An alternative thermodynamic model for PZT

A thermodynamic model is proposed to account for the monoclinic phase observed in the solid solution system Pb(Zr_1-xTi_x)O₃. The free energy comprises three sets of terms: two expansions of polarization, one representing each of the end-members, weighted linearly with respect to composition, and 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 the composition of the morphotropic phase boundary between the rhombohedral and tetragonal phases lies at x=0.45 and is virtually independent of temperature and the strength of coupling between the two order parameters. The range of existence of the monoclinic phase depends upon the strength of the coupling, but in general, is broadest at low temperature.