Structural perspective on the anomalous weak-field piezoelectric response at the polymorphic phase boundaries of (Ba,Ca)(Ti,M)O3 lead-free piezoelectrics ( M=Zr , Sn, Hf)

Although, as part of a general phenomenon, the piezoelectric response of $\mathrm{Ba}(\mathrm{T}{\mathrm{i}}_{1\ensuremath{-}y}{M}_{y}){\mathrm{O}}_{3}$ ($M=\mathrm{Zr}$, Sn, Hf) increases in the vicinity of the orthorhombic ($Amm2$)-tetragonal ($P4mm$) and orthorhombic ($Amm2$)-rhombohedral ($R3m$) polymorphic phase boundaries, experiments in the last few years have shown that the same phase boundaries show significantly enhanced weak-field piezoproperties in the Ca-modified variants of these ferroelectric alloys, i.e., $(\mathrm{Ba},\mathrm{Ca})(\mathrm{Ti},M){\mathrm{O}}_{3}$. So far there is a lack of clarity with regard to the unique feature(s) which Ca modification brings about that enables this significant enhancement. Here, we examine this issue from a structural standpoint with $M=\mathrm{Sn}$ as a case study. We carried out a comprehensive comparative structural, ferroelectric, and piezoelectric analysis of the $Amm2$ phase in the immediate vicinity of the $P4mm\text{\ensuremath{-}}Amm2$ phase boundaries of (i) Ca-modified $\mathrm{Ba}(\mathrm{Ti},\mathrm{Sn}){\mathrm{O}}_{3}$, as per the nominal formula $(1\ensuremath{-}x)\mathrm{BaT}{\mathrm{i}}_{0.88}\mathrm{S}{\mathrm{n}}_{0.12}{\mathrm{O}}_{3}\text{\ensuremath{-}}(x)\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\mathrm{Ti}{\mathrm{O}}_{3}$ and (ii) without Ca modification, i.e., $\mathrm{Ba}(\mathrm{T}{\mathrm{i}}_{1\ensuremath{-}y}\mathrm{S}{\mathrm{n}}_{y}){\mathrm{O}}_{3}$. We found that the spontaneous lattice strain of the $Amm2$ phase is noticeably smaller in the Ca-modified counterpart. Interestingly, this happens along with an improved spontaneous polarization by enhancing the covalent character of the Ti-O bond. Our study suggests that the unique role of Ca modification lies in its ability to induce these seemingly contrasting features (reduction in spontaneous lattice strain but increase in polarization).