Thermodynamic theory of the lead zirconate-titanate solid solution system, part V: Theoretical calculations

Abstract

In this final paper of a sequence of five papers presenting details of a thermodynamic phenomenology for the whole PbZrO3 : PbTiO3 solid solution family, the constants derived in the earlier papers are used to calculate the temperature and composition dependence of the Elastic Gibbs Free Energy ΔG 1 at zero stress, the spontaneous electric polarization and spontaneous tilt of the oxygen octahedra in a single domain, the anisotropic weak field dielectric permittivity and the piezoelectric constants for compositions all across the phase diagram. These data can be used to determine the intrinsic component of the behavior of any pure lead zirconate : lead titanate in any part of the phase field and at any temperature, and thus can form a first step in the separation of the experimentally observed properties into their intrinsic (single domain) component and their extrinsic domain and defect related responses. The function proposed is certainly not the final word for PZT, and will clearly be subjected to continuous modification and improvement as new and better experimental data becomes available. The purpose of the exercise has been to correlate a very wide panoply of experimental data with a single function, and to extract from it the constants which would be directly accessible if single domain single crystals could be grown at the interesting PbZrO3 : PbTiO3 compositions.