Interatomic forces, phonons, the Foreman-Lomer Theorem and the Blackman Sum Rule

Details Interatomic forces, phonons, the Foreman-Lomer Theorem and the Blackman Sum Rule Interatomic forces, phonons, the Foreman-Lomer Theorem and the Blackman Sum Rule

2011-11-30

arxiv.org/abs/1112.0209v1

International Journal of Modern Physics B 15 3439-3452 (2001)

Physics

Condensed Matter

Statistical Mechanics

13 pages pdf

Scientific paper

10.1142/S0217979201007269

Foreman and Lomer proposed in 1957 a method of estimating the harmonic forces between parallel planes of atoms of primitive cubic crystals by Fourier transforming the squared frequencies of phonons propagating along principal directions. A generalized form of this theorem is derived in this paper and it is shown that it is more appropriate to apply the method to certain combinations of the phonon dispersion relations rather than to individual dispersion relations themselves. Further, it is also shown how the method may be extended to the non-primitive hexagonal close packed and diamond lattices. Explicit, exact and general relations in terms of atomic force constants are found for deviations from the Blackman sum rule which itself is shown to be derived from the generalized Foreman-Lomer theorem.

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