Theory of the Third-Order Elastic Constants of Diamond-Like Crystals

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Abstract
A calculation of the third-order elastic constants of silicon, germanium, and other diamond-like crystals is presented which is based on a previously published method of setting up a suitable form for the elastic strain energy of a crystal. The six third-order constants are calculated in terms of three anharmonic first-and second-neighbor force constants and the two previously determined harmonic force constants. The experimental values of the six coefficients are well fitted by the theoretical expressions involving these three anharmonic force constants. The valence-electron interactions are discussed in the light of the values deduced for these force constants.