A two-parameter thermodynamic model for PZT

A two-parameter thermodynamic model is proposed for the ferroelectric solid solution system Pb(Zr1-xTix)O-3 . 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 polarization contributions. Employing previously published coefficients for PbTiO3 and values extrapolated from Zr-rich PZT compositions for PbZrO3 , calculations predict the morphotropic phase boundary lies at x=0.45 and is independent of the strength of coupling between the two order parameters. A monoclinic phase is predicted, the range of existence of which depends upon the strength of the parameter coupling, but in general, is broadest at low temperature. It is proposed that the two contributions to the polarization have their origins in the two types of cation shifts identified in PZT: the major, homogenous shifts parallel to the polar direction and randomly-oriented, or heterogeneous, minor shifts away from the polar axis. The field-induced ordering of the minor shifts is identified as the origin of the large intrinsic piezoelectric coefficient in PZT.