Higher Order Dipole Moments of Harmonic and Anharmonic Crystals

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Abstract
It is shown that the dipole moment of a harmonic crystal is a linear function of the nuclear displacements and thus that the higher order moment coefficients vanish in this case. Formal expressions for the first- and second-order moment coefficients which are also suitable for calculation have been derived for general anharmonic crystals. These expressions have been used in an explicit calculation of these two coefficients for a simple one-dimensional model of an anharmonic NaCl-type crystal in which the ions are approximated by the shell model. The first-order moment includes a small deformability contribution which is essentially the same as that obtained by Dick and Overhauser. The second-order moment for this model is proportional to the anharmonicity and to the deformability term in the first-order coefficient. It is shown that the contribution of the second-order moment to the two-phonon infrared absorption is much less important in ionic crystals than that due to anharmonicity alone.

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