Charge-transfer electrostatic model of compositional order in perovskite alloys

We introduce an electrostatic model including charge transfer that is shown to account for the observed B-site ordering in Pb-based perovskite alloys. The model allows charge transfer between A sites and is a generalization of Bellaiche and Vanderbilt's [Phys. Rev. Lett. 81, 1318 (1998)] purely electrostatic model. The large covalency of Pb²⁺ compared to Ba²⁺ is modeled by an environment-dependent effective A-site charge. Monte Carlo simulations of this model successfully reproduce the long-range compositional order of both Pb- and Ba-based complex A(BB^'B^'')O₃ perovskite alloys. The models are also extended to study systems with A- and B-site doping, such as $({Na}1/2{La}1/2)({Mg}1/3{Ta}2/3){O}₃, ({Ba}_{1{-}x}{La}ₓ)({Mg}(1+x)/3{Nb}_{(2{-}x)/3}){O}₃,$ and $({Pb}_{1{-}x}{La}ₓ)({Mg}(1+x)/3{Ta}_{(2{-}x)/3}){O}₃.$ General trends are reproduced by purely electrostatic interactions, and charge-transfer effects indicate that local structural relaxations can tip the balance between different B-site orderings in Pb-based materials.