Isotope effect onBaTiO3ferroelectric phase transitions

Isotope effects on the ${\mathrm{BaTiO}}_3$ ferroelectric phase transitions and on its melting temperature are given. The materials used are a light ${}_{}{}^{46}{}_{}{}^{}\mathrm{rich}$ denatured ${\mathrm{BaTiO}}_3$ and ${\mathrm{a}}^{134}$Ba-rich ${\mathrm{BaTiO}}_3$, in which the molecular weight is lighter than in naturally occurring ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{48}{}_{}{}^{}$ ${\mathrm{TiO}}_3$ by about 1.3 and 2.8 a.u., respectively. In addition, heavy ${}_{}{}^{50}{}_{}{}^{}\mathrm{rich}$ ${\mathrm{BaTiO}}_3$ is measured, in which the molecular weight is heavier than the natural one by 1.2 a.u. The ferroelectric Curie temperature of the cubic-to-tetragonal structural phase transition is about 132 °C in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{46}{}_{}{}^{}$ ${\mathrm{TiO}}_3$, 138 °C in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}_{}^{48}{}_{}{}^{}$ ${\mathrm{TiO}}_3$, and 111 °C in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{50}{}_{}{}^{}$ ${\mathrm{TiO}}_3$, whereas it is 121 °C in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{48}{}_{}{}^{}$ ${\mathrm{TiO}}_3$ (natural). As the lighter isotope is introduced, the Curie temperature rises, and vice versa for the heavier isotope. Transition temperatures of the tetragonal-to-orthorhombic and orthorhombic-to-rhombohedral transitions are also given. The transition entropy Δ$S_t$ of the cubic-to-tetragonal transition is found to be reduced with light-isotope introduction, and vice versa. Δ$S_t$ is 0.66 in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{46}{}_{}{}^{}$ ${\mathrm{TiO}}_3$, 0.43 in ${}_{}{}^{134}{}_{}{}^{}\mathrm{Ba}_{}^{48}{}_{}{}^{}$ ${\mathrm{TiO}}_3$, and 2.5 in ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{50}{}_{}{}^{}$ ${\mathrm{TiO}}_3$ (heavy ${}_{}{}^{50}{}_{}{}^{}\mathrm{rich}$), normalized with respect to that of ${}_{}{}^{138}{}_{}{}^{}\mathrm{Ba}_{}^{48}{}_{}{}^{}$ ${\mathrm{TiO}}_3$ (natural).