Figure 1

Temperature dependence of some properties in disordered $\mathrm{Ba}({\mathrm{Zr}}_{0.5}{\mathrm{Ti}}_{0.5}){\mathrm{O}}_3$ solid solutions. Panel (a) shows the average between the three diagonal elements of the dielectric susceptibility, as computed from a direct approach (${\chi }^{\mathrm{direct}}$, triangles) and from the fluctuation-dissipation theorem (${\chi }^{\mathrm{CF}}$, dots). Panel (b) displays the total Edwards-Anderson parameter, as well as its contributions from cells centered on Ti and Zr ions. Panel (c) reveals the magnitude of the local modes centered on Ti and Zr ions. Panel (d) represents the square of the Fourier transform of the local modes’ configurations at ${\mathbf{k}}_{\max }$. Panel (e) provides the $\theta (\mathbf{r})$ correlation between Ti dipoles for $\mathbf{r}=a_{\mathrm{lat}}\mathbf{z}$ (first nearest neighbor), $a_{\mathrm{lat}}(\mathbf{y}+\mathbf{z})$ (second nearest neighbor), $a_{\mathrm{lat}}(\mathbf{x}+\mathbf{y}+\mathbf{z})$ (third nearest neighbor), $2a_{\mathrm{lat}}\mathbf{z}$, and $3a_{\mathrm{lat}}\mathbf{z}$. The solid line in Panel (a) represents the dielectric susceptibility arising from the fit of ${\chi }^{\mathrm{CF}}$ (between 500 and 800 K) by the Curie-Weiss law [22].Reuse & Permissions

Figure 2

Snapshots of the dipolar configurations in a given ($y$, $z$) plane for different temperatures. Panels (a), (b), (c), (d), (e), and (f) correspond to temperatures of 550 K (Region I), 250 K (Region II), 150 K (Region III), 100 K (Region IV), 50 K (Region IV) and 10 K (Region IV), respectively. Blue colors and red colors indicate that the corresponding local modes are centered on Ti and Zr ions, respectively.Reuse & Permissions