Phase transitions of Pb(Zr_xTi_1-x)O₃ ceramics

Recent experimental and theoretical reports on the structure of lead zirconate titanate [Pb(Zr_xTi_1-x)O₃ (PZT)] ceramics with compositions in the vicinity of the morphotropic phase boundary are discussed. There has been ambiguity concerning the low-temperature structure of x=0.52 samples, due to the superlattice reflections which were not explained by the reported monoclinic phase Cm [B. Noheda, D. E. Cox, G. Shirane, R. Guo, B. Jones, and L. E. Cross, Phys. Rev. B 63, 014103 (2001)]. Neutron powder diffraction (NPD) and Rietveld refinement were used to identify the space group symmetries of x=0.52 and x=0.53 samples at 10 K. Both samples had two coexisting phases R3c and Cm at 10 K. At 10 K, monoclinic angles of both samples were larger than at 295 K, as was the octahedral tilt angle of the R3c phase of the x=0.53 sample. We analyzed our previous and current NPD data to study the structural changes in PZT ceramics, 0.20<~x<~0.53, as a function of x and temperature. Bond-valence calculations were carried out to test the models used in Rietveld refinements. Valences of Zr and Ti ions were larger and smaller than their nominal valences, respectively, although the anomaly decreased with increasing x. The composition-weighted-average valence of Zr and Ti ions was close to +4, and the relationship between the positions and valences of Zr and Ti ions explains the main structural features of PZT ceramics as a function of x. The valence of Pb ions was slightly below +2 and decreased with increasing x until it started to slightly increase for x>~0.50. Average oxygen valency was found to be close to -2. Also spontaneous polarization values were computed and found to be reasonable.