Morphotropic phase boundary of heterovalent perovskite solid solutions: Experimental and theoretical investigation ofPbSc1∕2Nb1∕2O3−PbTiO3

Abstract

X-ray and neutron diffraction techniques are combined with first-principles-based simulations to derive and understand the structural properties of $\mathrm{Pb}(\mathrm{Sc},\mathrm{Nb},\mathrm{Ti}){\mathrm{O}}_{3}$ (PSN-PT) near its morphotropic phase boundary (MPB). An analysis of our measurements yields, at room and low temperatures, an overall tetragonal $T$---monoclinic ${M}_{C}$---monoclinic ${M}_{B}$---rhombohedral $R$ path (when adopting the notations of Vanderbilt and Cohen, Phys. Rev. B 63, 94108 (2001) for the monoclinic phases) as the Ti composition decreases across the MPB. A composition- and temperature-dependent significant mixing between some of these phases is also measured and reported here. The overall $T\text{\ensuremath{-}}{M}_{C}\text{\ensuremath{-}}{M}_{B}\text{\ensuremath{-}}R$ path, which has also been proposed for $\mathrm{Pb}(\mathrm{Mg},\mathrm{Nb},\mathrm{Ti}){\mathrm{O}}_{3}$ [A. K. Singh and D. Pandey, Phys. Rev. B 67, 64102 (2003)] is rather complex since it involves a change in the polarization path: this polarization first rotates in a (100) plane for the $T\text{\ensuremath{-}}{M}_{C}$ part of the path and then in a (1--10) plane for the ${M}_{B}\text{\ensuremath{-}}R$ part of the path. Moreover, a comparison between these measurements and first-principles-based calculations raises the possibility that this complex path, and the associated ${M}_{C}$ and ${M}_{B}$ phases, can only occur if the samples exhibit a deviation from a perfectly homogeneous and disordered situation, e.g. possess nanoscale chemically-ordered regions. If not, homogeneously disordered PSN-PT is predicted to exhibit at low temperature the same polarization path as $\mathrm{Pb}(\mathrm{Zr},\mathrm{Ti}){\mathrm{O}}_{3}$, that is $T$-monoclinic ${M}_{A}\text{\ensuremath{-}}R$ which involves a ``single'' polarization rotation in a (1--10) plane. Nanoscale inhomogeneity may thus play a key role on the macroscopic properties of PSN-PT, in particular, and of other heterovalent complex solid solutions, in general, near their MPB.