Theory of nonstoichiometric ordering of Pb-containing relaxors with perovskite structure

Conditions that are imposed on the interatomic interaction and under which a certain ordered state of AB _x ^′ B _1?x ^″ perovskites arises are determined with allowance for effectively pairwise interactions and the configuration entropy of interchanges of B′ and B″ ions. It is shown that, for the interaction potential u(R) = u ₀/R ⁶, the highest temperature of ordering of the 1: 2 type (T _ord (1: 2)) corresponds to a structure observed at A ≡ Ba. The highest temperature of ordering of the 1: 1 type (T _ord (1: 1)) corresponds to a structure that typically occurs in the case of A ≡ Pb. Within the approximation used, it is found that T _ord (1: 1) > T _ord (1: 2) for all compositions and that the 1: 1-ordered phase is most stable. For models with u(R) = u ₀/R ⁿ (n = 1–6) including the interaction in the first m coordination shells (m = 3, 6, 8, 11), it is shown that the ground state of AB _x ^′ B _1?x ^″ O₃ corresponds either to a decomposed solid solution or to an ordered state similar to that observed in PbMg_1/3Nb_2/5O₃.