Updating binary system files: CaOAlO1.5

CALPHAD Printed in

~01.6,

the

~40.2, pp.

83-92,

1982

0364-5916/82/020083-10$03.00/O (c) 1982 Pergamon Press

USA.

UPDATING EINARY SYSTEM PILES:

C&-Al01

Ltd.

5

Do R. Chang, Reed A. Howald, and Binalenda N. Roy Department of Chemistry, Montana State University Boxeman, Rontana, 5971le

ABSTRACT

Whenever the thermodynamic properties of an end member pure compound are revised, it is necessary to revise all the terms used for binary systems including that A simple first approximation procedure for msking these changes is compound. presented, and illustrated by application to the CaD-Al01 5 binary system. Refinement to a second approximation is discussed and doabnstrated. A set of appropriate to a heat of fusion for CaO lowered parameters is given f_“r CaO-AlOl.5 from 68 to 59 hJ mol and an increased heat capacity for A101.5(l). The Alo1.5SiO2 system has been similarly updated.

The various mathematical models used in the computer calculation of phase diagrams refer the thermodynamic properties of solutions to the values for a set of plrre components. Unfortunately there are many cases where the data for binary or multicomponent systems are hnonn more accurately than that for the references &ases. This is true for certain solid phases which are never thermodynamically stable for some of their components. The CALWAD organization and the CALPRAD journal have played major roles (1, 2) in standardizing values for such materials as body centered cubic niche1 (31 and manganese (4). An extreme example is found in the sigma phase (5-6) which &es not occur for any pure metal. This situation OCCUTS for liquid phases containing refractory oxides the experimntal difficulties encountered at the higher temperatares where melt. One of our recent papers (7) points out that the various plblirhod CaO-Si02 system (7-10) differ substantially in the properties used for the compounds. Thus one expects to find, and often finds in practice, careful multicomponent systems in need of revision to accommodate new or improved reference materials. The major thrust of this paper is the consideration revising the parameters short of repeating the entire set of calculations study.

simply because of the pure oxides treatments of the reference studies of values for the of methods for of the original

The standard approach to multicomponent systems starts with two pllre materials and a By the time one reaches five or six colponentr, a single original single binary system. compound has been used in four or five binary systems and ten or fifteen ternaries. Considering the effort involved in analyzing a binary or ternary system, it is clear that one soon builds up a substantial investment in the values originally chosen for the pure A reluctance to go back and make changes is understandable, but the problem components. cannot be avoided. We hope that the procedures described here will be holpfnl to others in need of revising a substantial data set. The

CaO-AlOl.5

Svstem

When we started analyzing ryatema containing Co0 it was apparent that the heat of fusion of CaO was not well hnown. The latest JANAli value (111 is an estimate from a heat of fusion for MgO (11) which is in turn referenced to a 1936 study of the RgD-ZrO2 system (1% As discussed in our original CaD-A101.5 p a p or (13) we selected a heat of fusion of 68’4 hJ mol-’

*

The

address

for

Dr.

Chang

is

Averett

College,

----_----_______-----__________ Received

27 January

1982

a3

Danville.

Virginia

24541

a4

D.R.

Chang

et

al.

from an analysis (13) of the 5!;0-CsO system (1.4, 15). More recently we tried to get a heat of fusion for Kg0 in the same way, and soon found that a more &tailed study of the MgO-CaO This led to heats of fusion of 57.65 and system was in fact both possible and necessary (16). for Kg0 and CaO respectively. 59.05 kJ mol-’ At the same time enthalpy (17-18) measurements in the CeO-AlOls-Si02 ternary were leading us to question the heat capacity value we had selected threk years ago (19) for (20) and has no The value of 72.43 J mol-’ K-l goes back to an old JANAF estimate Al01 5(1). contribution from equilibria between the different coordination numbers for A13+, which should be present end which should be temperature dependent. In any cese, using it required a large Positive excess heat capacity of miring at every oompositior studied (17-18). pure Al01 5 liquid does have a substantially higher heat capacity et the temperature where it exists’ (21). One cannot extrapolate to lower temperatures using Shpil’rain’s (21) equation, C = 115.7294 .0123846(T-1000). However a quadratic equation for the heat capacity of A1015(f) with a manimus. at 1800 K, C = 94.6961 + .0198l6(T-1000) - .12385 x 10-4(T-1000)2 is ‘in reasonably good agreement with a 1 the heat cnpecity information. This lowers the enthapy at 1000 K for AlOl.s(l) by 28 kJ mol-‘, but the change is 6 kJ mol-’ or less above 19)O K.

