Study of the Homology between Silicon and Germanium by Thermal-Neutron Spectrometry

The phonon dispersion relations in silicon and germanium are found to be nearly homologous with small but significant deviations. These results, which have been obtained by thermal-neutron spectrometry, are strongly supported by an analysis in which comparison is made with elastic constants, heat capacities, and Raman frequencies for these elements. Previously observed discrepancies between results obtained from shell-model calculations and from heat-capacity measurements are explained. Attempts are made to elucidate the origin of the observed differences between the dimensionless phonon frequencies of group-IV $B$ elements with the diamond-type crystal structure.