Polytypism of Compounds with the General Formula Cs{Al2[TP6O20]} (T = B, Al): OD (Order-Disorder) Description, Topological Features, and DFT-Calculations

Abstract

The crystal structures of compounds with the general formula Cs{[6]Al2[[4]TP6O20]} (where T = Al, B) display order−disorder (OD) character and can be described using the same OD groupoid family. Their structures are built up by two kinds of nonpolar layers, with the layer symmetries Pc(n)2 (L2n+1-type) and Pc(a)m (L2n-type) (category IV). Layers of both types (L2n and L2n+1) alternate along the b direction and have common translation vectors a and c (a ~ 10.0 Å, c ~ 12.0 Å). All ordered polytypes as well as disordered structures can be obtained using the following partial symmetry operators that may be active in the L2n type layer: the 21 screw axis parallel to c [– – 21] or inversion centers and the 21 screw axis parallel to a [21 – –]. Different sequences of operators active in the L2n type layer ([– – 21] screw axes or inversion centers and [21 – –] screw axes) define the formation of multilayered structures with the increased b parameter, which are considered as non-MDO polytypes. The microporous heteropolyhedral MT-frameworks are suitable for the migration of small cations such as Li+, Na+ Ag+. Compounds with the general formula Rb{[6]M3+[[4]T3+P6O20]} (M = Al, Ga; T = Al, Ga) are based on heteropolyhedral MT-frameworks with the same stoichiometry as in Cs{[6]Al2[[4]TP6O20]} (where T = Al, B). It was found that all the frameworks have common natural tilings, which indicate the close relationships of the two families of compounds. The conclusions are supported by the DFT calculation data.

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.…”

Columbite supergroup of minerals: nomenclature and classification

“…The analysis of the crystal-chemical similarity is a useful tool to analyze the crystalchemical relation between different compounds with the same symmetry and unit-cell parameters for their systematics (Aksenov et al, 2021a(Aksenov et al, , 2022a. In accordance with the nomenclature of inorganic structure types, two structures are defined as configurationally isotypic if: (i) they are isopointal 1 and (ii) for all corresponding Wyckoff positions, both the crystallographic point configurations and their geometrical interrelationships are similar (Lima-de-Faria et al, 1990).…”

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

“…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].…”