Statistical Theory for Displacement Ferroelectrics

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Abstract
A statistical approximation is developed for displacement ferroelectrics which enables dielectric properties to be described directly in terms of a limited number of microscopic parameters. In particular, for systems with only one grossly temperature-dependent optic mode of lattice vibration, the number of parameters is sufficiently few that they can be overdetermined by a direct comparison of theory with dielectric properties alone. These microscopic parameters are very much more closely connected with the fundamental microscopic forces in the system than are the more familiar macroscopic (thermodynamic) parameters. For a single-soft-mode system, many dielectric properties are calculated quantitatively in terms of the microscopic parameters. These properties include polarization, soft-mode frequency, static and dynamic susceptibilities, all as functions of temperature both close to and away from the Curie point. Sections discussing the order of the phase transition and some nonlinear properties of the polar phase are also presented. In parts II and III of the present series of papers the method is extended and used to discuss in detail the dielectric properties of lithium tantalate.