

uid slags with a small number of parameters.

With these binary parameters and those from the op-

timization of the CaO-SiO2 system reported previ-

ously, m the quasichemical model was used to predict the

thermodynamic properties of the slag phase in the CaO-

A1203-SIO2 ternary system. Two additional small ternary

parameters were required to reproduce all available ter-

nary phase diagrams and thermodynamic data to within

experimental error limits.

The calculated optimized ternary phase diagram is

consistent with the ternary activity data, with the Gibbs

energies of formation of all compounds, and with the

most recent critically assessed phase diagrams of the three

binary subsystems. All isotherms and univariant lines have

been interpolated according to correct thermodynamic

principles. For these reasons, the calculated phase dia-

gram is considered to be the most reliable currently

available estimate of the true diagram.

In many ternary systems containing

SiO2

with two basic

oxides, very good predictions of the thermodynamic

properties of the slags and of the ternary phase diagrams

have been obtained with the quasichemical model by using

only parameters from the binary systems. I4,5,7-9,11'121 The

present calculations show that even in a system contain-

ing the amphoteric oxide

A1203,

quantitative results can

be obtained with only a very few small ternary parameters.

814--VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B

The quasichemical model can be used to predict the

thermodynamic properties of multicomponent slags from

the optimized binary and ternary parameters. We are

currently evaluating and optimizing data on all sub-

systems of the SiO2-AI203-CaO-MgO-FeO-MnO-TiO2-

Ti203-ZrO2-Na20-K20- S system.

ACKNOWLEDGMENTS

This work was supported by the Natural Sciences and

Engineering Research Council of Canada. The authors

are indebted to Paul Talley for the ternary graphics and

to Ping Wu for his help with all aspects of the work.

REFERENCES

1. G. Eriksson, P. Wu, M. Blander, and A.D. Pelton: Ecole Poly

technique, Montreal, Canad. Metall. Quart., in press.

2. A.D. Pelton and M. Blander:

Proc. 2ndlnt. Symp. Metall. Slags

and Fluxes,

TMS-AIME, Warrendale, PA, 1984, pp. 281-91.

3. M. Blander and A.D. Pelton:

Proc. 2nd Int. Syrup. Metall. Slags

and Fluxes,

TMS-AIME, Warrendale, PA, 1984, pp. 294-304.

4. A.D. Pelton and M. Blander:

Metall. Trans. B,

1986, vol. 17B,

pp. 805-15.

5. M. Blander and A.D. Pelton:

Geochim. et Cosmochim. Acta,

1987,

vol. 51, pp. 85-95.

6. A.D. Pelton and M. Blander:

Calphad,

1988, vol. 12, pp. 97-108.

7. A.D. Pelton, G. Eriksson, and M. Blander:

Proc. 3rdlnt. Syrup.

Metall. Slags and Fluxes,

The Institute of Metals, London, 1989,

pp. 66-69.

8. A.D. Pelton and G. Eriksson:

Advances in the Fusion of Glass,

Proc. 1st Int. Conf. on Advances in the Fusion of Glass, American

Ceramic Society, Westerville, OH, 1988, pp. 27.1-29.11.

9. A.D. Pelton, W.T. Thompson, C.W. Bale, and G. Eriksson:

Advances in Phase Transitions,

J.D. Embury and G.R. Purdy,

eds., Pergamon Press, New York, NY, 1988, pp. 52-67.

10. A.D.Pelton, G. Eriksson, and M. Blander:

Proc. 4th Int. Symp.

Metall. Slags and Fluxes,

Iron Steel Institute of Japan, Tokyo,

1992, pp. 79-84.

11. M. Blander, A.D. Pelton, and G. Eriksson:

Proc. 4th Int. Symp.

Metall. Slags and Fluxes,

Iron Steel Institute of Japan, Tokyo,

1992, pp. 56-60.

12. P. Wu, G. Eriksson, AD. Pelton, and M. Blander:

J. Iron Steel

Inst. Jpn.,

1993, vol. 33, pp. 25-34.

13. G. Eriksson and A.D. Pelton:

Metall. Trans. B,

1993, vol. 24B,

pp. 795-805.

14. M.L. Kapoor and M.G. Frohberg:

Symp. Chem. Metall. Iron and

Steel,

Sheffield, England, The Institute of Metals, London, 1971.

