Physics-based optimization of Landau parameters for ferroelectrics: application to BZT–50BCT

Abstract

In analogy to thermochemical parameter optimization in the CALculation of PHAse Diagrams (CALPHAD) approach that relies on a wide variety of experimental measurements, a thermodynamic parameter optimization strategy to describe the polarization response with single-crystal Landau coefficients is documented herein to bridge the gap between CALPHAD, Landau theory and the generality of phase field theory. As an example, anisotropic Landau coefficients are obtained by starting from experimental parameters for Pb-free 0.5Ba(Zr0.2Ti0.8)O3–0.5(Ba0.7Ca0.3)TiO3 (BZT–50BCT). Thermodynamic parameters are optimized separately for the rhombohedral (R) and tetragonal (T) ferroelectric phases using a combination of single-crystal and polycrystalline polarization and permittivity data. Parameters are validated against dielectric permittivity as a function of temperature from single-crystal and polycrystalline samples. The optimized parameters correctly predict the sequence of phase transitions as a function of temperature and the paraelectric–ferroelectric transition at 355.5 K is within the experimentally reported range. An upper thermodynamic limit is predicted for R + T metastable coexistence at 302.3 K in agreement with the experimentally measured transition to a stable single T phase for this chemistry at 302 K. The detailed parameter optimization procedure enables the identification of single-crystal tensor properties from experimental measurements for a wide variety of chemistries.