First-principles study of piezoelectric (Ba,Ca)TiO3-Ba(Ti,Zr)O3 solid solutions

High-performance piezoelectrics are key components of various smart devices and, recently, it has been discovered that (Ba,Ca)(Ti,Zr)O 3 (BCTZ) solid solutions show appealing electromechanical properties. Nevertheless, the microscopic mechanisms leading to such features are still unclear and theoretical investigations of BCTZ remain very limited. Accordingly, this thesis analyzes the properties of various compositions of (Ba,Ca)TiO3-Ba(Ti,Zr)O3 solid solutions 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 BaTiO3, CaTiO3, BaZrO3 and CaZrO3 in order to compare their properties and their different tendency towards ferroelectricity. Then, the core of our study is a systematic characterization of the binary systems (Ba,Ca)TiO3 and Ba(Ti,Zr)O3 within both the virtual crystal approximation (VCA) and direct supercell calculations. When going from BaTiO3 to CaTiO3 in (Ba,Ca)TiO3, the main feature is a gradual transformation from B-type to A-type ferroelectricity due to steric effects that largely determine the behavior of the system. In particular, for low Ca-concentration we found out an overall weakened B-driven ferroelectricity that produces the vanishing of the energy barrier between different polar states and results in a quasi-isotropic polarization. A sizable enhancement of the piezoelectric response results from these features. When going from BaTiO3 to BaZrO3 in Ba(Ti,Zr)O3, in contrast, the behavior is dominated by cooperative Zr-Ti motions and the local electrostatics. In particular, low Zr-concentration produces the further stabilization of the R3m-phase. Then, the system shows the tendency to globally reduce the polar distortion with increasing Zr-concentration. Nevertheless, ferroelectricity can be locally preserved in Ti-rich regions. We also found out an unexpected polar activation of Zr as a function of specific atomic ordering explained via a basic electrostatic model based on BaZrO3/mBaTiO3 superlattice. A microscopic factor behind the enhanced piezoelectric response in BCTZ, at low concentration of Ca and Zr, can thus be the interplay between weakened Ti-driven and emerging Ca-driven ferroelectricity, which produces minimal anisotropy for the polarization. In addition, our comparative study reveals that the specific microscopic physics of these solid solutions sets severe limits to the applicability of the virtual crystal approximation (VCA) for these systems.