4

Thus we needed to adjust the parameters for the CaO-A1015 system to accommodate substantial changes in the enthalpy o.T Got11 end members. We iirst considered adding a set of Bedlich-Kister coefficients which would add a constant value to H. ovar nine-tenths of the Unfortunately this put a lot o$ extra curvature into lie at concentration range, Xi = 0.0-0.9. the ends. To get a reasonable looking new curve it was more important to keep the overall shape constant than to preserve the calculated values over any particular composition range. Method

of

Correction,

Pirrt

Auuroximation

Cnt CEI izcp the shape of an Ke or log ye curve unchanged by neinteining the same ratio of all the Bedlich-Pister coefficients used. This leaves a multiplicative constant which can be selected to keep the total enthelpy or activity constant at one particular temperature and composition. For the CaC-A101.5 celouletion we selected X=0.5 and 1900 K. The calculation_lwas based on standard enthelpies (referzfd to the elements et 29815 K) of Hl’ = -485611 J mol for CEO(I) end H2e = -696934 J mol for AlO~~(‘)_;;,‘,O~ tol_te old Bedlich-Kister et X = .5._!0 the absolute coefficients shown in part I of Table 1 gave enthalpy for this compositicn was B = .SHls + .5H2s - 30791 = -:$2064 .J mol . The enthalpies of the pure liquids were changed to -494285 and -699922.5 J mol , an; keeping the total enthalpy at 1900 Y and X = .5 unchanged requires reducing the magnitude of He, to -24%0. J molql: - 622064. = .5(-494285) + .5(-699922.5) - 24960. Thus He shoulo be reduced by e factor of 0.8106. Beduciag for enthalpy by .8106 accomplishes this keeping the same shaped shown in pert II of Table 1.

each Eedlich-Kister curve, and gives

the

parameter valms

compemeted by entropy adjustments, The enthelpy changes for CaO end AlOl.5 ere largely The Bedlich-Kister coefficients et 1900 log yigoO at X = .5 needs a change of only +.05001. change is accomplished by decreasing these are not shown explicitely in Table 1, but this parameters by II factor of .%?949 to -2.637235, 302780. -.036144, D55442 end 458169. The values for log ylooo were calculated from these using the enthalpy terms already evaluated. The Cao_AlOl 5 phase diagram recalculated using the revised paremeters (Table 1, Part are small enough that it is desirable to show the is plotted in Fig&e 1. The differences The entire liquidus curve for CaA1407 iS calculation as dotted lines on the same figure. The or iginel raised by about 35 K and the eutectic is lowered by about the same amount. calculation involved en adjustment of the Planck function values for CeA1407 to make the

and K

11) old

-14.606

TABLE2

24967.6 ‘581621

.581621 24967.6

.723201 30801.

C

+7:1;9 .

7241g;l;9

-.609788 -27056.

D

.458169

.45El69

.492925

E

TlOOO -635089.36 -578647.86 -837846.

"298

34333.9 38982.3 -826758.4 -824498.8 41911.128 -905488.73 43266.744 -902656.16 513962.56 109202.4 187443.2 180372.24 -10605185. -3587780. -2326304. -3977728.8

35237.648 31446.944 38982.328

E1000-~98

5.66514 5.9484 9.82027

b -1.4199 .4778% -1.4908 .50166 -5.32080 1.44829

25.38433 -5.02498 -7.44152 -5.0249

- 10-61 and CaA1407(o)

62.375 94.69605 19.816 9.82027 -12.3850 -5.32205 1.4485 69.963802 8.59251 -6.9111 2.70412 69.49624 13.50093 5.18147 292.00136 214.72144 172.21344 813.62064 22.92832 69.852 19.16272 -4.0635 24.9366

53.742225 56.429608 62.375072

a

Cp Equation*

l) Cp = a + b I 10m3(T - 1000) + c I 1O-6(T - 1000)2 + d 1.la-'(T - 1000)3 + e I **I There are substantial changes from values in references 13 and 19 for CaO(I), AlO

