Specific-heat measurements and critical exponents of the ferroelastic phase transition in Pb3(PO4)2 and Pb3(P1−xAsxO4)2

Abstract

The ferroelastic phase transitions in ${\mathrm{Pb}}_3$ ${\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ and ${\mathrm{Pb}}_3{\left({\mathrm{P}}_{1-x}{\mathrm{As}}_x{\mathrm{O}}_4\right)}_2$ are accompanied by large excess specific heats in a wide temperature range above $T_c$ and critical crossover above and below $T_c$. Critical exponents of the specific heat ${\alpha }^{\prime }=0.363\mathrm{}\left(4\right), 0.360\left(5\right), \mathrm{and} 0.36\left(1\right)\mathrm{}$ for ${\mathrm{Pb}}_3$(${\mathrm{P}{\mathrm{O}}_4)}_2$, ${\mathrm{Pb}}_3$ ${\left({\mathrm{P}}_{0.97}{\mathrm{As}}_{0.03}{\mathrm{O}}_4\right)}_2$, and ${\mathrm{Pb}}_3$ ${{(\mathrm{P}}_{0.2}{\mathrm{As}}_{0.8}{\mathrm{O}}_4)}_2$, respectively, agree with theoretical predictions of a $q=3\mathrm{}$, $d=2\mathrm{}$, Potts model. Along with other experimental results of neutron and Raman scattering, the specific-heat behavior above $T_c$ indicates dynamical fluctuations in ${\mathrm{Pb}}_3$ ${\left(\mathrm{P}{\mathrm{O}}_4\right)}_2$ and a static intermediate phase in the mixed crystals. A strict proportionality between the transition entropy $\Delta S$ and the spontaneous birefringence $\Delta n_{\mathrm{bc}}$ was observed in ${\mathrm{Pb}}_3$(${\mathrm{P}{\mathrm{O}}_4)}_2$ at temperatures up to 415 K. Nonlinear behavior was found close to the transition point (453.6 K), which is interpreted in terms of a multicomponent order-parameter theory.