An empirical model for B-site cation ordering in Ba(Mg_⅓Ta_⅔)O₃

Processing-structure models are needed in both the lab and industry; however, few exist for cation ordering in perovskites. The perovskite Ba(Mg_1/3Ta_2/3)O₃ in its ordered form is one of the best known high-Q dielectric materials but requires extended high-temperature annealing to achieve high degrees of order; so an empirical model which describes the ordering as a function of an easily obtainable processing parameter would be useful. In this work, powders of Ba(Mg_1/3Ta_2/3)O₃ were synthesized using a conventional solid-state mixed-oxide method. The as-calcined compound had a cubic (lacking long-range B-site cation order) structure but contained short-range-ordered nanodomains. Upon annealing at 1500 °C for up to 40 h an increasingly ordered arrangement of Mg²⁺ and Ta⁵⁺ on the B site was generated, with the ordering causing a trigonal distortion. Empirical modeling as well as first-principles calculations via density functional theory showed that this ordering process was accompanied by a volume decrease despite the fact that ordered planes stack less efficiently. An empirical model was developed to describe the ordering parameter as a function of either annealing time or effective B-site contraction. The implication of this modeling method is that it may be possible to predict the degree of cation ordering in complex perovskite systems from ionic-radii data and experimentally-derived pseudocubic lattice constants alone. Conversely, it may also be possible to predict the degree of volume expansion/contraction upon ordering, which has implications for functional properties like ionic conduction.