Three-Phase States

Abstract

Experimental studies on FEs and related materials show that they are characterized by various heterophase states. Amongst the heterophase states that have been studied in the last decades, the three-phase states are of particular interest for a number of reasons. First, the three-phase states appear at almost equal volume densities of the free energy of the coexisting phases. This phase coexistence is often affected by an internal stress field [1, 2, 3, 4] caused by jumps in the unit-cell parameters at the first-order phase transition. Changes in temperature and molar concentration favour the appearance of the three-phase states in perovskite-type solid solutions [5, 6, 7, 8, 9] near the MPB. Second, the three-phase states in FEs and related materials are observed, as a rule, in fairly narrow temperature and molar-concentration ranges [1, 5, 6, 7, 8, 9, 10], under electric or mechanical fields [1] on certain directions, etc. Third, the effective stress relief in the three-phase region promotes a decrease in the energy of the heterophase system as a whole and, thereby, plays an important role in the kinetics of the structural phase transitions. Fourth, the presence of the neighbouring phases with different types of domains (including the intermediate FE phases in PZT, PMN–xPT, PZN–xPT, and \((1 - x)\mathrm{BiFe{O}_{3}} - x{\mathrm{PbTiO}}_{3}\)) [5, 7, 8, 9, 10, 11] makes the problem of the three-phase states more complicated. This circumstance stimulates the study of possible variants of domain orientations and elastic matching to describe the phase coexistence.