Size and orientation of polar nanoregions characterized by PDF analysis and using a statistical model in a Bi(Mg1/2Ti1/2)O3–PbTiO3 ferroelectric re-entrant relaxor

Abstract

Revealing the local structure information of relaxor ferroelectrics is necessary for a clear understanding of their structure–property relationships, especially the determination of the size of polar nanoregions (PNRs), which is still a long-standing challenge. In this work, the local structure of the pseudo-cubic solid solutions 0.60Bi(Mg_1/2Ti_1/2)O₃–0.40PbTiO₃ and 0.65Bi(Mg_1/2Ti_1/2)O₃–0.35PbTiO₃, which exhibit re-entrant relaxor behavior, has been determined using the statistical model and reverse Monte Carlo (RMC) modelling of total scattering data. The pair distribution function revealed significant deviation between the local and long-range structures with each of the cations exhibiting unique polyhedral configurations, which required the use of a phase coexistence model to characterize the local structure. The lone-pair bearing Bi and Pb cations exhibited the greatest amount of displacement and disordering. An effective method was proposed to determine the size and orientation of PNRs (∼2 nm) based on the correlation angle between displaced A-site pairs. The size of these regions below freezing temperature is in agreement with the result of the statistical model. This method is suitable for relaxor systems, which lack long-range ferroelectric order, providing an excellent characterization of PNRs and an understanding of the physical properties of relaxor ferroelectrics.