Download PDF by A. Baldereschi, R. Resta (auth.), J. T. Devreese, V. E. Van: AB Initio Calculation of Phonon Spectra

By A. Baldereschi, R. Resta (auth.), J. T. Devreese, V. E. Van Doren, P. E. Van Camp (eds.)

ISBN-10: 1461335639

ISBN-13: 9781461335634

ISBN-10: 1461335655

ISBN-13: 9781461335658

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H. Panofsky and M. Phillips, "Classical Electricity and Magnetism", Addison-Wesley, Reading (1962) : Sec. 1 - 10. M. Rev. B9 : 1998(1974). R. Car and A. Lett. 42 : 1365 (1979). 24 A. BALDERESCHI AND R. RESTA 20. C. Pennetta and A. Ba1dereschi, Solid State Commun. to be puolished. 21. K. Rev. 126 : 1427 (1962). 22. W. Cochran, eRC Critical Rev. K. Sinha, ibid. K. Sinha, "Lattice Dynamics", F1ammarion, Paris (1978) : 7. 23. See for example W. Rev. B15 : 4789 (1977) and references therein. 24. E. E.

4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. M. T. L. Lett. 45 : 1004 (1980). J. Baur, K. Maschke and A. Ba1dereschi, Solid State Commun. 39 : 1297 (1981). C. Martin and J. Rev. L. Rev. 126 : 413 (1962); N. Rev. 129 : 62 (1963). M. H. M. Rev. A. Lorentz, "The Theory of E1etrons", Dover, New York (1952). Y. Phys. 49 : 37 (1973). P. L. Rev. W. Vinsome and D. Richardson, J. Phys. C4 2650 (1971). K. Shindo and H. Soc. Japan 43 : 899 (1977). A. Ba1dereschi and E. Tosatti, Phys. Rev. B 17 : 4710 (1978).

Using the transformation law Eq. (24) of the wave functions in the expression of the polarizability matrix Eq. e. : X(q,G,G') Furthermore + +') X (+q,G,G = (26) X is symmetric: X(q, G, G') = X(q,G' ,G) , (27) as can easily be seen from Eq. (25). The application of the above symmetry relations greatly reduces the number of independent elements of X as can be seen from Table IV. 35 AS-INITIO CALCULATION OF LATTICE DYNAMICS OF Si Table IV. Number of elements in j( for wavevectors in I::, and ions versus the number of independent elements.

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AB Initio Calculation of Phonon Spectra by A. Baldereschi, R. Resta (auth.), J. T. Devreese, V. E. Van Doren, P. E. Van Camp (eds.)


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