Dynamics of Simple Lattices
- 15 January 1955
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review B
- Vol. 97 (2), 290-303
- https://doi.org/10.1103/PhysRev.97.290
Abstract
The critical points (points where for all ) of the frequency of the lattice vibrations in wave number space (), 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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