The formation and temperature evolution of polar nanoregions (PNRs) in relaxor ferroelectrics is an intriguing issue that is still under debate. Therefore, we present an approach to estimate the volume fraction of PNRs by the example of the relaxor ferroelectric, $(1-x)\left(\mathrm{B}{\mathrm{i}}_{0.5}\mathrm{N}{\mathrm{a}}_{0.5}\right)\mathrm{Ti}{\mathrm{O}}_3-x\mathrm{BaTi}{\mathrm{O}}_3$ (BNT-$x\mathrm{BT}$). A detailed analysis of the Young's modulus, which is highly sensitive to small structural distortions, at temperatures $25{}^{\circ }\mathrm{C}<T<800{}^{\circ }\mathrm{C}$ for both poled and unpoled samples, is correlated to the temperature evolution of PNRs by utilizing a composite model. The extracted volume fraction of the PNRs and the increasing Young's modulus above the formerly suggested Burns temperature indicate that the formation of the PNRs does not occur at a defined temperature but rather in a broad temperature range starting around $\sim 720{}^{\circ }\mathrm{C}$.

• Received 21 July 2016
• Revised 20 November 2016

DOI:https://doi.org/10.1103/PhysRevB.95.024104