Basic and Appl ied R e s e a r c h : S e c t i o n I

Calcu la t ion of Phase Diagrams for Comme r c ia l Materials

L. Kaufman Cambridge Technology Center Alcan Aluminum Corporation

21 Erie St., Cambridge, Massachuset ts , 0 2 1 3 9 USA

The contributions of Oswald Kubaschewski and coworkers in the field of applied chemical thermo- dynamics serve as a guide for future workers who are interested in practical applications of the vast thermochemical literature that Kubaschewski helped to assemble and refine. Three recent examples of the calculation of multicomponent phase diagrams for commercial alloy steels, aluminum alloys, and ceramic composites illustrate how modern computer-based methods can be used to facilitate such applications.

1. In troduc t ion

It is a pleasure for me to participate in this memorial volume for Dr. O. Kubaschewski and mention some recent work in a field that was particularly close to "Kuba's" heart, i.e., "saving lots of money for your company by telling them what they shouldn't do!" My first awareness of Kuba's work came in 1953 during my thesis work on the iron-nickel system 1 when I found a fascinating paper by Kuba and Ortrud yon Goldbeck 2 (his thesis student and later his wife) describing the construc- tion of Gibbs energy vs composition curves at several iso- therms in the Fe-Ni system from several different sets of thermochemical and phase diagram data. This was a very early example of the CALPH,KD method that we know today. Shortly thereafter we all began to benefit from the first compi- lations of Kuba's work3, 4 with various co-workers that pro- vided invaluable data for metals, alloys, and compounds. These early volumes were the forerunners of a whole series of periodic publications with Alcock, Knacke, Barin, and others, which provided practicing thermochemists with reliable sources of data essential for the prediction of phase stability and transformations in solids.

I began corresponding with Kuba in 1956 ia an unsuccessful attempt to participate in the NPL Symposium No. 9,5 which he organized in London in 1958. Travel funds for neophyte ther- mochemists were in short supply so I could not meet Kuba in 1958, but we corresponded and finally met in Geneva 6 in 1967. By this time Kuba was aware of my interest in coupling phase diagrams and thermochemistry in multicomponent systems with a special focus on lattice stabilities. 7 The Brunel/Shef- field conferences of 19718 were the last major undertakings for Kuba in England; these meetings and the Munster Conference in 19729 laid the groundwork for the annual CALPHAD meet- ings, which started in 1973 and continue today. Kubaschewski participated in many of the CALPHAD meetings and this par- ticipation was celebrated on 31 August 1983 during CAL- PHAD XIII in Aachen, West Germany with a banquet in his honor and a special technical program in which many of his colleagues participated. 10 His lecture that day entitled "With One Auspicious and One Dropping Eye ''11 is a beautifully

written testament to his career, his view of modem science, and our major focus on the calculation of multicomponent phase diagrams!

During this thirty-year period that I had the pleasure of know- ing Kubaschewski and studying his work I was always im- pressed with the high esteem in which he was held by many of his colleagues, including Spencer, Chart, Ansara, Hack, and Hayes. Indeed, several generations of thermochemists bene- fited from his research, teaching, writing, good counsel, and fellowship. It is, therefore, an honor for me to contribute to this memorial volume.

2. Calculat ion of M u l t i c o m p o n e n t Phase Diagr .ares and the A p p l i c a t i o n to C o m m e r c l a l Matermls

During the above-mentioned symposium to honor O. Kubaschewski in Aachen on 31 August 1983,9,10 Kuba re- called how difficult his first calculations of binary and ternary phase diagrams with "I~m Chart and Philip Spencer were and was surprised to see the computer extension of four- and five- component phase diagrams ! In reality, most commercial mate- rials often have six or more important alloying ingredients. Thus, calculation of multicomponent phase diagrams for com- mercial materials must deal with such problems routinely. In- deed, successful calculation of such phase equilibria and the representation of the results in a manner useful to the materials engineer is a real test of the applicability of all the experimental and theoretical studies of thermochemistry and phase equili- bria to problems of the real world.

To consider such problems, we must first address how best to represent the behavior of a real multicomponent material. One simple method, which has been suggested by J.E. Morral, H. Gupta, and co-workers, is to provide a graph of the ZPF (zero phase fraction) points during equilibrium heating or cool- ing.12,13 The phase fraction NP(*) vs temperature plot has been refined and incorporated into the Thermo-Calc software for computing multicomponent phase equilibria at the Royal Institute of Technology in Stockholm by Bo Sundman and Bo

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S e c t i o n I: B a s i c a n d A p p l i e d R e s e a r c h

i . . . . . . . . . I . . . . . . . ~ . . . . . . I " ' I . . . . . . ] . . . . . . . .

