On the theory of ferroelectricity and anharmonic effects in crystals

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Abstract
A microscopic theory of ferroelectricity is developed in which the temperature dependence of the normal modes of vibration arises from the anharmonic interactions between those normal modes. The conditions for the stability of the crystal are discussed and detailed expressions given for the physical properties of both the distorted and undistorted phases. The parameters of the thermodynamic theory of ferroelectricity are obtained in terms of those of the microscopic theory, and the approximations and validity of the thermodynamic theory are discussed. By using a model of strontium titanate which includes the anharmonic interactions between the normal modes of vibration in a very simple way, detailed calculations have been made of the infra-red reflectivity, linear expansion and dielectric properties of strontium titanate. The fairly quantitative agreement with experiment given by these calculations and the reproduction of the features of the ferroelectric transition in barium titanate suggest that the anharmonic interactions are indeed responsible for ferroelectricity in these crystals. The calculations are also used to show some of the features which arise when the anharmonic contributions to the frequencies are comparable with the harmonic ones.