Modeling structure–properties relations in compositionally disordered relaxor dielectrics at the nanoscale

The solid solution Ba $1 − x$Sr $x$TiO $3$ (BSTO) displays dielectric response that is highly tunable, while also exhibiting low losses in a broad frequency regime, including the microwave band. Therefore, there is a need for a better understanding of the influence of the BSTO microstructure on its relaxor properties and performance in a variety of technological applications. Since the local polarization in BSTO is strongly dependent on composition, so is its response to an applied AC field. In this work, we have adopted a phase field method to study the frequency-dependent dielectric response of this system while accounting for the local fluctuations in the solid-solution composition. By utilizing a thermodynamic potential that includes spatial dependence on the averaged Sr content, we connected relaxor-like features in the dielectric dispersion to local spatial inhomogeneities, such as average size of Sr- or Ba-rich regions, across a wide range of temperatures. These results show that the adopted simple coarse-grained approach to the relaxor problem is sensitive enough to reveal correlations between the frequency and temperature dependence of the dielectric response and modulations in the material morphology and microstructure.