Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-04T20:21:41.704Z Has data issue: false hasContentIssue false
  • English
  • Français

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

Published online by Cambridge University Press:  03 March 2011

Mark Asta ,
Didier de Fontaine  and
Mark van Schilfgaarde
Mark Asta
Affiliation:
Department of Materials Science and Mineral Engineering, University of California at Berkeley, Berkeley, California 94720 and Materials Science Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
Didier de Fontaine
Affiliation:
Department of Materials Science and Mineral Engineering, University of California at Berkeley, Berkeley, California 94720 and Materials Science Division, Lawrence Berkeley Laboratory, Berkeley, California 94720
Mark van Schilfgaarde
Affiliation:
SRI International, Menlo Park, California 94025
Get access

Abstract

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.

Type
Articles
Information
Journal of Materials Research , Volume 8 , Issue 10 , October 1993 , pp. 2554 - 2568
Copyright
Copyright © Materials Research Society 1993

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1Cahn, R. W., Mater. Res. Bull. XVI, 18 (1991).CrossRefGoogle Scholar
2Fleischer, R. L., Dimiduk, D. M., and Lipsitt, H. A., Annu. Rev. Mater. Sci. 19, 231 (1989).CrossRefGoogle Scholar
3Yamaguchi, M. and Umakoshi, Y., Prog. Mater. Sci. 34, 1 (1990).CrossRefGoogle Scholar
4Kattner, U. R., Lin, J-C., and Chang, Y. A., Metall. Trans. A 23A, 2081 (1992).CrossRefGoogle Scholar
5Murray, J. L., in Phase Diagrams ofBinary Titanium Alloys, edited by Murray, J.L. (ASM INTERNATIONAL, Metals Park, OH, 1987), pp. 12–24.Google Scholar
6Loiseau, A., van Tendeloo, G., Portier, R., and Ducastelle, F., J. Physique 46, 595 (1985).CrossRefGoogle Scholar
7Müda, R., Hashimoto, S., and Watanabe, D., Jpn. J. Appl. Phys. 21, L59 (1982).CrossRefGoogle Scholar
8Loiseau, A. and Lasalmonie, A., Acta Crystallogr. B 41, 411 (1985).CrossRefGoogle Scholar
9Raman, A. and Schubert, K., Z. Metallk. 56, 44 (1965).Google Scholar
10van Loo, F.J. and Rieck, G.D., Acta Metall. 21, 73 (1973).CrossRefGoogle Scholar
11Loiseau, A., Thesis, L'Universite Pierre et Marie Curie, (1985).Google Scholar
12Schuster, J. C. and Ipser, H., Z. Metallk. 81, 389 (1990).Google Scholar
13Oehring, M., Klassen, T., and Bormann, R., unpublished.Google Scholar
14Srinivasan, S., Desch, P. B., and Schwarz, R. B., Scripta Metall. 25, 2513 (1991).CrossRefGoogle Scholar
15Schwarz, R. B., Srinivasan, S., and Desch, P. B., Mater. Sci. Forum 89–90, 595 (1992).CrossRefGoogle Scholar
16Schwarz, R. B., Desch, P. B., Srinivasan, S., and Nash, P., Nano Structured Materials 1, 37 (1992).CrossRefGoogle Scholar
17Janowski, G. M. and Stafford, G. R., Metall. Trans. A 23A 2715 (1992).CrossRefGoogle Scholar
18Raman, A. and Schubert, K., Z. Metallk. 56, 40, 99 (1965).Google Scholar
19Virdis, P. and Zwicker, U., Z. Metallk. 62, 46 (1971).Google Scholar
20Mabuchi, H., Hirakawa, K., Tsuda, H., and Nakayama, Y., Scripta Metall. 24, 505 (1990).CrossRefGoogle Scholar
21Mabuchi, H., Hirukawa, K., and Nakayama, Y., Scripta Metall. 23, 1761 (1989).CrossRefGoogle Scholar
22Mazdiyasni, S., Miracle, D. B., Dimiduk, D. M., Mendiratta, M. G., and Subramanian, P. R., Scripta Metall. 23, 327–331 (1989).CrossRefGoogle Scholar
23Karpe, N., Kyllesbech Larsen, K., and Bøttiger, J., Phys. Rev. B 46, 2686 (1992).CrossRefGoogle Scholar
24Hong, T., Watson-Yang, T. J., Guo, X-Q., Freeman, A. J., Oguchi, T., and Xu, J-h., Phys. Rev. B 43, 1940 (1991).CrossRefGoogle Scholar
25Hong, T., Watson-Yang, T. J., Freeman, A. J., Oguchi, T., and Xu, J-h., Phys. Rev. B 41, 12462 (1990).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
27Fu, C. L., J. Mater. Res. 5, 971 (1990).CrossRefGoogle Scholar