12 19

g;.;;; gUamcl) 55.852049 50.11475 SiO lo, ~=ist~balite)75.77SS87 sio9 (1) 76.050894 ~~~~~~~~~ 0)c * 326.68672 311.163 187.35952 753.299s c

caO(o) 62.462936 CaO(l)*+ 81.51769 A101~3S(c,+~wzxidxus) 51.11802

Substance

Thermodynsmic Properties fox Pore Materials in the Ca@-Al01 .3and AlOI.3-SiO2 Systems in S.I. Units

cp

Final Adjusted Revised Values ZEX4;y -4.9460684 -86692.6

III 33878.6 -7750506

Revised Values - First Approximation loSlOrlOOO -5.1074926 .9410266 8, enthalpy -9983B. 33878.6

II

1.144671 41194.

Old Parameters - Reference -5.884709 I*Q3~looo -123164. 8, enthalpy

B

I

A

Bedlioh-Kiater Parameters for the CsD_AIOl . 5 System in Units of J. mol, and K

TAELZ 1

D.R.

Chang

et

al.

2000

1500

‘0

.2

.4

.a

.6

XCRO Figure &wIparison diagrams

1 of using

calcufatefi Darts

CaO-A1O1 T anil

11

of

fj phase . Table 1.

1

a7

UPDATING BINARY SYSTEM FILES

rbeltirg point come out correct, and reducing this adjustment by 1.3 J m01-~K-l is all that is needed to fix this part of the curve. This is well within the uncertainty in t5e entropy anti planok function for CaA140,. The lowering of the eutectic to 1650 X gives improved agreemeut with the literature value of 1633 K (221. Refinement

of

the

Calculation,

Second

Annroximation

The Redlich-Kister terms for enthalpy in the CaO-Al01 5 were originally based (131 upon heat of fusion estimates for the various calcium aluninatds. Keeping tl‘c crt.% shape and the same value at r = .5 allows slight changes in the heats of fusion, but the full enthalpy wave can be considered reliable at temperatures near the melting points, i.e near 19OOK. Since our original treatment, Navrotsky et al. have completed a series of heat of solution measurements on calcium aluminum silicate glasses at 985 K (37). In fact these measurements provide a Rowever using the major portion of the evidence for a higher heat capacity for Al01 5. enthalpy values in part II of Table 1 does not give precise agreement with the best current an excess heat value (171 for the heat of dcl-itrificatior of CaAl 04, at 985 K, unless oapacity of mixing term is included as in part II 3 of Table 1. It is of course possible to refine a set of Redlich-Kister parameters such as those in Table 1 by a least squares nnalysis of all the input data. Starting with a close approximation like that in part IX*of Table 1 is a convenience, but it is certainly not necessary for this general approach. The major disadvantages of this procedure lie in the time required to analyze the original experimental data, and in the tendency of least squares calculations to give ridiculous behavior in regions where the data are sparse or unreliable. It is easier and safer to make small adjustments in two or three parameters to achieve the desirrd ccrrections. For example the eutcctio could be raised by about 20 K by raising log ye lrincrily an increase of about 0.034 in the A value, as at x = A8 by 0.0085. This require: the equation is Alogye = X(1-X)[AA + (-1 * 2X) ABI .0085 = .2496 M - .009984 AB Actnallp

it

would

be better

to

lower

the

-.0072

eutectic

= .2496

by 17 I;, AA -,009984

corresponding

to

the

equation

AR

A second equation in these two unknowns can be obtained by adjusting or holding constant The calcium aluminate whose thermodynamic properties are log 7’ at any other composition. best known is CaA1204, so we chose to use X = l/3 for the second equation. The solid line in Figure 1 gives a meltin point of 1865 K for CaA1204. The phase diagram (22) shows oongraent melting point should be slightly incongruent nelting at 1875 K. The hypothetical higher, about 1876 K, so we would like to increase the calculated melting point by 11 K. The react ion CaAl2O4(c) = CaO(l) + 2AlOl_5tl) h&s a heat at X = l/3

for

which

of reaction of f 152 kJ mol-’ so for melting to the mixture

AR is

i/3

CaA1204(c)

t26.8

kJ mol-‘.