L=2 0 7 -

~176 i o2

O4

bee=B 0 2 bcc

! ~ .5=M2aC8 / l: B=3

~oo soo 1ooo 12oo 14oo 16oo

Tempera ture ~

Fig. 1 Calculated phase fraction NP(*) vs temperature curves for a steel with 0.4 wt.% C, 9.0 wt.% Co, 14.5 wt.% Cr, 5.0 wt.% Mo, 4.0 wL% Ni, and 0.35 wt.% V.

r,.,) 0

E'--

1500 ~[ ~ T

0.4 wt.7. C

I 4 0 0 ~

L+B+A

1300 - B=bce

I b c c + f c c

12oo- (B+A

Ii00.

1000.

900-

fcc+M23C7 (A+23)

A+B+23+k

8 0 0 -

700 .+ o o5

23+A+73

L

L+A(fce)

A+73 L+A+73

A+21+23

A+B+23

i 15 Welght Percent Carbon

1: *MTC $ = 73 2 : * b c c _ X 2 = B 3 : * c p h , . A 3 + 2 = KzC = 21 4" �9 *M~Co - Z3 5: *Laves p h a s e = X 6 : * fcc . .A1 = A 7: *L iqu id + L

Note: N u m b e r s 1 - 7 a t t a c h e d t o b o u n d a m e s d e n o t e a p p e a r a n c e o r d i s a p p e a r a n c e of t h e d e s i g = a t e d p h a s e .

Fig. 2 Isopleth for Fe-9 wt.% Co- 14,5 wt.% Cr-5 u t.% Mo-4 wt.% Ni-0.35 wt.% V vs wt.% C. The phase fraction NP(*) vs Tcurves shown in Fig. 1 are desigTmted at 0.4 wt.% C.

Jansson.14,15 This software and the accompanying database permit calculation o f the phase fraction NP(*) vs T curve for a

six-component high-strength steel, as shown in Fig. 1. Here the bcc phase begins to freeze just above 1400 ~ so that the

414 Journal of Phase Equilibria Vol. 14 No. 4 1993

B a s i c a n d A p p l i e d R e s e a r c h : S e c t i o n I

e, o

g r-"

1

09.

08

07.

06-

05-

o4-

03-

oz-

o.1-

o , 200

(tcc)

AA2519

(AIzCu)

, i . . . . . . . . . i . . . . . . . . . i . . . . . . . . . 300 400 500 600 T e m p e r a t u r e ~

(L)

700 800

2 5 . . . . . . . . . , . . . . . . . . . , . . . . . . . . . ''I A l 2 C u ' ~ . ~

AlzoCuzMn3 L

20 ~ 4

Z , 5 Q ~ ~ e

AITCuZFel

AA2519 I0

Mg2Siz

5 5

E-3

o . . . 2 0 0 3 0 0 4 0 0 500

'l'<.',w I,t'~ . t u I (' " ( '

I c e

AI2,?,C u l F e 4

' 5

6 0 0 7 0 0 800

Fig.3 Calculated phase fraction vs temperature curves for AlIoy AA25 I9 with 6.4Cu, 0.3Fe,0.4Mg, 0.5Mn, 0.25Si, 0.1"1"i, 0-1Zn, 0.2Zr, 0.1V (vet-%), balance A1. Note that the ordinate has been magnified in the lower panel.

fraction of liquid, which is equal to 1 above this temperature, starts to drop, vanishing just above 1200 ~ where freezing is complete. In the intervening temperature range, the fraction of the bcc (ferrite) reaches a maximum just below 1400 ~ at 0.4

(or 40 wt.%) before being replaced by the fcc (austenite), which starts to form just below 1400 ~ At 1200 ~ this alloy is completely austenitic. At lower temperatures, M7C3, M23C6, and Laves phases form, decreasing the fraction of

