Lattice Dynamics of Grey Tin and Indium Antimonide

We have measured the phonon-dispersion relations in symmetry directions for $\alpha -\mathrm{S}\mathrm{n}$ at 90 °K and InSb at 300 °K. A limited number of measurements were made at 240 °K in $\alpha -\mathrm{S}\mathrm{n}$ to look for effects associated with the phase transition, but none were found. The two dispersion relations are qualitatively similar, the main differences arising from the lower symmetry and a slight general drop in frequency in going from $\alpha -\mathrm{S}\mathrm{n}$ to InSb. Systematic trends in the comparison with other group-IV and III-V semiconductors can be seen. We have found second-neighbor shell models which give a reasonable description of the dispersion relations but in which the parameters are poorly defined and apparently devoid of physical meaning. The microscopic implications of this fact are discussed.