Breakdown of the Landau Theory in the Ferroelectric Phase Transition of Dicalcium Strontium Propionate

Abstract

Measurements of the thermal expansion coefficient ${\beta }_3$, the dielectric constant ${\epsilon }_{33}$, and the spontaneous polarization $P_s$ are made for annealed ${\mathrm{Ca}}_2$Sr${\left({\mathrm{C}}_2{\mathrm{H}}_5{\mathrm{CO}}_2\right)}_6$ near the Curie point. Systematic deviations from mean-field theory are observed. The critical indices are determined to be $\gamma =1.33\mathrm{}\pm 0.10$ for ${\epsilon }_{33}$ in the range $0.5°C<T-T_c<9\mathrm{}°C$, $\beta =0.31\mathrm{}\pm 0.03$ for $P_s$ in the range $0.5°C<\mathrm{}{T}_c-T<\mathrm{}5\mathrm{}°C$, and $\alpha =0\mathrm{}$ (logarithmic singularity) for ${\beta }_3$ in the range $0.4°C<T-T_c<3\mathrm{}°C$.