= i/3

Ca0fl.X

The change Alogy’

i.0044

, or 50.7 kJ per mole of 1 iquid. one has the reaction = i/3) in log

+ 213 Az01.~(l.X ye should

be

= (AT/TlT21(AR/19.14464)

= (11/(1876)

(1865))

(26800/19.14464)

He = -23-P

= 2/3)

kJ mol

-1

D.R.

aa

T,

3000

-

2500

-

Chang et al.

K

1500 0

.2

.4

.6 X cao

Figure Final

2 CaO-AlO*_

5 phase

diagram.

.a

1

89

UPDATING BINARY SYSTEM PILES

.8

.2

0 0

.a

.2

X

Fiqure

CkiO

3

Calculated of

.8

.h

and experimental

CaO and A101,5

in liquids

(29) activities at

2058K.

1

Chang et al.

D.R.

90

TABLE3 Eedliah-Skirter Coefficientsfor the AlOl3-SiO2 System . A Part X

PrsvioarValues (19) loSlO~lOOO Ix,J mK1

Part

II

B

1.330516

C

-.212719

.096297

26771.6

Valaer

Correctedfor New Cp for A101,3(1) 13302655 l"~lo~looo

8, J ml-

-211929

.0959393

26853.8

Table 4 Revised T

11

Redlich-Kister Coefficients for the CaO-Si02 SYSteiiI.

Acid

slags

log10 Y

-10.638009

-9.4294345

-I..851460 4.687918

3.9l.8341

H

-231391.4

-185775.9

-58477.4

38973.2

c

23.4303

P Basic slags

51802.3

log10 f

-15.32977

3.016330

6.480548 -4.3363336

H

-340067.85

72673.44

223467.73-172821.50

C

P

23.4303

UPDATING BINARY SYSTEM FILES

this

Expressing

in

terms

the

of

Redtioh-Kirtsr i.0044

Solving

this

together

pataamters

= .222222

91

A and

AA -.074074

B gives

AR

with -.0072

= .24%

AA -

.0099&t

AB

gives AA = -.(!355 and AR = -.166. These are the values used to get part III of Table 1 from part II except for the number of significant firures used in the calculation. This computation allowed lo;, ye at X = 20, the CaAl@$ cofposition, to vary. It was necessary to make CaA1407(11 less stable by P = -2.252 J no1 Kto match its melting point to the Table 2 shows the final values fcr tlr thermodynamic properties of the phase diayam (22). calcium aluminates. These were ssed witB the parameters of part IX1 of Table 1 to calculate in Figure 2 is off by about 5. = the final phase diagram shown in Figure 2. The CaO 1 iquidns .02 from the points Gf Ikrse et al. (221, but this error is the same order of magnitude as the differences between published CaO-A101+5 phase diagrams (22-24). The incongruent meltin& point of Ca3A1206 in Figure 2 is substantially too low. This uan be corrected by changing the but vo have not carried the calculation that far. entbrlpy and entropy fcr tbix solid, There are a number of experimental studies of CaO activities near 1823 K (25-28). Of these onlv the values of Rein and Chinti.s.r. (25) were within a factor of 2 of our Previous caloulatibns (131. This is still true for the present values. Louxtau’s (291 effusion study weighted in the original least sqnrres calculation Q31. Figure 3 at 2058 K was quite heavily shows activities calculated at 2058 from part III of Table 1 along with Lourtau’s experimental is satisfactory, but not quite s.5 close as before (13). ;loints (29). The agrsemect The AlOl+S~,

Svstem

(If in Table 2 also necessitates a change in The revised heat capacity equation for Al0 Cost of this phase diagram the Bedlich-Kister coefficients 1191 for the Al is at temperatures over 2000 K where we wtre (211 high he!; capacities more The enthalyy of Al01 9 is now 50.8 J mol so the change required is quite small. negative nt 2050 K, and we selected this temperature and X =‘1/3 for the invariant point. Tbus A(E) should be increased by (l/31(50.8)(9/2) = 76.2 The liquid is now slightly less stable, with activities and equilibrium constants changed by a factor of ll\E40, .fron which ‘we calculated that the Bedlich-Kister coefficients at 2050 K should be lowered by a factor of The new values ure shown in part II of Table 3 since they are the values to be used .9 96285. liowever the changes in the in current treatments of three and four component systems. calculated Al01 .5-Si02 phase diagram are trivial.

obtain

We have also applied the new parnwters

the methods described shown in Table 4.

in

this

paper

to

the

CeO-Si02

system

(7) to

Acknowlsdnement This material kJo. I,%‘-8011449.

is

based

upon

wcrk

snpltorted

by the

National

Science

Foundation

under

BRPERENCKS A.P. Riodownik. “Project p. 86. Stuttgart/Schloss

Weitenburg

2.

