Specific-heat measurements and critical exponents of the ferroelastic phase transition in Pb 3 ( P O 4 ) 2 and Pb 3 ( P 1 − x As x O 4 ) 2

TLDR: The ferroelastic phase transitions in this article are accompanied by large excess specific heat in a wide temperature range above and below the critical crossover point, which is interpreted in terms of a multicomponent order-parameter theory.

Abstract: The ferroelastic phase transitions in ${\mathrm{Pb}}_{3}$${(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ and ${\mathrm{Pb}}_{3}{({\mathrm{P}}_{1\ensuremath{-}x}{\mathrm{As}}_{x}{\mathrm{O}}_{4})}_{2}$ are accompanied by large excess specific heats in a wide temperature range above ${T}_{c}$ and critical crossover above and below ${T}_{c}$. Critical exponents of the specific heat ${\ensuremath{\alpha}}^{\ensuremath{'}}=0.363(4), 0.360(5), \mathrm{and} 0.36(1)$ for ${\mathrm{Pb}}_{3}$(${\mathrm{P}{\mathrm{O}}_{4})}_{2}$, ${\mathrm{Pb}}_{3}$${({\mathrm{P}}_{0.97}{\mathrm{As}}_{0.03}{\mathrm{O}}_{4})}_{2}$, and ${\mathrm{Pb}}_{3}$${{(\mathrm{P}}_{0.2}{\mathrm{As}}_{0.8}{\mathrm{O}}_{4})}_{2}$, respectively, agree with theoretical predictions of a $q=3$, $d=2$, Potts model. Along with other experimental results of neutron and Raman scattering, the specific-heat behavior above ${T}_{c}$ indicates dynamical fluctuations in ${\mathrm{Pb}}_{3}$${(\mathrm{P}{\mathrm{O}}_{4})}_{2}$ and a static intermediate phase in the mixed crystals. A strict proportionality between the transition entropy $\ensuremath{\Delta}S$ and the spontaneous birefringence $\ensuremath{\Delta}{n}_{\mathrm{bc}}$ 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.