Phonons in Perfect Crystals

Abstract

In writing this article we have kept in mind the fact that two articles dealing with aspects of lattice dynamics have already appeared in Vol. VII of this series [9], [10]. The subject has however undergone very considerable development in the intervening decade. In particular, the experimental technique of neutron inelastic scattering has made possible the determination of the form of phonon dispersion curves for practically the first time, and unexpected features of interatomic forces have become apparent. Secondly, new mathematical techniques have made it possible to evaluate the influence of anharmonic effects on the physical properties of crystals in almost as much detail as these had been worked out formerly on the basis of the harmonic approximation. We have therefore devoted a considerable part of this article to these new developments. In order to make the account more nearly complete, we have included sections (notably A and C) which cover much the same ground as was covered in the articles by Blackman [9] and Leibfried [10]; where possible we have discussed the topics concerned from a different approach. In an Appendix we have summarised the principal features of the theory of thermodynamic Green’s functions, as applied to the evaluation of those physical properties of crystals which involve phonons.