Phase states of solid solution (1-x)PbFe$_{0.5}$Nb$_{0.5}$O$_{3-x}$PbTiO$_3$. Description based on multiminimum models

Based on the composition of two multiminimum models, a statistical model has been developed on the basis of which the formation of tetragonal and monoclinic ferroelectric phases in a solid solution (1-x)PbFe$_{0.5}$Nb$_{0.5}$O$_{3-x}$PbTiO$_3$ has been investigated and described. By selecting the parameters of the model, it was possible to reproduce the diagram $T(x)$ of this solid solution. The peculiarity of the diagram is that when approaching the concentration of $x\sim$ 0.1, the temperature of the phase transition between the tetragonal and monoclinic phases decrease sharply, turning to zero. It is shown that the disappearance of the monoclinic phase is due to the specifics of the statistical properties of the eight-minimum model describing the subsystem of octahedra with eight minima. The features of the thermodynamic properties of a solid solution in the vicinity of the morphotropic boundary between the tetragonal and monoclinic phases are also investigated.