Accurate Numerical Method for Calculating Frequency Distribution Functions in Solids. III. Extension to Tetragonal Crystals

The extrapolation method, initially developed by Gilat, Dolling, and Raubenheimer, has proved to be an accurate, rapid, and efficient method of calculating phonon densities of states in solids. In the present paper it is extended to tetragonal crystals and applied to white tin. The computation employs a Born—von Kármán model following Brovman and Kagan, and is based on recent experimental data by Rowe. The singularities appearing in the phonon density of states $g\left(\nu \right)$ are correlated to critical points predicted by the dispersion relations. It is found that six conspicuous singularities originate from off-symmetry directions. The resultant $g\left(\nu \right)$ is correlated to the tunneling data, and is employed for the calculation of specific-heat Debye temperature ${\Theta }_c\mathrm{}\left(T\right)\mathrm{}$.