The effect of off-center Cu2+ ions on the phase transition in lead germanate crystals

The properties of Pb₅Ge₃O₁₁: Cu²⁺ crystals near the temperature of the ferroelectric phase transition are discussed in terms of a phenomenological approach. Assuming a quadratic interaction with the order parameter, the effect of Cu²⁺ is considered a result of static distortions, which result from the off-center position of the copper impurity ions in the lead germanate structure. In this approximation, Cu²⁺ jumps between off-center positions do not affect the dynamic properties of the crystal matrix near T _C.