A phenomenological thermodynamic energy function for PIN-PMN-PT relaxor ferroelectric single crystals

Domain engineered rhombohedral relaxor ferroelectric single crystals of PIN-PMN-PT near the morphotropic phase boundary (MPB) have stable domain structures that increase piezoelectric constants and reduce dielectric loss. They also undergo domain switching and phase transformation with temperature and applied field that make modeling the energetics of the domain formation and evolution challenging. In this work a 10th order Landau-Devonshire energy function is developed to describe the dielectric, piezoelectric and ferroelectric properties of PIN-PMN-PT with a composition near the MPB. Coefficients of the energy function were determined based on the results of many experimental measurements. The resulting energy function reproduces temperature induced phase transformations as well as polarization and strain hysteresis loops of domain engineered rhombohedral crystals at multiple temperatures. This energy function is suitable for implementation in a phase field model to further investigate the evolution of engineered rhombohedral domain structures and the energetics associated with other characteristics of rhombohedral PIN-PMN-PT ferroelectric single crystals.