Thermodynamics of pseudoproper and improper ferroelastic inclusions and polycrystals: Effect of elastic clamping on phase transitions

A new form of the thermodynamic potential is derived, in which minima correspond to the equilibrium thermodynamic states of an ellipsoidal ferroelastic inclusion surrounded by a linear elastic matrix. This potential takes into account the elastic energy stored in the matrix and enables the correct thermodynamic description of phase transitions in pseudoproper and improper ferroelastic inclusions in the framework of the mean field Landau theory. It is found that, in the presence of strong bilinear coupling between the order parameter and strain, the mechanical inclusion/matrix interaction shifts the temperature of ferroelastic phase transition largely. The elastic three-dimensional clamping by the matrix may also change the order of this transition with respect to a stress-free crystal, and induce the formation of new phases, which do not exist in a free standing single crystal. The broadening of phase transitions in polycrystals due to the dispersion of the elastic clamping of crystallites is predicted and shown to be especially large (several tens of degrees) in pseudoproper ferroelastics with strong bilinear coupling like LaP5O14, BiVO4, and KH3(SeO3)(2).