Polymorphism, polytypism and modular aspect of compounds with the general formula A 2 M 3 (TO 4 ) 4 (A = Na, Rb, Cs, Ca; M = Mg, Mn, Fe 3+ , Cu 2+ ; T = S 6+ , P 5+ ): order-disorder, topological description and DFT calculations.

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 Cmc2 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)c2 1 (L 2n+1 type) and P(b)cm (L 2n 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.