Many-body forces in solids: elastic constants of diamond-type crystals

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Abstract
A microscopic theory of the elastic constants of diamond-type crystals is presented. With a potential range not exceeding the third-nearest-neighbour distance, a crystal potential function of the most general form is constructed, subject only to the requirements of translational and rotational invariance. This potential is shown to contain two-, three- four- and five-body interaction terms. Neglecting anharmonic terms, the potential is completely described by six parameters Pi. Expressions for the first-order elastic constants, and for the partial, inner and total elastic constants at second order, are obtained in terms of these six parameters. A detailed comparison is made with previous models. Some are shown to be special cases of the general potential introduced here and to be approximately equivalent to each other.

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