Improper relaxor state in ${\left({\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\right)}_8{\left[\mathrm{Al}{\mathrm{O}}_2\right]}_{12}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$

Dielectric and elastic properties of aluminate-sodalite-type oxides, ${\left({\mathrm{Ca}}_{1-x}{\mathrm{Sr}}_x\right)}_8{\left[\mathrm{Al}{\mathrm{O}}_2\right]}_{12}{\left(\mathrm{Mo}{\mathrm{O}}_4\right)}_2$ with $x=1/16$ and 1/4, are investigated in the present study. A well-defined improper ferroelectric phase transition is demonstrated in the composition of $x=1/16$ by the onset of spontaneous strain and sharp anomalies in the dielectric and elastic responses around 600 K. As the Sr concentration increases to $x=1/4$, strong frequency dispersion appears in the dielectric and elastic responses, indicating that the system changes into a short-range ordered state. The dielectric and elastic anomalies are found to follow a single Vogel-Fulcher equation over a wide frequency range from ${10}^{-1}$ to ${10}^6\mathrm{Hz}$. The present results suggest an improper relaxor state at the composition of $x=1/4$, in which polar nanoregions form under spatially heterogeneous strain due to differences in the local coordination environments around Ca and Sr.

Figure 1

Powder x-ray-diffraction patterns of (a) (CS)AM-1/4 and (b) (CS)AM-1/16, observed at room temperature. (c) The calculated pattern for the Ca end-member.

Figure 2

Temperature dependence of dielectric responses observed at frequencies ${10}^3$, ${10}^4$, ${10}^5$, and ${10}^6\mathrm{Hz}$ in (CS)AM-$x$ with (a),(b) $x=1/16$ and (c),(d) $x=1/4$. Panels (a),(c) and (b),(d) present the permittivity and $tan\delta$, respectively.

Figure 3

Temperature dependence of dielectric permittivity for (CS)AM-$x$ ($x=0.10$, 0.15, and 0.20), which was measured at the frequencies of ${10}^4$, ${10}^5$, and ${10}^6\mathrm{Hz}$.

Figure 4

Temperature dependence of the elastic responses observed with several frequencies in (CS)AM-$x$ with (a),(b) $x=1/16$ and (c),(d) $x=1/4$. Panels (a),(c) and (b),(d) present the storage modulus and $tan\delta$, respectively. Insets in panels (c) and (d) present magnified views.

Figure 5

Temperature dependence of the shear strain observed in (CS)AM-1/16 and (CS)AM-1/4, which was measured on heating without bias stress after cooling under the loading of bias stress.

Figure 6

The measurement frequencies used in the dielectric and elastic measurements vs the inverse of the specific temperatures obtained in (CS)AM-1/4 at which extrema were observed in the temperature dependence of dielectric permittivity and storage modulus. The solid curve denotes the most adequate fit obtained with the Vogel-Fulcher law (see text for detail).

Figure 7

Schematic illustrations of the local environments around Ca and Sr in the Ca and Sr end-members of (CS)AM-$x$ showing their high- and low-temperature structures. See text for details.