Ferroelectric phase transitions in Sr$_{9}$Tm(VO$_4$)$_{7}$ upon substitution of calcium and lead for strontium

In Sr$_{9}$Tm(VO$_4$)$_{7}$ system, solid solutions with M = Ca (0 $\le x\le$ 2) and M = Pb (0 $\le x\le$ 1) have been prepared by solid-phase synthesis at 1373 K. At room temperature, the single-phase samples are isostructural to the Ca$_{3}$(VO$_4$)$_{2}$ ferroelectric (space group $R$3$c$, $Z$ = 6). The materials have been characterized by methods of the X-ray phase analysis (XPA), the second harmonic generation (SHG), and the dielectric spectroscopy. The intensity of the change in the SHG signal is changed within the range of 30–50 units with respect to a quartz standard in the dependence on cation–substitute and its concentration. A reversible ferroelectric phase transition is observed in the temperature range 850–960 K. The transition is accompanied by a sharp maximum in the curve of the dependence of the dielectric permittivity on temperature. The absence of the SHG signal at temperatures higher than the transition temperature indicates the centrosymmetricity of the paraelectric phase.