Temperature-dependent elasticity of Pb [ ( M g 0.33 N b 0.67 ) 1 − x T i x ] O 3

Relaxor ferroelectric materials, such as $\mathrm{Pb}[{(\mathrm{M}{\mathrm{g}}_{0.33}\mathrm{N}{\mathrm{b}}_{0.67})}_{1\text{\ensuremath{-}}x}\mathrm{T}{\mathrm{i}}_{x}]{\mathrm{O}}_{3}$ (PMN-PT) with generic stoichiometry, undergo a ferroelectric-to-paraelectric phase transition as a function of temperature. The exact transition characterized by Curie temperature (${T}_{c}$) varies as a function of chemistry ($x$), i.e., the concentration of Ti. In this study, we investigated the structural phase transition by exploring the temperature dependence of the single-crystal elastic properties of $\mathrm{Pb}[{(\mathrm{M}{\mathrm{g}}_{0.33}\mathrm{N}{\mathrm{b}}_{0.67})}_{0.7}\mathrm{T}{\mathrm{i}}_{0.3}]{\mathrm{O}}_{3}$, i.e., $x\ensuremath{\approx}0.3$. We used resonant ultrasound spectroscopy to determine the elasticity at elevated temperatures, from which ${T}_{c}=398\phantom{\rule{4pt}{0ex}}\ifmmode\pm\else\textpm\fi{}5\phantom{\rule{4pt}{0ex}}\mathrm{K}$ for PMN-PT ($x\ensuremath{\approx}0.3$) was determined. We report the full elastic constant tensor (${C}_{ij}={{C}_{11},\phantom{\rule{4pt}{0ex}}{C}_{12},\phantom{\rule{4pt}{0ex}}{C}_{44}$}), acoustic attenuation (${Q}^{\ensuremath{-}1}$), longitudinal (${V}_{P}$) and shear (${V}_{S}$) sound velocities, and elastic anisotropy of PMN-PT as a function of temperature for $400\phantom{\rule{4pt}{0ex}}lTl\phantom{\rule{4pt}{0ex}}871\phantom{\rule{4pt}{0ex}}\mathrm{K}$. Temperature trends of the elastic constants ${C}_{11},\phantom{\rule{4pt}{0ex}}{C}_{44}$ and bulk modulus indicate that at $Tg\phantom{\rule{4pt}{0ex}}{T}_{c}$ the material first stiffens and reaches maxima in the vicinity of the Burns temperature (${T}_{b}\ensuremath{\sim}673\phantom{\rule{4pt}{0ex}}\mathrm{K}$), followed by a more typical gradual softening of the elastic constants. Similar temperature-dependent anomalies are also observed with anisotropy and ${Q}^{\ensuremath{-}1}$, with minima in the vicinity of ${T}_{b}$. We used the temperature dependence of ${C}_{ij}$, ${Q}^{\ensuremath{-}1}$, ${V}_{P},\phantom{\rule{4pt}{0ex}}{V}_{S}$, and anisotropy to infer the evolution of polar nanoregions as the material evolved from $Tg{T}_{c}$.