The role of unpaired forces in the lattice dynamics of covalent crystals

TLDR: In this article, a model for the lattice dynamics of covalent crystals was developed, which is used to calculate the phonon dispersion relations of diamond, silicon, and germanium at all the irreducible points of the first Brillouin zone and to calculate phonon density of states, lattice specific heats, and Debye characteristic temperatures.

Abstract: To study the lattice dynamics of covalent crystals, a model which, in addition to central (two‐body) forces, involves unpaired forces of the type of D.C. Gazis, F. Herman, and R.F. Wallis [Phys. Rev. 119, 533 (1960)] has been developed. The model is used to calculate the phonon dispersion relations of diamond, silicon, and germanium at all the irreducible points of the first Brillouin zone and to calculate phonon density of states, lattice specific heats, and Debye characteristic temperatures. The R. Brout [Phys. Rev. 113, 43 (1954)] sum rule for ionic crystals as extended by H.B. Rosenstock [Phys. Rev. 129, 1959 (1963)]; H.B. Rosenstock and G. Blanken [Phys. Rev. 145, 546 (1966)] for diamond and zincblende crystals has also been verified by calculating the compressibilities of the above crystals. The model satisfies all the symmetry requirements of the perfect crystals. Results show reasonably good agreement with available experimental data.