Joumal of Phase Equilibria Vol. 14 No. 4 I993 415

S e c t i o n I: B a s i c a n d Appl i ed R e s e a r c h

austenite. The latter phase fraction curve drops substantially when the ferrite starts to form again just above 800 ~ This program permits retrieval of the composition of all the phases present at equilibrium at each temperature. Figure 2 shows an isopleth for the base alloy as a function of carbon concentra- tion; the composition of the Fig. 1 alloy is indicated by arrows for Fig. 2 at a composition corresponding to 0.4 wt.% C. Thus, Fig. 2 is a collection of many NP(*) vs T curves at different carbon concentrations where the ZPF, i.e., NP(*) = 0 points are collected. It should be noted that the equilibrium tie lines do not lie in the plane of Fig. 2, and that with the exception of the single-phase ferrite (low carbon, near 1400 ~ liquid (above 1460 ~ and austenite (1200 ~ near 0.4 wt.% C) fields, the phase fractions of each phase are not provided by Fig. 2, except that a given phase appears (or disappears) at the boundaries. It should be noted that nucleation effects or meta- stability can readily be simulated by suppressing or suspend- ing one or more phases and removing it from consideration. When this is done, new phases or old phases of different com- positions and phase fractions are displayed, as is the case in practice.

Figures 3 and 4 show similar calculations for a ten-component aluminum alloy (AA2519), 16 in which many compounds can form at low temperatures at very low phase fractions. Note that the lower panel of Fig. 3 shows NP(*) running from 0 to 0.025 (i.e., 0 to 2.5 wt.%), whereas in the upper panel NP(*) runs be- tween 0 and 1 (i.e., 0 to 100 wt.%). Figure 3 shows that the

T

=- o

o

?

4

t z 45-~

40! CU

35! AA2519 f

;%00 300 400 500 600 700 800

Temperature ~

Fig. 4 Equilibrium concentration of Cu, Mg, Mn, and Si in the fcc phase as a function of temperature.

, o o o \ . . . . . . , . . . . . . < ~ . . . . . . . . . . , . . . . . . \ , . . . . . . . . . . . . . . . . . . ~ . . . . . . . . .

900- \4 TE+CR+MN ~ \ CB+TE+CR+AY

\ TE+CR+UN+Au 5

600- AY+MN+CB

I /3 AY+MN+CB+YZ 5 o o : .~

[ [ / 2: MN = monoelime .It 4oo: I I / 3: CR ...... dum (AIz03~ ~

r I [ AY+MN+YZ 4: TE = tetragonal "~ ' / / 5: AY = 5A lzO3.3Yz0 3 I~

I /7 6. cz = CaZrO~ IF [ [ 7: YZ = ZrsY4Ox2 1[-

3 0 ~ %/7 ~ AY+MN+CZ ' -

200 . . . . . . . . . ~ . . . . , . . . . . . . . , . . . . . . , . . . . . . . . . ~ . . . . . . . . . ~ . . . . . . . .

1 2 3 4 5 6 7

Weigh t P e r c e n t Y203

Fig, 5 Thermochemical model predicting the phase field of a seven-component oxide mixture (92.6 wt.% 21"O2, 0.1 wt,% MgO, 0.1 wt.% CaO, 0.1 wt.% SiO2, 0.1 wt.% A1203, 7 wt.% TiO 2 + Y203). Note: Periclase (MgO) is present throughout this entire phase field and, therefore, is not labeled.

416 Journal of Phase Equilibria Vol. 14 No. 4 1993

B a s i c a n d A p p l i e d R e s e a r c h : S e c t i o n I

o

c~

c~

0 9 t . . . . . . . . . 1 . . . . . . . . i . . . . . . . . . i . . . . . . . . . i . . . . . . . . . i . . . . . . . . . , . . . . . . . .

�9 Tetragonal 0a I [] Monoelinic

ovq

~176 1 0 4 ~

: D

0 1 2 3 4 5 6

Weight Percent YeOa

Fig. 6 Equilibrium phase fractions of the monoclinic and tetragonal phases as a function of weight percent. Y203 in 93 wt. % Z/O2-Y203- TiO 2 solid solutions at 800 ~

main precipitate is A12Cu, which begins to form near 520 ~ Figure 4 shows the composition of the elements dissolved in the fcc aluminum-rich matrix. It shows that copper is the most prominent solute whose concentration increases to about 4.5 wt.% at 525 ~ Below 525 ~ the precipitation of A12Cu de- pletes the fcc aluminum-rich matrix of copper. The descrip- tions of this alloy shown in Fig. 3 and 4 mirror the suggested heat treatment of AA2519 which calls for solution treatment at 537 ~ to maximize Cu in solution followed by aging at 163 ~ to precipitate A12Cu. Isopleths for AA2519 vs Cu, Mg, Mn, and Si can be readily generated comparable to Fig. 2 in order to investigate changes in phase stability across the accepted com- positional limits for this commercial alloy or to predict the be- havior when the alloy is brazed with a filler alloy containing high silicon concentrations.

