Dynamics of Simple Lattices

Abstract
The critical points (points where ωxi=0 for all i=1, 2, 3) of the frequency ω of the lattice vibrations in wave number space (x1, x2, x3), shown by Van Hove to exist for a very general class of crystals, are located for the monatomic simple, face-centered, and body-centered cubic lattices. The position and nature of the resulting singularities in the frequency distribution are found as a function of the ratio of force constants for second-nearest neighbors and nearest neighbors, and the qualitative features of the frequency distribution are thus determined. A method for using the information so obtained to determine the frequency distribution quantitatively is outlined.

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