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Defects in Aluminum: A Density Functional Study

Published online by Cambridge University Press:  10 February 2011

R. Ramprasad
Affiliation:
Department of Physics and Astronomy and Center for Advanced Studies, University of New Mexico, Albuqerque, NM 87131
S. R. Atlas
Affiliation:
Department of Physics and Astronomy and Center for Advanced Studies, University of New Mexico, Albuqerque, NM 87131
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Abstract

We describe a new method of examining defects and their interactions with each other at a microscopic level of detail. This involves efficiently calculating local properties at arbitrary spatial points, applicable in periodic supercell calculations. In particular, we have identified two quantities, the local energy density, ε(r) and the local stress density, σαβ(r), which are constrained to yield the total energy and the average macroscopic stress tensor, respectively, when integrated over the entire volume of the supercell. In systems with defects, these microscopic quantities provide important insights about the local nature and environment of defects. For the test case of bulk Al with a point defect, we demonstrate that these concepts result in meaningful local quantities characteristic to the point defect. We propose to use these methods to study the microscopic nature of vacancies at a grain boundary and their interaction with each other.

Type
Research Article
Copyright
Copyright © Materials Research Society 1998

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References

REFERENCES

[1] Oates, A. S., Microelectron. Reliab. 36, p. 925 (1996).Google Scholar
[2] (a) Chetty, N. and Martin, R. M., Phys. Rev. B 45, p. 6074 (1992);Google Scholar
(b) Chetty, N. and Martin, R. M., Phys. Rev. B 45, p. 6089 (1992).Google Scholar
[3] (a) Schrödinger, E., Ann. Phys. (Leipzig) 82, p. 265 (1927);Google Scholar
(b) Feynmann, R. P., Bachelors' thesis (MIT, 1939, unpublished);Google Scholar
(c) Pauli, W., in Handbuch der Physik, Band XXIV, Teil 1 (Springer, Berlin, 1933), pp. 83272; Vol. V, Part 1 (1958).Google Scholar
[4] (a) Nielsen, O. H. and Martin, R. M., Phys. Rev. B 32, p. 378U (1985), and references therein;Google Scholar
(b) Nielsen, O. H. and Martin, R. M., Phys. Rev. B 32, p. 3792 (1985).Google Scholar
[5] Ziesche, P., Gräfenstein, J. and Nielsen, O. H., Phys. Rev. B 37, p. 8167 (1988);Google Scholar
(b) Godfrey, M. J., Phys. Rev. B 37, p. 10176 (1988);Google Scholar
(c) Folland, N. O., Phys. Rev. B 34, p. 8296 (1986); and references therein.Google Scholar
[6] Ho, I., Lee, S. and Chang, K. J., Phys. Rev. B, 51, p. 14697 (1995).Google Scholar
[7] Ramprasad, R. and Atlas, S. R., in preparation.Google Scholar
[8] (a) Hohenberg, P. and Kohn, W., Phys. Rev. 136, p. B864 (1964);Google Scholar
(b) Kohn, W. and Sham, L. J., Phys. Rev. 140, p. A1133 (1965).Google Scholar
[9] Pickett, W. E., Comp. Phys. Reports 9, p. 115 (1989).Google Scholar
[10] Teter, M. P., Payne, M. C. and Allan, D. C., Phys. Rev. B 40, p. 12255 (1989).Google Scholar
[11] Hamman, D. R., Phys. Rev. B 40, p. 2980 (1989);Google Scholar
Kleinman, L. and Bylamler, D. M., Phys. Rev. Lett. bf 48, p. 1425 (1982).Google Scholar
[12] Wright, A. F. and Atlas, S. R., Phys. Rev. B 50, p. 15248 (1994).Google Scholar
[13] Murr, L. E., Interfacial Phenomena in Metals and Alloys (addison-Wesley, 1976), Vol. 2.Google Scholar
[14] Chetty, N., Weinert, M., Rahman, T. S. and Davenport, J. W., Phys. Rev. B, 52, p. 6313 (1995).Google Scholar
[15] Ehrhart, P., Jung, P., Schulta, H. and Ullmaier, H., in Atomic Defects in Metals, edited by Ullmaier, H., Landolt-Börnstein, New Series, Group III, Vol. 25 (Springer-Verlag, Berlin, 1990).Google Scholar