A Boltzmann statistical approach for the analysis of polarization states in mixed phase ferroelectric materials: Application to morphological phase boundary

Ferroelectrics are widely used for a broad array of technological applications due to their attractive electrical and electromechanical properties. In order to obtain large functional properties, material compositions are often designed to favor the coexistence of multiple ferroelectric phases. For such compositions, the macroscopically observed properties are variously attributed to easier domain switching and/or phase transition. Nevertheless, modeling of concurrent domain switching and phase transition in mixed phase ferroelectrics remains a challenging task. Here, a methodology is presented to quantitatively evaluate the volume fractions of different domain variants in a mixed phase ferroelectric under complex electromechanical loading. The methodology combines the phenomenology of Landau free energy of ferroelectric phases with Boltzmann statistical analysis and is presented for Pb(Zr,Ti)O3 near the morphotropic phase boundary (MPB). It is shown that specific grain orientation has a significant effect on how proximity to phase boundary affects microscopic phenomena at the single-crystal level. An estimate of phase and domain switching behavior in a polycrystalline aggregate is subsequently obtained, and the resultant polarization and strain responses at the macroscopic level are computed for a material with random texture. The results indicate the progressive evolution of domain and phase fractions in a material near MPB with mixed ferroelectric phases. We show that in polycrystalline materials with compositions slightly on the tetragonal side of the MPB, grains that exhibit large 90° domain switching have a larger contribution to the macroscopic strain response as compared to grains that undergo tetragonal-to-rhombohedral phase switching.