Abstract
The Born–von Kármán 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.
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