Structure–Curie temperature relationships inBaTiO3-based ferroelectric perovskites: Anomalous behavior of(Ba,Cd)TiO3from DFT, statistical inference, and experiments

Abstract

One of the key impediments to the development of ${\mathrm{BaTiO}}_{3}$-based materials as candidates to replace toxic-Pb-based solid solutions is their relatively low ferroelectric Curie temperature (${T}_{C}$). Among many potential routes that are available to modify ${T}_{C}$, ionic substitutions at the Ba and Ti sites remain the most common approach. Here, we perform density functional theory (DFT) calculations on a series of $A{\mathrm{TiO}}_{3}$ and $\mathrm{Ba}B{\mathrm{O}}_{3}$ perovskites, where $A=\mathrm{Ba}$, Ca, Sr, Pb, Cd, Sn, and Mg and $B=\mathrm{Ti}$, Zr, Hf, and Sn. Our objective is to study the relative role of $A$ and $B$ cations in impacting the ${T}_{C}$ of the tetragonal ($P4mm$) and rhombohedral ($R3m$) ferroelectric phases in ${\mathrm{BaTiO}}_{3}$-based solid solutions, respectively. Using symmetry-mode analysis, we obtain a quantitative description of the relative contributions of various divalent ($A$) and tetravalent ($B$) cations to the ferroelectric distortions. Our results show that Ca, Pb, Cd, Sn, and Mg have large mode amplitudes for ferroelectric distortion in the tetragonal phase relative to Ba, whereas Sr suppresses the distortions. On the other hand, Zr, Hf, and Sn tetravalent cations severely suppress the ferroelectric distortion in the rhombohedral phase relative to Ti. In addition to symmetry modes, our calculated unit-cell volume also agrees with the experimental trends. We subsequently utilize the symmetry modes and unit-cell volumes as features within a machine learning approach to learn ${T}_{C}$ via an inference model and uncover trends that provide insights into the design of new high-${T}_{C}\phantom{\rule{4pt}{0ex}}{\mathrm{BaTiO}}_{3}$-based ferroelectrics. The inference model predicts ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ solid solutions to have a higher ${T}_{C}$ and, therefore, we experimentally synthesized these solid solutions and measured their ${T}_{C}$. Although the calculated mode strength for ${\mathrm{CdTiO}}_{3}$ in the tetragonal phase is even larger than that for ${\mathrm{PbTiO}}_{3}$, the ${T}_{C}$ of ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ solid solutions in the tetragonal phase does not show any appreciable enhancement. Thus, ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ does not follow the inference model, which is based on established data and trends for $A{\mathrm{TiO}}_{3}$. Rather, our experimental phase diagram for ${\mathrm{CdTiO}}_{3}\ensuremath{-}{\mathrm{BaTiO}}_{3}$ suggests that it behaves markedly differently from any other ${\mathrm{BaTiO}}_{3}$-based systems studied so far.