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First-principles study of phase stability of Ti–Al intermetallic compounds

  • Mark Asta (a1), Didier de Fontaine (a1) and Mark van Schilfgaarde (a2)


Thermodynamic and structural properties of fcc- and hcp-based Ti–Al alloys are calculated from first-principles and are used to perform an ab initio study of phase stability for the intermetallic compounds in this system. The full potential linear muffin tin orbital method is used to determine heats of formation and other zero-temperature properties of 9 fcc- and 7 hcp-based intermetallic compounds, as well as of elemental fcc and hcp Ti and Al. From the results of these calculations, sets of effective cluster interactions are derived and are used in a cluster variation method calculation of the solid-state portion of the composition-temperature phase diagram for fcc- and hcp-based alloy phases. The results of our calculations are compared with those of experimental studies of stable and metastable phases in the Ti–Al system.



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1Cahn, R. W., Mater. Res. Bull. XVI, 18 (1991).
2Fleischer, R. L., Dimiduk, D. M., and Lipsitt, H. A., Annu. Rev. Mater. Sci. 19, 231 (1989).
3Yamaguchi, M. and Umakoshi, Y., Prog. Mater. Sci. 34, 1 (1990).
4Kattner, U. R., Lin, J-C., and Chang, Y. A., Metall. Trans. A 23A, 2081 (1992).
5Murray, J. L., in Phase Diagrams ofBinary Titanium Alloys, edited by Murray, J.L. (ASM INTERNATIONAL, Metals Park, OH, 1987), pp. 1224.
6Loiseau, A., van Tendeloo, G., Portier, R., and Ducastelle, F., J. Physique 46, 595 (1985).
7Müda, R., Hashimoto, S., and Watanabe, D., Jpn. J. Appl. Phys. 21, L59 (1982).
8Loiseau, A. and Lasalmonie, A., Acta Crystallogr. B 41, 411 (1985).
9Raman, A. and Schubert, K., Z. Metallk. 56, 44 (1965).
10van Loo, F.J. and Rieck, G.D., Acta Metall. 21, 73 (1973).
11Loiseau, A., Thesis, L'Universite Pierre et Marie Curie, (1985).
12Schuster, J. C. and Ipser, H., Z. Metallk. 81, 389 (1990).
13Oehring, M., Klassen, T., and Bormann, R., unpublished.
14Srinivasan, S., Desch, P. B., and Schwarz, R. B., Scripta Metall. 25, 2513 (1991).
15Schwarz, R. B., Srinivasan, S., and Desch, P. B., Mater. Sci. Forum 89–90, 595 (1992).
16Schwarz, R. B., Desch, P. B., Srinivasan, S., and Nash, P., Nano Structured Materials 1, 37 (1992).
17Janowski, G. M. and Stafford, G. R., Metall. Trans. A 23A 2715 (1992).
18Raman, A. and Schubert, K., Z. Metallk. 56, 40, 99 (1965).
19Virdis, P. and Zwicker, U., Z. Metallk. 62, 46 (1971).
20Mabuchi, H., Hirakawa, K., Tsuda, H., and Nakayama, Y., Scripta Metall. 24, 505 (1990).
21Mabuchi, H., Hirukawa, K., and Nakayama, Y., Scripta Metall. 23, 1761 (1989).
22Mazdiyasni, S., Miracle, D. B., Dimiduk, D. M., Mendiratta, M. G., and Subramanian, P. R., Scripta Metall. 23, 327331 (1989).
23Karpe, N., Kyllesbech Larsen, K., and Bøttiger, J., Phys. Rev. B 46, 2686 (1992).
24Hong, T., Watson-Yang, T. J., Guo, X-Q., Freeman, A. J., Oguchi, T., and Xu, J-h., Phys. Rev. B 43, 1940 (1991).
25Hong, T., Watson-Yang, T. J., Freeman, A. J., Oguchi, T., and Xu, J-h., Phys. Rev. B 41, 12462 (1990).