1.. Kaufman

Calphad

3.

P.J. Spence r , in 0. Playsical Laboratory,

1.

and

B. Nesor,

Meeting

Calphrd VII” (19781.

2,

55

Kubascbewshi, ed., London (1972).

Mar. Placci

Inst.

ft:i

!!ctsllforschung,

(19781. “Metallurgical

Chemistry”,

p.488.

National

Grant

92

D-R. Chang et al.

4.

D. Den Hughes and L. Kaufman, Calphad 3, 175 (1979).

5.

T.G. Chart, P. Pntland, and A. Dinsdalr, Calphad 4, 27 (1980).

6.

F. H. Hayes in L. Kaufman, Calphad 3, 166 (1979).

1.

K.J. Byker, R.&R. Craig, I. Eliezer, N.Eliezer, R.A.Kowald and P. Viswanadhem. Calphad 5, 211 (1981).

a.

L. Kaufman, Calphad 3, 27 (1979).

9.

G. Kaestle, Ph.D. Thesis, Tech. Univ. Clausthal (19761.

10.

P.L. Lin and A.D. Pelton, Metal. Trans. 10B. 667 (1979).

11.

M.W. Chase, J.L. Cnrnatt. A.T. Ku, K. Prophet, A.N. Syverud, and L.C. Walker, J. Phyr. Chem. Ref. Data 3, 311 (1973).

12.

K.K. Kelley, U.S. Bur. Mines Bulletin 393 (1936).

13.

I. Eliezer, N. Eliezer, R.A. Kowald, and P. Viswanadham, J. Phyr. Chem. 85. 2835 (1981).

14.

M. Foer, Electricity from MKD, Symp. V, 3139 (1968).

15.

B.C. Doman. J.B. Barr, R.N. McNally, and A.R. Alper. J. Am. Ceramic Soc.46, 313 (1963).

16.

D.R. Chang and R.A. Korald, J. Phys. Chem., submitted.

17.

A. Navrotsky,

B. Kon, D.P. Weill, and D.J. Henry, Geochem. Cosmochim.Acta.44. 1409 (1980);A. Navrotsky, 6. Peraudeau, P. McMillan, and J.-P. Coutlver, Geochem. Cosmochim. Aota, submitted.

18.

D.F. Weill, J.F. Stebbins, B. Bon and I.S.E.Carmichael Contrib. Rinoral.Petrol. 74. 95 (1980).

19.

B.A. Kowald and I. Eliezer, I.

20.

D.R. Stall and K. Prophet, "JANAFThermochemicalTabler"Nat1. NBS37 (1971).

21.

E.E. Shpil'rain, D.N. Kogan, and L.S. Barkhatov, High Temp. High Press. 4, 605 (1972).

22.

R.W. Nurse, J.K. Welch and A.J. Majumdar, Trans. Brit. Ceramic SOO.. 64, 409 (19651.

23.

J.A. Imlach and F.P. Glasser, Trans. Brit. Ceramic Sot. 67. 581 (1968).

24.

E.Y.Lsvin, C.R.Robbins and K.F. BoYurdie, "Phase Diagrams for Ceramists", p.102. American Ceramic Sot., Columbus, Ohio (1964).

25.

R.K. Rein and J. Chipman, Trans. Metall. Soo., AlME 233, 415 (1965).

26.

D.Y. Edmund and J. Taylor, J. Iron Steel Inst. 210, 280 (1972).

27.

J. Cnmeron and J. Taylor, J. Iron Steel Inst. 204, 1223 (1966).

28.

B.A. Sharma and F.D. Richardson, J. Iron Steel Inst. 198, 386 (19611.

29.

R. Lourtau, Ph.D. Thesis, L'Inrt. Nat. Polyteoh de Grenoble, Grenoble, France (1977).

PhyS.

Chem.

82, 2199 (1978). Stand.Ref. Data Ser.,