15. H. Gaye and J. Welfringer:

Proc. 2nd Int. Symp. Metall. Slags

and Fluxes,

TMS-AIME, Warrendale, PA, 1984, pp. 357-76.

16. G.W. Toop and C.S. Samis:

TMS-AIME,

1962, vol. 224, p. 878.

17. P. Wu: Ph.D. Thesis, l~cole Polytechnique, Montr6al, 1992.

18. R.G. Berman, T.H. Brown, and H.J. Greenwood: Report No.

TR-377,

Atomic Energy of Canada Limited,

1985.

19. JANAF Thermochemical Tables, 3rd ed.,

J. Phys. Chem. Ref.

Data,

1985, vol. 14.

20. I. Barin, O. Knacke, and O. Kubaschewski:

Thermochemical

Properties of Inorganic Substances,

Springer-Verlag, Berlin, 1977.

21. I.

Barin: Thermochemical Data of Pure Substances,

VCH,

Weinheim, Germany, 1989.

22. J.F. Elliott and M. Gleiser:

Thermochemistry for Steelmaking,

Addison-Wesley, Reading, MA, 1960.

23. O. Kubaschewski, E.L. Evans, and C.B. Alcock:

Metallurgical

Thermochemistry,

Pergamon, London, 1967.

24. R.G. Berman and T.H. Brown:

Contrib. Mineral Petrol.,

1985,

vol. 89, pp. 168-83.

25. R.G. Berman and T.H. Brown:

Contrib. Mineral. Petrol.,

1986,

vol. 94, p. 262.

26. E.S. Shepherd, G.A. Rankin, and F.E. Wright:

Am. J. Sci., 1909,

vol. 28, pp. 293-333.

27. G.A. Ranldn and F.E. Wright:

Am. J. Sci.,

1915, vol. 39, pp. 1-79.

28. K. Lagerqvist, S.Wallmark, and A. Westgren:

Z. Anorg. Allg.

Chem.,

1937, vol. 234, pp. 1-16.

29. N.E. Filonenko and I.V. Lavrov:

Dokl. Akad. Nauk S.S.S.R.,

1949, vol. 66, pp. 673-76.

30. L.G. Wisnyi: Ph.D. Thesis, Rutgers University, New Brunswick,

New Jersey, 1955.

31. A.L. Gentile and W.R. Foster:

J. Am. Ceram. Soc.,

1963,

vol. 46, pp. 74-76.

32. N.E Filonenko and I.V. Lavrov:

Zh. Priklad. Khim.,

1950,

vol. 23, pp. 1040-46.

33. M. Rolin and H.T. Pham:

Rev. Hautes Temp. R(fractaires,

1965,

vol. 2, pp. 175-85.

34. R.W. Nurse, J.H. Welch, and A.J. Majumdar:

Trans. Br. Ceram.

Soc.,

1965, vol. 64, pp, 323-32.

35. R.W. Nurse, J.H. Welch, and A.J. Majumdar:

Trans. Br. Ceram.

Soc.,

1965, vol. 64, pp. 409-18.

36. N. Nityanand and H.A. Fine:

Metall. Trans. B,

1983, vol. 14B,

pp. 685-92.

37. R.A. Sharma and F.D. Richarson:

J. Iron Steel Inst., London,

1961, vol. 198, pp. 386-90.

38. M. Allibert, C. Chatillon, K.T. Jacob, and R. Lourtau:

J. Am.

Ceram. Soc.,

1981, vol. 64, pp. 307-14.

39. J.P. Coughlin:

J. Am. Chem. Soc.,

1956, vol. 78, pp. 5479-82.

40. O. Kubaschewski and C.B. Alcock:

Metallurgical

Thernzochemistry,

5th ed., Pergamon, N.Y. 1979.

41. E.G. King:

J. Phys. Chem.,

1955. vol. 59, pp. 218-19.

42. B.S. Hemingway:

J. Phys. Chem.,

1982, vol. 82, pp. 2802-03.

43. R.V. Kumar and D.A.R. Kay:

Metall. Trans. B,

1985, vol. 16B,

pp. 107-12.

44. N.L. Bowen and J.W. Greig:

J. Am. Ceram. Soc.,

1924, vol. 7,

pp. 238-54.

