Evidence of distinct nonpolar/polar ordering at long/short ranges in relaxor ferroelectrics

Distinct atomic nonpolar/polar ordering is determined at long, intermediate, and short ranges using synchrotron x-ray diffraction, Raman scattering, and pair distribution function data in ${\mathrm{K}}_{0.5}{\mathrm{Na}}_{0.5}{\mathrm{NbO}}_{3}$-doped ${\mathrm{BaTiO}}_{3}$-based relaxor ferroelectrics, viz., $(1\ensuremath{-}x){\mathrm{Ba}}_{0.9}{\mathrm{Sr}}_{0.1}{\mathrm{TiO}}_{3}\text{\ensuremath{-}}x\mathrm{KNN}50$. Two different polar phases with distinct symmetries are identified at short/intermediate ranges for $x=0.10$, where a monoclinic phase at short ranges gradually transforms into a rhombohedral phase at intermediate ranges. In contrast, a nonpolar phase with average cubic symmetry is found to be stable at long ranges for a wide temperature range ($100\ensuremath{\le} T \ensuremath{\le}500$ K). The polar behavior of short/intermediate-range ordering is quantified in terms of the amplitude of ferroelectric phonon mode ${\mathrm{\ensuremath{\Gamma}}}_{4}^{\ensuremath{-}}$ ($q=0,0,0$) (which corresponds to the zone center of the cubic Brillouin zone). The amplitude of the ${\mathrm{\ensuremath{\Gamma}}}_{4}^{\ensuremath{-}}$ phonon mode increases with decreasing temperature, suggesting the enhancement of ferroelectric polarization at short/intermediate ranges on lowering temperatures. Enhanced ferroelectric polarization at low temperature is also visible and evident by ferroelectrostriction and is quantified by the increase in magnitude of spontaneous volume ferroelectrostriction. Consequently, Zero thermal expansion is observed at low temperatures.