Mathematics & Physics 2016, 9(1), 108–118 УДК 548.1:537.226.4 Phases of Anionic Ordering in Elpasolite Structures (Ordered Perovskites) Roman G. Sevryukov∗ Ivan N. Safonov† Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Maksim S. Molokeev‡ Kirensky Institute of Physics SB RAS Akademgorodok, 50/38, Krasnoyarsk, 660036 Far Eastern State Transport University Serysheva, 47, Khabarovsk, 680021 Russia Sergey V. Misyul§ Siberian Federal University Svobodny, 79, Krasnoyarsk, 660041 Russia Received 23.11.2015, received in revised form 09.12.2015, accepted 20.01.2016 The 108 dissymmetric phases were obtained as a result of X anions ordering in elpasolite structure A2BB′X6 (ordered perovskite) using group theoretical methods. <...> The critical order parameters which transform according to the irreducible representations of Γ and X points of Brillouin zone of O5 h—Fm¯ space group were considered only. <...> Polyhedral structures showed for dissymmetric phases which are accompanied by appearing of ferroelectricity at phase transition. <...> Keywords: elpasolite, structural data, a complete condensate of order parameters, irreducible representations, critical distortion, phase transition, dissymmetric phases. <...> Introduction A lot of compounds crystallized in space group O5 3m h — Fm¯ 3m, part of them have important practical properties. <...> Of particular interest are the numerous perovskite-like compounds with space group Fm¯ ∗srg06.6@mail.ru †isafonov@sfu-kras.ru ‡msmolokeev@mail.ru §smisyul@sfu-kras.ru ⃝ Siberian Federal University. <...> The crystals of elpasolite with general formula A2BB′X6 (A, B, B′ — cations, X — anion) are intensively studied at present and belong to this group of compounds. <...> Such Roman G. Sevryukov, Ivan N. Safonov, Maksim S. Molokeev, Sergey V.Misyul Phases of Anionic . compounds can be found among halides, oxides, oxohalides, cyanides, hydrides. <...> In elpasolites also called ordered perovskites there are two kinds of ionic groups BX6 and B′X6, which alternate along the three 4-fold axes (Fig. 1a), contrary to simple perovskite with equivalent octahedra only. <...> Thus, elpasolite cubic cell can be considered <...>