An equivalent dipole analysis of PZT ceramics and lead-free piezoelectric single crystals - Andrew J. Bell (Journal of Advanced Dielectrics, 2016)
The recently proposed Equivalent Dipole Model for describing the electromechanical properties of ionic solids in terms of 3 ions and 2 bonds has been applied to PZT ceramics and lead-free single crystal piezoelectric materials, providing analysis in terms of an effective ionic charge and the asymmetry of the interatomic force constants. For PZT it is shown that, as a function of composition across the morphotropic phase boundary, the dominant bond compliance peaks at 52% ZrO2. The stiffer of the two bonds shows little composition dependence with no anomaly at the phase boundary. The effective charge has a maximum value at 50% ZrO2, decreasing across the phase boundary region, but becoming constant in the rhombohedral phase. The single crystals confirm that both the asymmetry in the force constants and the magnitude of effective charge are equally important in determining the values of the piezoelectric charge coefficient and the electromechanical coupling coefficient. Both are apparently temperature dependent, increasing markedly on approaching the Curie temperature.