Formation of phase states in PbFe$_{0.5}$Nb$_{0.5}$O$_3$: Description based on multiminima models

Two ferroelectric phase transitions are observed in the PbFe$_{0.5}$Nb$_{0.5}$O$_3$ crystal. The first is between the cubic and tetragonal phase, the second is between the tetragonal and monoclinic phases. To describe phase transitions and emerging phases, a statistical model is proposed, based on the composition of two multi-minimum models – a six-minima model for the Pb cation and an eight-minima model for the Nb cation. Adjusting the model parameters, makes it possible to reproduce all the characteristic features of the thermodynamic behavior of the crystal. The most interesting is the formation of a ferroelectric, complexly ordered monoclinic phase with Cm symmetry. It is shown that the mentioned monoclinic phase arises due to the fact that the first-order phase transition to the rhombohedral ferroelectric phase occurs in the presence of an “external field” of tetragonal symmetry. The contribution of the subsystems of Pb and Nb cations to the features of the dielectric and structural properties of the crystal is estimated.