First-principles calculation of the phonon spectrum of (formula presented) spinel

Physical Review B - Condensed Matter and Materials Physics

Volumn 65, Issue 9, 2002, Pages 1-5

  De Wijs, G A ^a   Fang, C M ^b   Kresse, G ^c   De With, G ^b  

^a Faculty of Sciences   (Netherlands)

^b EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

^c UNIVERSITY OF VIENNA   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84883132185     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.65.094305     Document Type: Article

References (50)

1. F. S. Galasso, Structure and Properties of Inorganic Solids (Pergamon, Oxford, 1970).
2. N. W. Grimes, Phys. Technol. 6, 22 (1975);
3. A. Zerr, G. Miehe, G. Serghiou, M. Schwarz, E. Kroke, R. Riedel, H. Fuess, P. Kroll, and R. Boehler, Nature (London) 400, 340 (1999);
4. K. E. Sickafus and R. Hughes, J. Am. Ceram. Soc. 82, 3277 (1999), and references therein.
5. E. G. Ravenstein, Nature (London) 44, 423 (1891).
6. J. M. Leger, J. Haines, M. Schmidt, J. P. Petitet, A. S. Pereira, and J. A. H. Da Jornada, Nature (London) 383, 401 (1996);
7. W. Jones and L. J. Miles, Proc. Br. Ceram. Soc. 19, 161 (1971).
8. R. J. Bratton, J. Am. Ceram. Soc. 57, 283 (1974);
9. A. Ghosh, et al., J. Am. Ceram. Soc. 74, 1624 (1991).
10. A. Govindaraj, E. Flahaut, C. Laurent, A. Peigney, A. Rousset, and C. N. R. Rao, J. Mater. Res. 14, 2567 (1999).
11. P. P. L. Regtien, Sens. Actuators 2, 85 (1981/82);
12. G. Gusmano, G. Montesperelli, E. Traversa, and G. Mattogno, J. Am. Ceram. Soc. 76, 743 (1993).
13. A. Larbot, G. Philip, M. Persin, and L. Cot, Key Eng. Mater. 132-136, 1719 (1997).
14. International Tables for Crystallography (Reidel, Dordrecht, 1983), Vol. A.
15. W. H. Bragg, Philos. Mag. 30, 305 (1915).
16. S. Nishikawa, Proc. Math. Phys. Soc. Tokyo 8, 199 (1915).
17. M. P. O’Horo, A. L. Frisillo, and W. B. White, J. Phys. Chem. Solids 34, 23 (1973).
18. L. M. Fraas, J. E. Moore, and J. B. Salzberg, J. Chem. Phys. 58, 3585 (1973).
19. J.-M. Malézieux and B. Piriou, Bull. Mineral. 111, 649 (1988).
20. A. Chopelas and A. M. Hofmeister, Phys. Chem. Miner. 18, 279 (1991).
21. H. Cynn, S. J. Sharma, T. F. Cooney, and M. Nicol, Phys. Rev. B 45, 500 (1992).
22. S. Hafner and S. Laves, Z. Kristallogr. 115, 321 (1961).
23. G. A. Slack, Phys. Rev. 134A, 1268 (1964).
24. J. Preudhomme and P. Tarte, Spectrochim. Acta, Part A 27, 1817 (1971).
25. N. W. Grimes and A. J. Collett, Phys. Status Solidi B 43, 591 (1971).
26. M. E. Striefler, and S. I. Boldish, J. Phys. C 11, L237 (1978).
27. N. W. Grimes, P. J. O’Connor, and P. Thompson, J. Phys. C 11, L505 (1978).
28. P. Thompson and N. W. Grimes, Solid State Commun. 25, 609 (1978).
29. B. Lawn, Fracture of Brittle Solids (Cambridge University Press, Cambridge, 1993);
30. T. E. Mitchell, L. Hwang, and A. H. Heuer, J. Mater. Sci. 11, 264 (1976).
31. G. Kresse and J. Hafner, Phys. Rev. B 47, 558 (1993);
32. Phys. Rev. BG. Kresse, J. Hafner49, 14251 (1994).
33. G. Kresse and J. Furthmüller, Comput. Mater. Sci. 6, 15 (1996).
34. G. Kresse and J. Furthmüller, Phys. Rev. B 54, 11169 (1996).
35. G. Kresse, J. Furthmüller, and J. Hafner, Europhys. Lett. 32, 729 (1995).
36. The Mg mass used was 24.305 a.m.u., corresponding to the natural mixture of the isotopes.
37. G. Kern, G. Kresse, and J. Hafner, Phys. Rev. B 59, 8551 (1999).
38. This procedure yields a (formula presented) matrix of longitudinal interatomic force constants (all three species can experience forces due to displacements of planes with all three kinds of species). This information is overcomplete, as a knowledge of (formula presented) and two of the Born charges completely determines all nine force constants. The (formula presented) matrix is symmetrized observing the constraints resulting from this requirement.
39. K. Kunc and R. M. Martin, Phys. Rev. Lett. 48, 406 (1982).
40. A. M. Rappe, K. M. Rabe, E. Kaxiras, and J. D. Joannopoulos, Phys. Rev. B 41, 1227 (1990).
41. D. Vanderbilt, Phys. Rev. B 41, 7892 (1990).
42. G. Kresse and J. Hafner, J. Phys.: Condens. Matter 6, 8245 (1994).
43. R. D. King-Smith, M. C. Payne, and J. S. Lin, Phys. Rev. B 44, 13063 (1991);
44. G. Kresse (unpublished).
45. D. M. Ceperley and B. J. Alder, Phys. Rev. Lett. 45, 566 (1980);
46. J. P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).
47. The cell choice 1 of International Tables for Crystallography (Ref. 9) was used.
48. E. J. Samuelson and O. Steinsvoll, J. Phys. C 8, L427 (1975).
49. W. B. White and B. A. De Angelis, Spectrochim. Acta, Part A 23, 985 (1967).
50. The four LO modes are linear combinations of the four “missing” TO modes. It is possible, however, to assign each TO mode to a specific LO mode by slowly “switching on” the corrections for the LO-TO splitting, and noting which TO mode develops from which LO mode. Assignments in Table III have been made accordingly.