Accurate Numerical Method of Calculating Frequency Distribution Functions in Solids. II. Extension to hcp Crystals

Abstract

In a recent article by the same authors, an accurate and rapid method for calculating frequency distribution functions has been described. This method is here extended to include hexagonal close-packed crystals only, but it is shown that it can be used for crystals of any symmetry. This method is applied to beryllium, magnesium, and zinc, for which there exist satisfactory force models derived from experiments of inelastic coherent scattering of slow neutrons. These models have also been used to derive the phonon dispersion relations along nine high-symmetry directions, which are used to identify critical points observed in the frequency distribution functions. For each metal, there is at least one major critical point which could not be correlated to the high-symmetry branches. The phonon frequency distribution function $g\left(\nu \right)$ of beryllium indicates that it should be a favorable case for studying effects associated with heavy-impurity modes. The merits and also possible sources of error of this procedure are discussed. It is strongly recommended that the method be applied to calculations of electronic density of states.