Lattice theory of third order elastic constants of germanium and silicon

Abstract

The lattice theory of third order elastic constants is applied to germanium and silicon. For general interactions up to second neighbors, the second and third order coupling parameters are worked out for the germanium lattice. There are 26 independent parameters which reduce to 3 when only nearest neighbor interaction is considered. In the latter case 3 simple identities are obtained among the second and third order elastic constants. These identities are not satisfied by the experimental values indicating that forces of longer range are important for third order elastic constants in these crystals. Cochran's nearest neighbor shell model does not resolve this difficulty. The present results are compared with the recent work of Keating on the second and third order elastic constants of these crystals.