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 ${\mathrm{Pb}}^{2+}$ compared to ${\mathrm{Ba}}^{2+}$ 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 ${A(BB}^{\prime }{B}^{″}){\mathrm{O}}_3$ perovskite alloys. The models are also extended to study systems with A- and B-site doping, such as $\left({\mathrm{Na}}_{1/2}{\mathrm{La}}_{1/2}\right)\left({\mathrm{Mg}}_{1/3}{\mathrm{Ta}}_{2/3}\right){\mathrm{O}}_3,\hspace{0.5em}\left({\mathrm{Ba}}_{1-x}{\mathrm{La}}_x\right)\left({\mathrm{Mg}}_{\mathrm{}(1+x)/3\mathrm{}}{\mathrm{Nb}}_{\left(2\mathrm{}-x\right)/3\mathrm{}}\right){\mathrm{O}}_3,$ and $\left({\mathrm{Pb}}_{1-x}{\mathrm{La}}_x\right)\left({\mathrm{Mg}}_{\mathrm{}(1+x)/3\mathrm{}}{\mathrm{Ta}}_{\left(2\mathrm{}-x\right)/3\mathrm{}}\right){\mathrm{O}}_3.$ 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.