Collective Behavior of Polar Impurities in Ionic Crystals

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Abstract
The purpose of this work is to construct a theory which will explain recent low-temperature measurements of the dielectric properties of KCl crystals containing substitutional hydroxyl ions. The Onsager theory of polar liquids, as extended by Pirenne to allow for the possibility of spontaneous polarization, is modified in order to take into account the strong short-range interactions that are important in solids. The theory leads to two simultaneous transcendental equations, which are solved numerically to obtain the dielectric constant for small applied fields and the spontaneous polarization as a function of temperature. The agreement with experiment is good except in the neighborhood of the Curie temperature, where the discrepancies are such as one might expect to arise from the nonuniform distribution of hydroxyl ions in the experimental samples. Theoretical results are also given for the dielectric constant measured in a large steady field or by means of a small alternating field in the presence of a large steady bias.

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