The force constants of germanium

Abstract

Abstract The Born–von Karman Theory of the diamond-type crystal has been developed, taking into account interactions between each atom and all its neighbours out to the sixth. Explicit expressions, in terms of the force constants, are given for the frequencies and eigenvectors for normal modes with wave vectors in the symmetry directions and for the elastic constants. A non-linear least squares fit to the elastic constants and measured dispersion curves in the symmetry directions shows that it is necessary to take fifth-neighbour interactions into account in order to represent the data. Statistically significant values for the force constants were found only for first neighbour interactions and possibly three others. It is shown that the Fourier components of the elements of the dynamical matrix in reciprocal space can be obtained by Fourier analysing certain linear combinations of the dispersion curves in the symmetry directions. Further, all the linearly independent combinations of force constants which can be obtained from this data are given directly in terms of the Fourier coefficients. Certain necessary conditions on the Fourier coefficients are also derived. The present experimental data is not sufficiently complete to determine such a set of Fourier coefficients.