Phase evolution in the ferroelectric relaxor Ba(Ti1−x,Zrx)O3 from atomistic simulations

Abstract

We develop and/or use a combination of first-principles density functional theory and first-principles-based effective Hamiltonian approaches to investigate phase evolution in $\mathrm{Ba}({\mathrm{Ti}}_{1\ensuremath{-}x},{\mathrm{Zr}}_{x}){\mathrm{O}}_{3}$ ferroelectric relaxor. Our simulations reveal two competing effects, which are associated with substitution of Ti with Zr and primarily responsible for the unusual phase evolution and the properties of this family of solid solutions. They are the negative chemical pressure that Zr exerts on the ${\mathrm{BaTiO}}_{3}$ matrix and the ferroelectric ``inactivity'' of Zr itself. While the former has a stabilizing effect on ferroelectricity, the latter disrupts the ferroelectric cooperation. These competing effects are responsible for the so-called pinched phase transition, where the three phases of parent ${\mathrm{BaTiO}}_{3}$ merge together, and the loss of ferroelectricity at the onset of relaxor behavior. The origin of the controversial diffuse phase transition is attributed to the coexistence of the three ferroelectric phases. In the region of the diffuse phase transition, we detect polar nanoregions, which often exhibit unusual nanopillar geometry.