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

The crystal structure of NaMn(SO) [unit-cell parameters a = 14.8307 (18), b = 9.9107 (18), c = 8.6845 (12) Å, space group Cmc2] 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 (L type) and P(b)cm (L type) (category IV). A new hypothetical MDO polytype has been proposed and the geometry optimization demonstrates its reasonability as another possible stable polytype. Compounds NaMnMg(SO) 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 and S modules:…|ASASASAS|… or (ASAS), together with MDO (ASAS) and MDO (ASAS). The crystal structures of itelmenite, NaCaFe(PO), and CaMgFe(PO) are crystal-chemical isotypic to NaMnMg(SO) and should be considered as (A*SA*S) derivatives of the (ASAS)-type structure.