45. V. Skola:

Keram. Rundschau,

1937, vol. 45, pp. 188-215.

46. E.C. Shears and W.A. Archibald:

Iron and Steel, London,

1954,

vol. 27, pp. 26-30, 61-66.

47. K. Konopicky:

Bull Soc. Franc. Ceram.,

1956, vol. 33, pp. 33-36.

48. G.Gelsdorf, H. Mueller-Hesse, and H.E. Schwiete:

Arch.

Eisenhiittenw.,

1958, vol. 29, pp. 513-19.

49. N.A. Toropov and F. Ya. Galakhov:

Dokl. Akad. Nauk S.S.S.R.,

1951, vol. 78, pp. 299-302~

50. S. Ararnaki and R. Roy:

J. Am. Ceram. Soc.,

1962, vol. 45,

pp. 229-42.

51. A. Staronka, H. Pham, and M. Rolin:

Rev. Int. Hautes Temp.

R(fract.,

1968, vol. 5, pp. 111-15.

52. S.P. Chaudhuri:

Ceram. Int.,

1987, vol. 13, pp. 167-75.

53. G. Troemel, K.H. Obst, K. Konopicky, H. Baur, and I. Patzsak:

Ber. Deut. Keram. Ges,

1957, vol. 34, pp. 397-402.

54. R.F. Davis and J.A. Pask:

J. Am. Ceram. Soc.,

1972, vol. 55,

pp. 525-31.

55. I.A. Aksay and J.A. Pask:

J. Am. Ceram. Soc.,

1975, vol. 58,

pp. 507-12.

56. F.J. Klug, S. Prochazka, and R.H. Doremus:

J. Am. Ceram.

Soc.,

1987, vol. 70, pp. 750-59.

57. J.F. Schairer and N.L. Bowen:

Am. J. Sci.,

1955, vol. 253,

pp. 681-746.

58. J.F. MacDowell and G.H. Beall:

J. Am. Ceram. Soc.,

1969,

vol. 52, pp. 17-25.

59. C.M. Jantzen, D. Schwahn, J. Schelten, and H. Herman:

Phys.

Chem. Glasses,

1981, vol. 22, pp. 122-37.

60. A. Dhima, B. Stafa, and M. Allibert:

High Temp. Sci.,

1986,

vol. 21, pp. 143-59.

61. H. Schmalzried:

Solid State Reactions,

Academic Press, New York,

NY, 1974, pp. 35-51.

62. J.W. Greig:

Am. J. Sci.,

1927, vol. 13, pp. 1 and 133; vol. 14,

p. 473.

63. G. Troemel, W. Fix, and R. Heinke:

Tonind. Ztg. Keram.

Rundschau,

1969, vol. 93, p. 1.

64. J.D. Tewhey and P.C. Hess:

Phys. Chem. Glasses,

1979, vol. 20,

p. 41.

65. V.B.M. Hageman, G.J.K. van den Berg, H.J. Janssen, and H.A.J.

Oonk:

Phys. Chem Glasses,

1986, vol. 27, p. 100.

66. E.F. Osborn and A. Muan:

Phase Diagrams for Ceramists,

E.M.

Levin, C.R. Robbins, and H.F. McMurdie, eds., The American

Ceramic Society, Columbus, OH, 1964, vol. 1, p. 219.

67. A.L. Gentile and W.R. Foster:

J. Am. Ceram. Soc.,

1963,

vol. 46, p. 76.

68. R.H. Rein and J. Chipman:

TMS-AIME,

1963, vol. 227,

pp. 1193-203.

METALLURGICAL TRANSACTIONS B VOLUME 24B, OCTOBER 1993--815

69. R.H. Rein and J. Chipman:

TMS-AIME,

1965, vol. 233,

pp. 415-25.

70. D.A.R. Kay and J. Taylor:

Trans. Faraday Soc.,

1960, vol. 56,

pp. 1372-84.

71. B. Ozturk and R.J. Fruehan:

Metall. Trans. B,

1987, vol. 18B,

pp. 746-48.

72. M.R. Kalyanram, T.G. MacFarlane, and H. Bell:

J. Iron Steel

Inst.,

1960, vol. 58, p. 195.

816-- VOLUME 24B, OCTOBER 1993 METALLURGICAL TRANSACTIONS B