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

TL;DR

This study demonstrates a method to determine critical exponents of diffuse ferroelectric phase transitions in lead germanate-based crystals using optical rotation data, offering advantages over existing techniques.

Contribution

The paper introduces a novel approach to extract critical exponents from optical rotation measurements in lead germanate crystals, accounting for local Curie temperature variations.

Findings

Critical exponents were determined for various lead germanate-based crystals.

The proposed method shows advantages over traditional techniques.

The approach effectively characterizes diffuse ferroelectric phase transitions.

Abstract

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.