Crystal Vibrations of Silicon by the Use of Valence Force Potentials

The dispersion curves for silicon in the symmetry directions [ζ, 0, 0], [ζ, ζ, 0] and [ζ, ζ, ζ] are calculated using valence force potentials. Two different models have been used, the one with three valence force constants and the other with six valence force constants. The initial set of three valence force constants have been derived by incorporating Lippincott potential in the general valence force field for silicon. The force constants have been refined using a manual method and further by a least square fitting program with some known neutron scattering frequencies. The results with the six adjusted valence force constants potential model are in good agreement with the experimental results. The Debye characteristic temperatures have been calculated and they are in good agreement with the experimental values.