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