A Boltzmann statistical approach for the analysis of polarization states in mixed phase ferroelectric materials

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 a coexistence of multiple ferroelectric phases. For such compositions, the macroscopically observed enhanced properties are variously attributed to easier domain switching and/or phase transition. Nevertheless, modelling 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 morphotropic phase boundary (MPB). It is shown that specific grain orientation has a significant effect on how proximity to phase boundary affects microscopic phenomena, and consequently functional responses.