Structural perspective on the anomalous weak-field piezoelectric response at the polymorphic phase boundaries of $\left(\mathrm{Ba},\mathrm{Ca}\right)\left(\mathrm{Ti},M\right){\mathrm{O}}_3$ lead-free piezoelectrics ($M=\mathrm{Zr}$, Sn, Hf)

Although, as part of a general phenomenon, the piezoelectric response of $\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{1-y}{M}_y\right){\mathrm{O}}_3$ ($M=\mathrm{Zr}$, 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., $\left(\mathrm{Ba},\mathrm{Ca}\right)\left(\mathrm{Ti},M\right){\mathrm{O}}_3$. 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 $P4mm\text{−}Amm2$ phase boundaries of (i) Ca-modified $\mathrm{Ba}\left(\mathrm{Ti},\mathrm{Sn}\right){\mathrm{O}}_3$, as per the nominal formula $\left(1-x\right)\mathrm{BaT}{\mathrm{i}}_{0.88}\mathrm{S}{\mathrm{n}}_{0.12}{\mathrm{O}}_3\text{−}\left(x\right)\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\mathrm{Ti}{\mathrm{O}}_3$ and (ii) without Ca modification, i.e., $\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{1-y}\mathrm{S}{\mathrm{n}}_y\right){\mathrm{O}}_3$. 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).

Figure 1

Composition dependence of (a) piezoelectric coefficient $\left(d_{33}\right)$, (b) remanent polarization, and (c) saturated polarization of BCTS at room temperature.

Figure 2

X-ray Bragg profiles of the BCTS for $x=0$, 0.12, 0.13, 0.21, 0.22, and 0.29.

Figure 3

Rietveld fitted x-ray powder-diffraction patterns of BCTS−$100x$ for (a) $x=0.13$ with $Amm2$, (b) $x=0.21$ with $Amm2$, (c) $x=0.22$ with $P4mm$, and (d) $x=0.22$ with $P4mm+Amm2$. The arrows highlight the misfit regions.

Figure 4

Temperature dependence of the real part of relative permittivity of BCTS for $x=0$, 0.10, 0.13, 0.21, 0.22, and 0.29 measured at 1 kHz.

Figure 5

Temperature-dependent dielectric loss tangent of BCTS for $x=0.10$, 0.13, 0.17, 0.21, 0.22, and 0.29 measured at 1 kHz.

Figure 6

(a) Phase diagram of (a) BTS–$100y$ and (b) $(1-x)\text{BCTS}–100x$ ceramics on the basis of the dielectric anomalies observed in the imaginary part of the permittivity.

Figure 7

Temperature variation of (a) real part and (b) imaginary part of the permittivity at different frequencies of BCTS with $x=0.13$. The inset in (a) shows the Vogel-Fulcher fit as per the equation $\omega ={\omega }_{0}exp\left[-E_{\mathrm{a}}/k\left(T_{\mathrm{m}}-T_{\mathrm{f}}\right)\right]$, where ${\omega }_0$ (best fit $\mathrm{value}=5.12\times {10}^{10}\mathrm{Hz}$) is the theoretical maximum frequency for the vibration of $\mathrm{PN}{\mathrm{R}}_{\mathrm{s}}$, $E_{\mathrm{a}}$ (best-fit $\mathrm{value}=25\mathrm{meV}$) is an activation energy, $k$ is the Boltzmann constant, $T_{\mathrm{m}}$ is the temperature of the permittivity maximum at frequency $\omega$, and $T_{\mathrm{f}}$ (best-fit $\mathrm{value}=48.8{}^{\circ }\mathrm{C}$) is the freezing temperature that indicates the transition between the ergodic and the nonergodic states. (c) shows the Curie-Weiss fit of the real part of the permittivity data. $T_{\mathrm{B}}$ corresponds to Burn's temperature. (d) shows the variation of cubic lattice parameter with temperature. The inset in (d) shows percentage electrostrictive volume strain as a function of temperature below Burn's temperature.

Figure 8

(a) polarization and (b) strain-field hysteresis loops of BTS-05 and BCTS-21.

Figure 9

SEM micrographs of (a) BTS-05 and (b) BCTS-21.

Figure 10

Comparison of the x-ray powder-diffraction Bragg profiles of selected pseudocubic peaks of (a) $\mathrm{BaT}{\mathrm{i}}_{0.95}\mathrm{S}{\mathrm{n}}_{0.05}{\mathrm{O}}_3$ (BTS-05) and (b) $0.79\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{0.88}\mathrm{S}{\mathrm{n}}_{0.12}\right){\mathrm{O}}_3\text{–}0.21\left(\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\right)\mathrm{Ti}{\mathrm{O}}_3$ (BCTS-21).

Figure 11

Rietveld fitted neutron powder-diffraction pattern of (a) $\mathrm{BaT}{\mathrm{i}}_{0.95}\mathrm{S}{\mathrm{n}}_{0.05}{\mathrm{O}}_3$ (BTS-05) and (b) $0.79\mathrm{Ba}\left(\mathrm{T}{\mathrm{i}}_{0.88}\mathrm{S}{\mathrm{n}}_{0.12}\right){\mathrm{O}}_3\text{–}0.21\left(\mathrm{B}{\mathrm{a}}_{0.7}\mathrm{C}{\mathrm{a}}_{0.3}\right)\mathrm{Ti}{\mathrm{O}}_3$ (BCTS-21) with the $Amm2$ structural model.

Figure 12

Crystal structure of the orthorhombic phase of BCTS-21. The large spheres in light maroon color represent Ba/Ca atoms and the medium spheres in red color represent O atoms. Small spheres in light blue color represent Ti/Sn atoms.