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.Google Scholar
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.Google Scholar
30Carlsson, A. E. and Meschter, P. J., J. Mater. Res. 4, 1060 (1989).CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
32Morinaga, M., Saito, J., Yukawa, N., and Adachi, J., Acta Metall. 38, 25 (1990).CrossRefGoogle Scholar
33Asta, M., de Fontaine, D., van Schilfgaarde, M., Sluiter, M., and Methfessel, M., Phys. Rev. B 46, 5055 (1992).CrossRefGoogle Scholar
34Kikuchi, R., Phys. Rev. 81, 988 (1951).CrossRefGoogle Scholar
35Sanchez, J. M. and de Fontaine, D., Phys. Rev. B 17, 2926 (1978).CrossRefGoogle Scholar
36Sanchez, J. M., Ducastelle, F., and Gratias, D., Physica 128A, 334 (1984).CrossRefGoogle Scholar
37Asta, M., Wolverton, C., de Fontaine, D., and Dreyssé, H., Phys. Rev. B 44, 4907 (1991).CrossRefGoogle Scholar
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).CrossRefGoogle Scholar
39Gratias, D., Sanchez, J. M., and de Fontaine, D., Physica 113A, 315 (1982).CrossRefGoogle Scholar
40Barker, J. A., Proc. R. Soc. A 216, 45 (1953).Google Scholar
41Morita, T., J. Phys. Soc. Jpn. 12, 753 (1957); J. Math. Phys. 13, 115 (1972).CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
43Lu, Z. W., Wei, S-H., Zunger, A., Frota-Pessoa, S., and Ferreira, L.G., Phys. Rev. B 44, 512 (1991).CrossRefGoogle Scholar
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.CrossRefGoogle Scholar
45McCormack, R., Asta, M., de Fontaine, D., Garbulsky, G., and Ceder, G., Phys. Rev. B (in press).Google Scholar
46Kudo, T. and Katsura, S., Prog. Theor. Phys. 56, 435 (1976).CrossRefGoogle Scholar
47Singh, A. K. and Lele, S., Philos. Mag. B 65, 967 (1992).CrossRefGoogle Scholar
48Singh, A. K. and Lele, S., Philos. Mag. B 64, 275 (1991).CrossRefGoogle Scholar
49Singh, A. K., Singh, V., and Lele, S., Acta Metall. 39, 2847 (1991).CrossRefGoogle Scholar
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).Google Scholar
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.Google Scholar
52Asta, M., McCormack, R., and de Fontaine, D., Phys. Rev. B (in press).Google Scholar
53Kaburagi, M. and Kanamori, J., Prog. Theor. Phys. 54, 30 (1979).CrossRefGoogle Scholar
54Richard, M. J. and Cahn, J. W., Acta Metall. 19, 1263 (1971).CrossRefGoogle Scholar
55Allen, S. M. and Cahn, J. W., Acta Metall. 20, 423 (1972).CrossRefGoogle Scholar
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.Google Scholar
57Hohenberg, P. and Kohn, W., Phys. Rev. B 136, 864 (1964).CrossRefGoogle Scholar
58Kohn, W. and Sham, L. J., Phys. Rev. A 140, 1133 (1965).CrossRefGoogle Scholar
59Andersen, O. K., Jepsen, O., and Sob, M., in Electronic Band Structure and Its Applications, edited by Yussouff, M. (Springer Lecture Notes, 1987).Google Scholar
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).Google Scholar
61Methfessel, M., Phys. Rev. B 38, 1537 (1988).CrossRefGoogle Scholar
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.Google Scholar
63von Barth, U. and Hedin, L., J. Phys. C 5, 1629 (1972).CrossRefGoogle Scholar
64Gschneider, K. Jr., Solid State Physics 16, 275 (1964).CrossRefGoogle Scholar
65Kubaschewski, O. and Dench, W. A., Acta Metall. 3, 339 (1955).CrossRefGoogle Scholar
66Kubaschewski, O. and Heymer, G., Trans. Faraday Soc. 56, 473 (1960).CrossRefGoogle Scholar
67Bormann, R., Oehring, M., PoeBnecker, W., and Leitner, G., private communication.Google Scholar
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.Google Scholar
69Bormann, R., private communication.Google Scholar
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.Google Scholar
71Fox, A., private communication.Google Scholar
72de Fontaine, D. and Kulik, J., Acta Metall. 33, 145 (1985).CrossRefGoogle Scholar
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.Google Scholar