Compositional ordering in relaxor ferroelectric Pb ( B B ′ ) O 3 : Nearest neighbor approach

Relaxor ferroelectrics, which form a peculiar class of functional materials, are often composed of complex perovskites $\mathrm{Pb}({BB}^{\ensuremath{'}}){\mathrm{O}}_{3}$, as represented by $\mathrm{Pb}({\mathrm{Mg}}_{1/3}{\mathrm{Nb}}_{2/3}){\mathrm{O}}_{3}$ where the compositional ordering of Mg and Nb is believed to be essential to its relaxor properties. In this work, analysis using a first-principles-based model shows that, while the electrostatic interactions are important, the nearest neighbor assumption, which was used for metallic alloys, can be adopted to understand the compositional ordering in $\mathrm{Pb}({BB}^{\ensuremath{'}}){\mathrm{O}}_{3}$. Numerical simulations with the Kawasaki Monte Carlo method can model the experimentally observed compositional ordering by maximizing the number of the unlike $B\text{\ensuremath{-}}{B}^{\ensuremath{'}}$ pairs (or the Bethe's parameter), which is the overriding factor that determines the ordering. Subtle points of configuration energy degeneracy are also discussed, which explains the partial disorder inherently present in such systems.