Thermodynamicactivities in the Pb(Zr_1−XTi_X)O₃ solid solution at 1373 K

Abstract

Although Pb(Zr_1−XTi_X)O₃ solid solution is the cornerstone of the piezoelectric ceramics, there is no information in the literature on thermodynamic activities of the component phases in the solid solution. Using inter-crystalline ion exchange equilibria between Pb(Zr_1−XTi_X)O₃ solid solution with cubic perovskite structure and (Zr_1−YTi_Y)O₂ solid solutions with monoclinic and tetragonal structures, activities of PbTiO₃ and PbZrO₃ in the perovskite solid solution have been derived at 1373 K using the modified Gibbs–Duhem integration technique of Jacob and Jeffes. Tie-lines from the cubic solid solution are skewed towards the ZrO₂ corner. Activities in the zirconia-rich (Zr_1−YTi_Y)O₂ solid solutions are taken from a recent emf study. The results for the perovskite solid solution at 1373 K can be represented by a sub-regular solution model: ΔG^E,M(J mol^-1 )=X_PbTiO3X_PbZrO3(15280X_PbTiO3-1980X_PbZrO3) where ΔG^E,M is the excess Gibbs energy of mixing of the cubic solid solution and Xi represents the mole fraction of component i. There is a significant positive deviation from ideality for PbTiO₃-rich compositions and mild negative deviation near the PbZrO₃ corner. The cubic solid solution is intrinsically stable against composition fluctuations at temperatures down to 840 K. The results contrast sharply with the recent calorimetric data on enthalpy of mixing which signal instability of the cubic perovskite solid solution.