One final application of this method is shown in Fig. 5 and 6 applied to plasma-sprayed ceramic thermal barrier coatings (TBC's) for high-temperature engines composed of ZrO2, Y203, TiO 2 with minor quantities of MgO, CaO, SiO 2, and A120 3. My colleague, Derek Mess, has been synthesizing a va- riety of ZrO2-Y203-based TBC powders by means of sol gel methods for plasma spraying applications. He was interested in defining the relative fraction of tetragonal and monoclinic phases in such "alloys" as a function of Y203 and "riO 2 con- centration, since TiOz is a much cheaper additive than Y203, and the coating lifetime is thought to be increased when the fraction of non-transformable tetragonal phase is increased. Accordingly, we created a database for the seven-component ZrO2-based system from our earlier study 17 and computed the

phase fraction and isopleth shown in Fig. 5 and 6 as an initial guide to our study.

3. C o n c l u s i o n

At the end of Kuba's "Good-bye Speech," "With One Auspi- cious and One Dropping Eye, ''11 he recalled that our old friend John Elliott used to say (and Kuba agreed) that there are some investigators "who seem to believe that it is easier to perform new measurements than to look up the results of their prede- cessors."

I believe that the currently available software and databases for computing multicomponent phase diagrams for commercial materials provide a convenient and accurate means for "look- ing up" results we can reasonably infer before we launch ex- pensive experimental studies. By doing this, we can lower the cost and increase the efficiency of our work.

C i ted R e f e r e n c e s

1. L. Kaufman and M. I-fillert, Martensite, A Tribute to Morris Cohen, G.B. Olson and W.S. Owen, Ed., ASM Intemalional, Metals Park, OH,44 (1992).

2. O. Kubaschewski and O.von Goldbeck, Trans. Faraday Soc., 45, 958 (1949).

3. O.KubaschewsldandE.L.Evans, MetaUurgicalThermochemistry, Pergamon Press, London (1955).

4. O. Kubaschewski and J.A. Caterall, Thermochemical Data of Al- loys, Pergamon Press, London (1956).

5. "l'he Physical Chemistry of Metallic Solutions and Intermetallic Compounds," National Physical Laboratory Symposium No. 9, 4-6 June 1958, Organized by O. Kubaschewski, I-IMSO, London (1959).

6. O. Kubaschewski, Phase Stability inMetals andAlloys, P.S. Rud- man, J. Stringer, and R.I. Jaffee, Ed., McGraw-Hill, New York, 67 (1967).

7. O. Kubaschewski and W. Slough, Prog. Mater. Sc~, 14, 1 (1969). 8. "Metallurgical Chemistry," Proceedings of a symposium held at

Brunel University and the National Physical Laboratory, July 1971, Organized by O. Kubaschewski, HMSO, London (1972).

9. L. Katffman and H. Nesor, Z MetallkzL, 64, 2 49 (1973 ).

10. L. Kaufman, CALPHAD, 7, 290(1983). 11. O. Kubaschewsld, CALPHAD, 8, 355 (1984). 12. J.E. Morral and H. Gupta, CALPHAD, 13, 317 (1989). 13. H. Gupt~ J.E. Mortal, and H. Nowotny, Scr. MetalL, 20, 889 (1986). 14. B. Sundman, B. Jansson, and J.-O. Andersson, CALPHAD, 9, 153

(1985). 15. B. Sundman, Computer Aided Innovation of New Materials, M.

Doyama, et al., Ed., North-Holland Publishers, Amsterdam, 733 (1991).

16. L. Kaufman, "Calculation of Phase Diagrams for Commercial Alu- minum Alloys," to be published in Conference Proceedings, CAMSE 92, Yokohama, Japan, 23 September 1992, M. Doyam~ Ed., North-Holland Publishers, Amsterdam (1993).

17. L. Kaufman, UserApplications of Alloy Phase Diagrams, ASM In- ternational, Metals Park, Ohio, 145-176 (1987).

Journal of Phase Equilibria VoI. 14 No. 4 1993 417