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Vacancy Properties In 5d Bcc Transition Metals: Ab Initio Study At Finite Electron Temperature

Published online by Cambridge University Press:  10 February 2011

Alessandra Satta ,
F. Willaimel  and
Stefano de Gironcoli
Alessandra Satta
Affiliation:
Section de Recherches de Métallurgie Physique, CEA/Saclay, 91191 Gif/Yvette, France Istituto Nazionale per la Fisica della Materia (INFM) and Dipart. di Scienze Fisiche, Universitá di Cagliari, via Ospedale 72, 09124 Cagliari, Italy
F. Willaimel
Affiliation:
Section de Recherches de Métallurgie Physique, CEA/Saclay, 91191 Gif/Yvette, France
Stefano de Gironcoli
Affiliation:
Istituto Nazionale per la Fisica della Materia (INFM) and Scuola Internazionale Superiore di Studî Avanzati (SISSA) via Beirut 2–4, 34014 Trieste, Italy
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Abstract

The self-diffusion constants for the monovacancy mechanism in the 5d transition-metals with bcc structure (β-Hf, Ta and W) are investigated by first-principles pseudopotential calculations within the framework of the Local Density Functional Theory. The formation and migration energies, calculated for relaxed configurations using supercells containing 27 and 54 atomic sites, are in quite good agreement with experimental data in Ta and W, with a discrepancy lower than 10 %. Preliminary results in β-Hf using smaller supercells suggest very large relaxation energies. The effect of finite electron-temperature is shown to be quite important, and very different from one element to the other: the electron contribution to the activation entropy is negative in Ta and positive in W, reaching respectively −2 kB and 2 kB at the melting temperature. Using simple estimates for the attempt frequencies and the vibrational formation entropies, the calculated self-diffusion coefficient is in exceptional agreement with experiments in W, and clearly reproduces an accelerated diffusivity in Ta.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 481: Symposium P – Science and Technology of Semiconductor Surface Preparation , 1997 , 189
Copyright
Copyright © Materials Research Society 1998

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References

REFERENCES

1. Martin, G. and Bellon, P., Sol. Stat. Phys. 50, 189 (1997).Google Scholar
2. Flynn, C. P., in Point Defects and Diffusion, (Clarendon Press, Oxford, 1972).Google Scholar
3. De Vita, A., and Gillan, M. J., J. Phys. Cond. Matt. 3, 6225 (1991).Google Scholar
4. Frank, W., Breier, U., Elsässer, C. and Fähnle, M., Phys. Rev. B 48, 7676 (1993).Google Scholar
5. Breier, U., Frank, W., Elsässer, C., Fiänle, M. and Seeger, A., Phys. Rev. B 50, 5928 (1994).Google Scholar
6. Korhonen, T., Puska, M. J. and Nieminen, R. M., Phys. Rev. B 51, 9526 (1995).Google Scholar
7. Frank, W., Breier, U., Elsässer, C. and Fähnle, M., Phys. Rev. Lett. 77, 518 (1996).Google Scholar
8. Köhler, U., and Herzig, C., Phil. Mag. A 58, 769 (1988).Google Scholar
9. Hamann, D. R., Schl¨ter, M. and Chiang, C., Phys. Rev. Lett. 43, 1494 (1979).Google Scholar
10. Chadi, D. J. and Cohen, M. L., Phys. Rev. B 8, 5747 (1973); H.J. Monkhorst and J.D. Pack Phys. Rev. B, 13, 5188 (1976).Google Scholar
11. Methfessel, M. and Paxton, A. T., Phys. Rev. B 40, 3616 (1989).Google Scholar
12. de Gironcoli, S., Phys. Rev. B 51, 6773 (1995).Google Scholar
13. Gillan, M. J., J. Phys. Cond. Matt. 1, 689 (1989).Google Scholar
14. Marchese, M., Jacucci, G., and Flynn, C. P., Phil. Mag. Lett. 57, 25 (1989).Google Scholar
15. Willaime, F. and Massobrio, C., in Defects in Materials edited by Bristowe, Paul D., Ernest Epperson, J., Griffith, Joseph E., Liliental-Weber, Zuzanna (Mater. Res. Soc. Proc. 209, Pittsburgh, PA, 1991) pp. 293–298.Google Scholar
16. Kittel, C., Introduction to Solid State Physics 5th ed. (John Willey, New York, 1976).Google Scholar
17. Schultz, H., in Atomic Defects in Metals, Landolt Börnstein, New Series, group III, edited by H., Ullmaier, Vol.25 (Springer, Berlin, 1991), p. 115.Google Scholar
18. Herzig, C., Manke, L. and Bussmann, W., Point Defects and Defect Interactions in Metals, edited by Takamura, J. I., Doyama, M. and Kiritani, M. (Univ. Tokyo Press, 1982) p. 578–581.Google Scholar
19. Schober, H. R., Petry, W. and Tramapenau, J., J. Phys. Condens. Mat. 4, 9321 (1992).Google Scholar
20. Er\sson, O., Wills, J. M., and Wallace, D., Phys. Rev. B 46, 5221 (1992).Google Scholar
21. Callaway, J. and March, N. H., Solid State Phys. 38, 136 (1984).Google Scholar
22. Satta, A., Willaime, F., and de Gironcoli, S., Phys. Rev. B (to be published).Google Scholar
23. Watson, R. E. and Weinert, M., Phys. Rev. B 30, 1641 (1984).Google Scholar
24. Hatcher, R. D., Zeller, R., and Dederichs, P. H., Phys. Rev. B 19, 5083 (1979).Google Scholar