Critical exponents of the order parameter of diffuse ferroelectric phase transitions in the solid solutions based on lead germanate: studies of optical rotation

In this work we show that the critical exponents of the order parameter (CEOPs) of diffuse ferroelectric phase transitions (DFEPTs) occurring in lead germanate-based crystals can be determined using experimental temperature dependences of their optical rotation. We also describe the approach that suggests dividing a crystal sample into many homogeneous unit cells, each of which is characterized by a non-diffuse phase transition with a specific local Curie temperature. Using this approach, the CEOPs have been determined for the pure Pb$_{5}$Ge$_{3}$O$_{11}$ crystals, the solid solutions Pb$_{5}$(Ge$_{1-x}$Si$_{x}$)$_{3}$O$_{11}$ ($x =$0.03, 0.05, 0.10, 0.20, 0.40) and (Pb$_{1-x}$Ba$_{x}$)$_{5}$Ge$_{3}$O$_{11}$ ($x =$ 0.02, 0.05), and the doped crystals Pb$_{5}$Ge$_{3}$O$_{11}$:Li$^{3+}$ (0.005 wt. %), Pb$_{5}$Ge$_{3}$O$_{11}$:La$^{3+}$ (0.02 wt. %), Pb$_{5}$Ge$_{3}$O$_{11}$:Eu$^{3+}$ (0.021 wt. %), Pb$_{5}$Ge$_{3}$O$_{11}$:Li$^{3+}$, Bi$^{3+}$ (0.152 wt.~\%) and Pb$_{5}$Ge$_{3}$O$_{11}$:Cu$^{2+}$ (0.14 wt. %). Comparison of our approach with the other techniques used for determining the Curie temperatures and the CEOPs of DFEPTs testifies to its essential advantages.