Phenomenological theory of size effects on the cubic-tetragonal phase transition in BaTiO3 nanocrystals

We study the first order tetragonal --> cubic ferrodistortive phase transition in single domain mechanically unconstrained BaTiO3 nanocrystals with no depolarization fields. We demonstrate that Landau coefficients up to the sixth order as a function of particle size are needed to describe the nanoparticle size induced changes in tetragonal phase stability as well as dielectric properties in the vicinity of the phase transition. The thermodynamic potential developed in this work is self-consistent, fully commensurate polar point group 4 mm, and is able to predict the size-induced phase transition, as well as the metastable tetragonal phase in the cubic phase field. We also evaluate the changes in single domain static dielectric susceptibilities demonstrate significant deviations from bulk properties. Specifically, we find a decrease in dielectric susceptibility at the transition temperature with decreasing particle size, which we verify and find to be in agreement with the predictions from lattice dynamics considerations.