26Yoo, M. H. and Fu, C. L., ISIJ Int. 31, 1049 (1991); Fu, C.L. and Yoo, M.H., Mater. Chem. Phys. 32, 25 (1992) and Philos. Mag. Lett. 62, 159 (1990).
27Fu, C. L., J. Mater. Res. 5, 971 (1990).
28Nicholson, D. M., Stocks, G. M., Temmerman, W. M., Sterne, P., and Pettifor, D. G., in High Temperature Ordered Intermetallic Alloys III, edited by Liu, C.T., Taub, A. I., Stoloff, N. S., and Koch, C.C. (Mater. Res. Soc. Symp. Proc. 133, Pittsburgh, PA, 1989), p. 17.
29Singh, P. P., Asta, M., de Fontaine, D., and van Schilfgaarde, M., in Alloy Phase Stability and Design, edited by Stocks, G. M., Pope, D. P., and Giamei, A. F. (Mater. Res. Soc. Symp. Proc. 186, Pittsburgh, PA, 1991), p. 41.
30Carlsson, A. E. and Meschter, P. J., J. Mater. Res. 4, 1060 (1989).
31Chubb, S. R., Papconstantopoulos, D. A., and Klein, B. M., Phys. Rev. B 38, 12120 (1988); Mehl, M.J., Osburn, J. E., Papaconstantopoulos, D. A., and Klein, B. M., in Alloy Phase Stability and Design, edited by Stocks, G. M., Pope, D. P., and Giamei, A.F. (Mater. Res. Soc. Symp. Proc. 186, Pittsburgh, PA, 1991), p. 277.
32Morinaga, M., Saito, J., Yukawa, N., and Adachi, J., Acta Metall. 38, 25 (1990).
33Asta, M., de Fontaine, D., van Schilfgaarde, M., Sluiter, M., and Methfessel, M., Phys. Rev. B 46, 5055 (1992).
34Kikuchi, R., Phys. Rev. 81, 988 (1951).
35Sanchez, J. M. and de Fontaine, D., Phys. Rev. B 17, 2926 (1978).
36Sanchez, J. M., Ducastelle, F., and Gratias, D., Physica 128A, 334 (1984).
37Asta, M., Wolverton, C., de Fontaine, D., and Dreyssé, H., Phys. Rev. B 44, 4907 (1991).
38Sanchez, J. M., Stark, J. P., and Moruzzi, V. L., Phys. Rev. B 44, 5411 (1991); Takizawa, S., Terakura, K., and Mohri, T., Phys. Rev. B 39, 5792 (1989); Mohri, T., Mohri, K., Terakura, K., Oguchi, T., and Watanabe, K., Acta Metall. 36, 547 (1988); Carlsson, A.E. and Sanchez, J. M., Solid State Commun. 65, 527 (1988).
39Gratias, D., Sanchez, J. M., and de Fontaine, D., Physica 113A, 315 (1982).
40Barker, J. A., Proc. R. Soc. A 216, 45 (1953).
41Morita, T., J. Phys. Soc. Jpn. 12, 753 (1957); J. Math. Phys. 13, 115 (1972).
42Connolly, J.W.D. and Williams, A.R., Phys. Rev. B 27, 5169 (1983); Connolly, J.W.D. and Williams, A.R., in The Electronic Structure of Complex Systems, edited by Phariseau, P. and Temmerman, W. M. (1984), p. 581.
43Lu, Z. W., Wei, S-H., Zunger, A., Frota-Pessoa, S., and Ferreira, L.G., Phys. Rev. B 44, 512 (1991).
44Sluiter, M., de Fontaine, D., Guo, X. Q., Podloucky, R., and Freeman, A. J., Phys. Rev. B 42, 10460 (1990). The experimental value of the bulk modulus for fee Al given in Table I is taken from the value quoted in this reference; this value was obtained by averaging the results of various experimental measurements which were extrapolated to T = 0 K.
45McCormack, R., Asta, M., de Fontaine, D., Garbulsky, G., and Ceder, G., Phys. Rev. B (in press).
