Heterophase states and dual structures in(1−x)PbZn1∕3Nb2∕3O3−xPbTiO3single crystals

Abstract

Important structural distinctions between the inside part and the outer layer of relaxor-ferroelectric $(1\ensuremath{-}x){\mathrm{PbZn}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3}\text{\ensuremath{-}}x\phantom{\rule{0.3em}{0ex}}{\mathrm{PbTiO}}_{3}$ single crystals have been revealed in recent $\mathrm{x}$-ray diffraction studies. Based on the structural data from papers by Xu et al. [Phys. Rev. B 67, 104102 (2003); Appl. Phys. Lett. 84, 3975 (2004)], different dual structures are considered in the present paper in terms of orientation states and their distortions. An elastic matching of inside and outer phases coexisting at molar concentrations $0\ensuremath{\leqslant}x\ensuremath{\leqslant}0.08$ is analyzed for unpoled and poled single crystals, and this analysis results in a series of diagrams of orientation states and interfaces. An idea on transition regions in the crystal samples with the dual structures is put forward, and factors are studied that play the key role in relieving the internal stress. Two possible models of the transition regions in the $(1\ensuremath{-}x){\mathrm{PbZn}}_{1∕3}{\mathrm{Nb}}_{2∕3}{\mathrm{O}}_{3}\text{\ensuremath{-}}x\phantom{\rule{0.3em}{0ex}}{\mathrm{PbTiO}}_{3}$ single crystals are proposed and discussed as well as different unit-cell parameter variations are determined within the framework of these models.