Figure 1

(a) Schematic view of a typical perovskite structure. (b) Temperature dependence of the dielectric constant (${\epsilon }^{\prime }$) of BCTO crystals. (c) Phase diagram derived from dielectric measurements. The filled and open circles indicate the cooling and heating processes, respectively. (d) The composition dependence of critical exponent of susceptibility for $T\mathrm{\text{−}}O$ phase transition. (e) The composition dependence of ${\epsilon }^{\prime }$ ($f=100\mathrm{kHz}$) observed at 2.5 K. (f) and (g) Frequency dependences of the dielectric response (${\epsilon }^{\prime }$ and ${\epsilon }^{\prime \prime }$) for BCTO crystal with $x=0.03$ and 0.23 at several temperatures.Reuse & Permissions

Figure 2

Unit-cell volume effects on the phase diagrams for BCTO crystals and pure BTO crystal under high pressure [13, 19]. The dashed straight line represents the hypothetical behavior of $T_C^{C\mathrm{\text{−}}T}$ based on the classical Vegard’s law, which is valid for simple solid-solution systems [21, 22]. The double arrow indicates a large discrepancy between the predicted and experimental values of $T_C^{C\mathrm{\text{−}}T}$.Reuse & Permissions

Figure 3

(a) Schematic view of Ca off-center displacement in the tetragonal structure of BCTO. Ba, Ca, and O (open spheres) ions are located at a plane different from that of Ti and O (filled spheres) by a distance of $a/2$. Short and long arrows indicate the electric dipoles induced by Ti and Ca displacement in the $T$-phase of BCTO, respectively. The large deformation of the crystal at high electric fields, as indicated by the dashed lines, may be closely related to the response of Ca displacement. (b) Relative change in the total energy of ${\mathrm{Ba}}_{1-x}{\mathrm{Ca}}_x{\mathrm{TiO}}_3$ ($x=0.125$) as a function of the displacement of the Ca ion from the center position along [001] (squares), [111] (triangles), and [113] (circles) directions utilizing the total energy of pure ${\mathrm{BaTiO}}_3$ (BTO) as the origin. Calculations were performed using the Tokyo ab initio program package [24, 25, 26]. The convergence of the calculations on pure BTO based on the experimentally obtained ratio of lattice constants $c/a$ ($=1.009$) was first confirmed, and unit-cells were then doubled to incorporate one Ca atom into the structure to calculate the total energy of ${\mathrm{Ba}}_{0.875}{\mathrm{Ca}}_{0.125}{\mathrm{TiO}}_3$.Reuse & Permissions

Figure 4

(a) Large electric field-induced strain in $c$-cut BCTO single crystals with $x=0.02$, 0.07, and 0.165 obtained from unipolar electric field measurements at 300 K. (b) and (c) Strain-field and polarization-field curves observed simultaneously by utilizing a bipolar field at 300 K for single crystals with $x=0.02$ and 0.165 in comparison with those of pure ${\mathrm{BaTiO}}_3$. $E_c$ and $E_c^S$, respectively, represent the coercive field for polarization reversal and the threshold field for triggering a dramatic change in strain.Reuse & Permissions