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Theory and applications of the stress density

Alessio Filippetti

Vincenzo Fiorentini

  • Istituto Nazionale per la Fisica della Materia and Dipartimento di Fisica, Università di Cagliari, Italy
  • Materials Department, University of California, Santa Barbara, California 93106-5050

  • Istituto Nazionale per la Fisica della Materia and Dipartimento di Fisica, Università di Cagliari, Italy
  • Walter Schottky Institut, Technische Universität München, Am Coulombwall, D-85748 Garching bei München, Germany

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Phys. Rev. B 61, 8433 – Published 15 March, 2000

DOI: https://doi.org/10.1103/PhysRevB.61.8433

Abstract

Drawing on the theory of quantum-mechanical stress, we introduce the stress density in density-functional theory, and give specific prescriptions for its practical and efficient implementation in the plane-wave ultrasoft pseudopotential method within the local-density approximation. In analogy with the Chetty-Martin energy density, the stress density provides a spatial resolution of the contributions to the integrated macroscopic stress tensor. While this resolution is inherently nonunique (gauge dependent), there exist gauge-independent ways of using it in practice. Here we adopt the following ones: (a) calculating integrated macroscopic stresses over appropriately defined parts of a system; (b) analyzing macroscopic averages of the stress density; (c) analyzing changes in the stress density in response to external perturbation. The abilities of the stress density are demonstrated for a set of representative test cases from surface and interface physics: in perspective, the stress density emerges as vastly more powerful and predictive than the integrated macroscopic stress.

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References (35)

  1. R. M. Dreizler and E. K. U. Gross, Density Functional Theory (Springer, Berlin 1988).
  2. N. Chetty and R. M. Martin, Phys. Rev. B 45, 6074 (1992).
  3. V. Fiorentini and M. Methfessel, J. Phys.: Condens. Matter 8, 6525 (1996).
  4. E. Schrödinger, Ann. Phys. (Leipzig) 82, 265 (1927); W. Pauli, Handbuch der Physik, Band XXIV, Teil 1 (Springer, Berlin, 1933), pp. 83–272; ibid. Vol. V, Part 1 (1958); P. C. Martin and J. Schwinger, Phys. Rev. 115, 1342 (1959); A. Kugler, Z. Phys. 198, 236 (1967).
  5. O. H. Nielsen and R. M. Martin, Phys. Rev. Lett. 50, 697 (1983).
  6. O. H. Nielsen and R. M. Martin, Phys. Rev. B 32, 3792 (1985).
  7. O. H. Nielsen and R. M. Martin, Phys. Rev. B 32, 3780 (1985).
  8. N. O. Folland, Phys. Rev. B 34, 8296 (1986); ibid.34, 8305 (1986).
  9. H. Ibach, Surf. Sci. Rep. 29, 193 (1997).
  10. A. Filippetti and V. Fiorentini, Phys. Rev. B 60, 14 366 (1999).
  11. A. Filippetti and V. Fiorentini (unpublished).
  12. A. Dal Corso and R. Resta, Phys. Rev. B 50, 4327 (1994).
  13. P. J. Feibelman, Phys. Rev. B 50, 1908 (1994).
  14. K. Laasonen, A. Pasquarello, R. Car, Changyol Lee, and D. Vanderbilt, Phys. Rev. B 47, 10 142 (1993).
  15. A. Baldereschi, S. Baroni, and R. Resta, Phys. Rev. Lett. 61, 734 (1988).
  16. L. Colombo, R. Resta, and S. Baroni, Phys. Rev. B 44, 5572 (1991).
  17. R. D. Meade and D. Vanderbilt, in Atomic Scale Calculations in Materials Science, edited by J. Tersoff, D. Vanderbilt, and V. Vitek, MRS Symposia Proceedings No. 141 (Materials Research Society, Pittsburgh, 1989), p. 451.
  18. V. Fiorentini, M. Methfessel, and M. Scheffler, Phys. Rev. Lett. 71, 1051 (1993).
  19. P. J. Feibelman, Phys. Rev. B 51, 17 867 (1995).
  20. R. J. Needs, M. J. Godfrey, and M. Mansfield, Surf. Sci. 242, 215 (1991).
  21. C. Messmer and J. C. Bilello, J. Appl. Phys. 52, 4623 (1981).
  22. W. Weiss, W. Ranke, D. Schmeisser, and W. Gödel, Surf. Sci. 221, 91 (1989).
  23. D. K. Biegelsen, R. D. Bringans, J. E. Northrup, and L.-E. Swartz, Phys. Rev. Lett. 65, 452 (1990).
  24. R. Nötzel, L. Däweritz, and K. Ploog Phys. Rev. B 46, 4736 (1992).
  25. N. Chetty and R. M. Martin, Phys. Rev. B 45, 6089 (1992).
  26. K. Rapcewicz, B. Chen, B. Yakobson, and J. Bernholc, Phys. Rev. B 57, 7281 (1998).
  27. N. Moll, A. Kley, E. Pehlke, and M. Scheffler, Phys. Rev. B 54, 8844 (1996).
  28. E. Kaxiras, Y. Bar-Yam, J. D. Joannopoulos, and K. C. Pandey, Phys. Rev. B 35, 9625 (1987); ibid.35, 9636 (1987).
  29. G. Quian, R. M. Martin, and D. J. Chadi, Phys. Rev. B 37, 1303 (1988); ibid.38, 7649 (1988).
  30. T. Ohno, Phys. Rev. Lett. 70, 631 (1993).
  31. J. E. Northrup and S. Froyen, Phys. Rev. Lett. 71, 2276 (1993); Phys. Rev. B 50, 2015 (1994).
  32. J. A. Appelbaum, G. A. Baraff, and D. R. Hamann, Phys. Rev. B 14, 1623 (1976).
  33. S. Oppo and V. Fiorentini, Phys. Rev. Lett. 81, 4278 (1998).
  34. A. Filippetti and V. Fiorentini, Surf. Sci. 377, 112 (1997).
  35. C. E. Bach, M. Giesen, H. Ibach, and T. L. Einstein, Phys. Rev. Lett. 78, 4225 (1997).

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Phys. Rev. B 61, 8433– Published 15 March, 2000
  • Received 23 July 1999

© 2000 American Physical Society

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