Polymorphism, polytypism and modular aspect of compounds with the general formula A ₂ M ₃(TO₄)₄ (A = Na, Rb, Cs, Ca; M = Mg, Mn, Fe³⁺, Cu²⁺; T = S⁶⁺, P⁵⁺): order–disorder, topological description and DFT calculations

Abstract

The crystal structure of Na2Mn3(SO4)4 [unit-cell parameters a = 14.8307 (18), b = 9.9107 (18), c = 8.6845 (12) Å, space group Cmc21] 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)c21 (L 2n+1 type) and P(b)cm (L 2n type) (category IV). A new hypothetical MDO2 polytype has been proposed and the geometry optimization demonstrates its reasonability as another possible stable polytype. Compounds Na2Mn3–x Mg x (SO4)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 MDO1 (AS 1 AS 1) and MDO2 (AS 2 AS 2). The crystal structures of itelmenite, NaCaFe3+ 3(PO4)4, and Ca2MgFe3+ 2(PO4)4 are crystal-chemical isotypic to Na2Mn3–x Mg x (SO4)4 and should be considered as (A*S 1 A*S 2) derivatives of the (AS 1 AS 2)-type structure.

Polytypism of Ln(SeO3)(HSeO3)·2H2O compounds: synthesis and crystal structure of the first monoclinic modification of Nd(SeO3)(HSeO3)·2H2O, DFT calculations and order/disorder description

“…The DFT calculations of both polytypes show that the polytype structures are extremely close energy-wise and almost equally viable as regards the total energy of the structure. A similar case with the close energies for the different polytypes has been previously found for Na 2 Mn 3 (SO 4 ) 4 (Aksenov et al, 2022) and compounds with the general formula Cs{Al 2 [TP 6 O 20 ]} (T = B, Al) (Aksenov et al, 2021). Close values of the energy per unit cell for the polytypes in different systems stimulate an interest in more detailed and accurate analysis of the polytypic structures.…”

“…A similar case with the close energies for the different polytypes has been also found for Na 2 Mn 3 (SO 4 ) 4 (Aksenov et al, 2022) and compounds with the general formula Cs{Al 2 [TP 6 O 20 ]} (T = B, Al) (Aksenov et al, 2021).…”

“…In the present work, we have synthesized and described a new monoclinic polytype of neodymium selenite Nd(SeO 3 )-(HSeO 3 )Á2H 2 O. This work also continues our systematic studies of the polytypism of inorganic compounds using the approach of OD theory (Aksenov et al, 2021(Aksenov et al, , 2022 and the new compound is compared with the known orthorhombic polytype. The place of Nd(SeO 3 )-(HSeO 3 )Á2H 2 O among other selenite compounds is also discussed from a crystal chemical point of view.…”

Symmetry Analysis of the Complex Polytypism of Layered Rare-Earth Tellurites and Related Selenites: The Case of Introducing Transition Metals

“…Except for different MDO and non-MDO structures, the modular structures can also be formed when the different types of the interstitial block between adjacent [Ln 12 (TeO 3 ) 12 ] type B slab are present. As a result, the different types of alternation can form a merotypic modular series [18,33,46,[57][58][59] [11]. Such mixed-layer structures are as yet observed only for selenites; note the compositional shift of the CsCl slabs from [M I 7 Cl 16 ] −9 in "bilayer" structures (Figure 1b) to [M I 6 X 16 ] −10 in their mixedlayer derivatives [11,53].…”

“…The symmetry analysis of such disordered compounds is based on the concepts of OD theory [22,23] and the symmetry of the OD structures is described by groupoids (instead of crystallographic space groups), which can contain the non-crystallographic symmetry operations [24][25][26]. This approach allows to determine the symmetry relations for the whole family of known polytypes and predict the hypothetical ones [27], which is important for the searching of new materials [28][29][30][31][32][33][34]. The OD structures with the different polytypes have been also described for the tellurium compounds, in particular, for the hydrous magnesium orthotellurate (VI) Mg [37].…”