A two order parameter thermodynamic model for Pb(Zr1-xTix)O3

A two order parameter thermodynamic model is proposed which accounts for a number of features of the solid solution system Pb(Zr1-xTix)O-3 not predicted by the conventional 6th order model. The free energy comprises three sets of terms: two expansions of polarization, representing contributions to the polarization of each of the solid solution end-members, weighted linearly with respect to composition, plus terms representing the coupling between the two contributions. Employing previously published coefficients for PbTiO3 and values extrapolated from Zr-rich PZT compositions for PbZrO3, calculations predict that the composition of the morphotropic phase boundary between the rhombohedral and tetragonal phases lies at x = 0.45 and is independent of the strength of coupling between the two order parameters. The model allows for the existence of a monoclinic phase, the composition range of which depends upon the strength of the coupling terms. A satisfactory fit to the lattice parameters of Pb(Zr0.52Ti0.48)O-3 is obtained over a wide range of temperature.