A survey of the structural models proposed for PbZr1−x Ti x O3 using mode analysis

Abstract

The numerous structures that have been reported for the different phases of the lead zirconate titanate system, PbZr1−x Ti x O3 (PZT), are analysed by means of a systematic symmetry-mode analysis. The distortion corresponding to the order parameter has been separated out and expressed in all phases in a comparable form. The fact that the physical origin of the PZT phases is an unstable threefold degenerate polar mode, plus in some cases an unstable octahedral tilting mode, produces structural correlations between the different phases. These correlations had remained unnoticed until now but are directly observable in a mode parameterization. They can be used both to characterize the evolution of the order parameters through the phase diagram and as a stringent test of the reported structural models. It is further shown that the activity of a single polar mode yields a specific feature in the mode decomposition of the monoclinic phases. This single-mode signature can be observed in the majority of the monoclinic structures proposed, making the others questionable. In fact, this internal constraint is satisfied by PZT to such a high degree that it drastically reduces the number of effective structural degrees of freedom. It is conjectured that this type of structural constraint beyond space-group symmetry can be a rather general property of low-symmetry distorted structures. As shown here, its existence can be detected and assessed by a symmetry-mode analysis, if considered in relation to the single underlying multidimensional order parameter.