46Kudo, T. and Katsura, S., Prog. Theor. Phys. 56, 435 (1976).
47Singh, A. K. and Lele, S., Philos. Mag. B 65, 967 (1992).
48Singh, A. K. and Lele, S., Philos. Mag. B 64, 275 (1991).
49Singh, A. K., Singh, V., and Lele, S., Acta Metall. 39, 2847 (1991).
50Crusius, S. and Inden, G., in Proc. Int. Symp. on Dynamics of Ordering in Cond. Matter, edited by Komura, S. and Furukawa, H. (Plenum Press, New York, 1988), p. 139; Bichara, C., Crusius, S., and Inden, G., Physica B 182, 42 (1992).
51The term corresponding to the “empty” cluster in the expansion (3) is a configurationally invariant one that is defined as the average value of the enthalpy of formation for all atomic configurations on a given parent lattice.
52Asta, M., McCormack, R., and de Fontaine, D., Phys. Rev. B (in press).
53Kaburagi, M. and Kanamori, J., Prog. Theor. Phys. 54, 30 (1979).
54Richard, M. J. and Cahn, J. W., Acta Metall. 19, 1263 (1971).
55Allen, S. M. and Cahn, J. W., Acta Metall. 20, 423 (1972).
56Ducastelle, F., Order and Phase Stability in Alloys, Vol. 3 of Cohesion and Structure, edited by De Boer, F. R. and Pettifor, D. G. (North-Holland, New York, 1991), p. 462.
57Hohenberg, P. and Kohn, W., Phys. Rev. B 136, 864 (1964).
58Kohn, W. and Sham, L. J., Phys. Rev. A 140, 1133 (1965).
59Andersen, O. K., Jepsen, O., and Sob, M., in Electronic Band Structure and Its Applications, edited by Yussouff, M. (Springer Lecture Notes, 1987).
60Andersen, O. K., Jepsen, O., and Glotzel, D., in Highlights of Condensed Matter Theory, edited by Bassani, F., Fumi, F., and Tosi, M. P. (North-Holland, Amsterdam, 1985).
61Methfessel, M., Phys. Rev. B 38, 1537 (1988).
62van Schilfgaarde, M., Paxton, A. T., Pasturel, A., and Methfessel, M., in Alloy Phase Stability and Design, edited by Stocks, G. M., Pope, D. P., and Giamei, A. F. (Mater. Res. Soc. Symp. Proc. 186, Pittsburgh, PA, 1991), p. 107.
63von Barth, U. and Hedin, L., J. Phys. C 5, 1629 (1972).
64Gschneider, K. Jr., Solid State Physics 16, 275 (1964).
65Kubaschewski, O. and Dench, W. A., Acta Metall. 3, 339 (1955).
66Kubaschewski, O. and Heymer, G., Trans. Faraday Soc. 56, 473 (1960).
67Bormann, R., Oehring, M., PoeBnecker, W., and Leitner, G., private communication.
68Schwarz, R., Desch, P. B., and Srinivasan, S., to be published in “Statics and Dynamics of Alloy Phase Transformations,” Proc. NATO Advanced Study Institute, June 21–July 3, 1992, Rhodes.
69Bormann, R., private communication.
70Villars, P. and Calvert, L. D., Pearson's Handbook of Crystallographic Data for Intermetallic Phases, 2nd ed. (ASM INTERNATIONAL, Materials Park, OH, 1991), and references listed therein.
71Fox, A., private communication.
72de Fontaine, D. and Kulik, J., Acta Metall. 33, 145 (1985).
73Perepezko, J. H., Chang, Y. A., Seitzman, L. E., Lin, J. C., Bonda, N. R., Jewett, T. J., and Mishurda, J. C., in High Temperature Aluminides and Intermetallics, edited by Whang, S. H., Liu, C. T., Pope, D. P., and Stiegler, J. O. (Min., Met. and Met. Soc, 1990), and references therein.


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