Lattice anharmonicity of diamond-structure crystals

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Abstract
Cubic and quartic anharmonic contributions to the Helmholtz free energy of a diatomic crystal are derived as functions of temperature for a general force-constant model of the crystal. The corresponding cubic and quartic anharmonic contributions to the specific heat at constant volume for diamond, germanium, silicon, and grey-tin are evaluated in the high-temperature limit with central force interactions between the atoms up to second-nearest neighbours. The effect of thermal expansion of the lattice is taken into consideration. There is excellent agreement between the experimental and calculated values of anharmonic coefficient A, defined by Cv/3Nk=1+AT, for germanium and silicon. Values of A for diamond and grey-tin are predicted for which the experimental results are not available. It is concluded that the second-nearest neighbours' contribution is much smaller than that of the nearest neighbours in the calculations of anharmonic coefficients. A for diamond-structure crystals.