First-principles study of (Ba,Ca)TiO$_3$ and Ba(Ti,Zr)O$_3$ solid solutions

TL;DR

This study uses first-principles calculations to analyze the ferroelectric properties and phase competition in (Ba,Ca)TiO$_3$ and Ba(Ti,Zr)O$_3$ solid solutions, highlighting the effects of doping and the limitations of approximation methods.

Contribution

It provides a systematic first-principles analysis of the ferroelectric behavior in these lead-free piezoelectric materials, comparing different doping effects and evaluating the Virtual Crystal Approximation's validity.

Findings

Ca doping causes a shift from A-site to B-site ferroelectricity.

Zr doping leads to cooperative Zr-Ti motions influencing ferroelectricity.

VCA has limited applicability due to specific microscopic physics.

Abstract

(Ba,Ca)TiO$_3$ and Ba(Ti,Zr)O$_3$ solid solutions are the building blocks of lead-free piezoelectric materials that attract a renewed interest. We investigate the properties of these systems by means of first-principles calculations, with a focus on the lattice dynamics and the competition between different ferroelectric phases. We first analyze the four parent compounds in order to compare their properties and their different tendency towards ferroelectricity. The core of our study is systematic characterization of the binary systems (Ba,Ca)TiO$_3$ and Ba(Ti,Zr)O$_3$ within both the Virtual Crystal Approximation and direct supercell calculations. In the case of Ca doping, we find a gradual transformation from $A$-site to $B$-site ferroelectricity due to steric effects that largely determines the behavior of the system. In the case of Zr doping, in contrast, the behavior is eventually dominated by cooperative Zr-Ti motions and the local electrostatics. In addition, our comparative study reveals that the specific microscopic physics of these solid sets severe limits to the applicability of the Virtual Crystal Approximation for these systems.