Lattice dynamics and the ferroelectric phase transition in ordered Pb$_2$B'B"O$_6$ (B' = Ga, In, Lu; B" = Nb, Ta) solid solutions

The lattice vibration spectrum, rf permittivity, and dynamic Born charges have been calculated for ordered Pb$_2$B'B"O$_3$ (B' = Ga, In, Lu; B" = Nb, Ta) solid solutions in terms of the generalized Gordon–Kim model. It has been shown that all compounds exhibit a ferroelectric instability and that the frequencies of “soft” ferroelectric modes are close in magnitude. The ferroelectric phase-transition temperatures and the spontaneous polarization in the ferroelectric phase of the solid solutions under consideration have been calculated by the Monte Carlo method using the model Hamiltonian in the local mode approximation. The transition temperature is found to increase with increasing atomic number of the B' ion.