Polymorphism, polytypism and modular aspect of compounds with the general formula <i>A</i> <sub>2</sub> <i>M</i> <sub>3</sub>(<i>T</i>O<sub>4</sub>)<sub>4</sub> (<i>A</i> = Na, Rb, Cs, Ca; <i>M</i> = Mg, Mn, Fe<sup>3+</sup>, Cu<sup>2+</sup>; <i>T</i> = S<sup>6+</sup>, P<sup>5+</sup>): order–disorder, topological description and DFT calculations
Sergey Aksenov, Andrey Antonov, Dina Deyneko, Sergey Krivovichev, Stefano Merlino
Abstract
The crystal structure of Na 2 Mn 3 (SO 4 ) 4 [unit-cell parameters a = 14.8307 (18), b = 9.9107 (18), c = 8.6845 (12) Å, space group Cmc 2 1 ] displays order–disorder (OD) character and can be described using the OD groupoid family, more precisely a family of OD structures built up by two types of non-polar layers, with layer symmetry P ( m ) c 2 1 ( L 2 n +1 type) and P ( b ) cm ( L 2 n type) (category IV). A new hypothetical MDO 2 polytype has been proposed and the geometry optimization demonstrates its reasonability as another possible stable polytype. Compounds Na 2 Mn 3– x Mg x (SO 4 ) 4 with the unit-cell parameters a ∼ 29.2–29.7 Å, b ∼ 9.5–9.9 Å, c ∼ 8.7 Å and space group Pbca can be described in terms of modularity as a sequence of A , S 1 and S 2 modules:…| AS 1 AS 2 AS 1 AS 2 |… or ( AS 1 AS 2 ), together with MDO 1 ( AS 1 AS 1 ) and MDO 2 ( AS 2 AS 2 ). The crystal structures of itelmenite, NaCaFe 3+ 3 (PO 4 ) 4 , and Ca 2 MgFe 3+ 2 (PO 4 ) 4 are crystal-chemical isotypic to Na 2 Mn 3– x Mg x (SO 4 ) 4 and should be considered as ( A * S 1 A * S 2 ) derivatives of the ( AS 1 AS 2 )-type structure.