Tricaesium dimolybdate(VI) bromide

The title compound, Cs3(Mo2O7)Br, was synthesized by the reaction of CsNO3, MoO3 and 1-ethyl-3-methyl­imidazolium bromide. Its crystal structure is isotypic with K3(Mo2O7)Br and contains (MoO4)2− tetra­hedra which share an O atom to produce a [Mo2O7]2− dimolybdate(VI) anion with a linear bridging angle and m2 symmetry. The anions are linked by Cs atoms (site symmetry m2), forming sheets parallel to (001). Br atoms (site symmetry m2) are also part of this layer. Another type of Cs atom (3m site symmetry) is located in the inter­layer space and connects the layers via Cs—O and Cs—Br inter­actions into a three-dimensional array

Embedding parallelohedra into primitive cubic networks and structural automata description

The main goal of the paper is to contribute to the agenda of developing an algorithmic model for crystallization and measuring the complexity of crystals by constructing embeddings of 3D parallelohedra into a primitive cubic network (pcu net). It is proved that any parallelohedron P as well as tiling by P, except the rhombic dodecahedron, can be embedded into the 3D pcu net. It is proved that for the rhombic dodecahedron embedding into the 3D pcu net does not exist; however, embedding into the 4D pcu net exists. The question of how many ways the embedding of a parallelohedron can be constructed is answered. For each parallelohedron, the deterministic finite automaton is developed which models the growth of the crystalline structure with the same combinatorial type as the given parallelohedron

Synchrotron diffraction study of the crystal structure of Ca(UO2)6(SO4)2O2(OH)6·12H2O, a natural phase related to Uranopilite

The crystal structure of a novel natural uranyl sulfate, Ca(UO2)6(SO4)2O2(OH)6·12H2O (CaUS), has been determined using data collected under ambient conditions at the Swiss–Norwegian beamline BM01 of the European Synchrotron Research Facility (ESRF). The compound is monoclinic, P21/c, a = 11.931(2), b = 14.246(6), c = 20.873(4) Å, β = 102.768(15), V = 3460.1(18) Å3, and R1 = 0.172 for 3805 unique observed reflections. The crystal structure contains six symmetrically independent U6+ atoms forming (UO7) pentagonal bipyramids that share O…O edges to form hexamers oriented parallel to the (010) plane and extended along [1–20]. The hexamers are linked via (SO4) groups to form [(UO2)6(SO4)2O2(OH)6(H2O)4]2− chains running along the c-axis. The adjacent chains are arranged into sheets parallel to (010). The Ca2+ ions are coordinated by seven O atoms, and are located in between the sheets, providing their linkage into a three-dimensional structure. The crystal structure of CaUS is closely related to that of uranopilite, (UO2)6(SO4)O2(OH)6·14H2O, which is also based upon uranyl sulfate chains consisting of hexameric units formed by the polymerization of six (UO7) pentagonal bipyramids. However, in uranopilite, each (SO4) tetrahedron shares its four O atoms with (UO7) bipyramids, whereas in CaUS, each sulfate group is linked to three uranyl ions only, and has one O atom (O16) linked to the Ca2+ cation. The chains are also different in the U:S ratio, which is equal to 6:1 for uranopilite and 3:1 for CaUS. The information-based structural complexity parameters for CaUS were calculated taking into account H atoms show that the crystal structure of this phase should be described as very complex, possessing 6.304 bits/atom and 1991.995 bits/cell. The high structural complexity of CaUS can be explained by the high topological complexity of the uranyl sulfate chain based upon uranyl hydroxo/oxo hexamers and the high hydration character of the phase

Cation Ordering and Superstructures in Natural Layered Double Hydroxides

Layered double hydroxides (LDHs) constitute an important group of materials with many applications ranging from catalysis and absorption to carriers for drug delivery, DNA intercalation and carbon dioxide sequestration. The structures of LDHs are based upon double brucite-like hydroxide layers [M2+nM3+m(OH)2(m+n)]m+, where M2+ = Mg2+, Fe2+, Mn2+, Zn2+, etc.; M3+ = Al3+, Fe3+, Cr3+, Mn3+, etc. Structural features of LDHs such as cation ordering, charge distribution and polytypism have an immediate influence upon their properties. However, all the structural studies on synthetic LDHs deal with powder samples that prevent elucidation of such fine details of structure architecture as formation of superstructures due to cation ordering. In contrast to synthetic materials, natural LDHs are known to form single crystals accessible to single-crystal X-ray diffraction analysis, which provides a unique possibility to investigate 3D cation ordering in LDHs that results in formation of complex superstructures, where 2D cation order is combined with a specific order of layer stacking (polytypism). Therefore LDH minerals provide an indispensable source of structural information for modeling of structures and processes happening in LDHs at the molecular and nanoscale levels

On the Origin of Crystallinity: a Lower Bound for the Regularity Radius of Delone Sets

The local theory of regular or multi-regular systems aims at finding sufficient local conditions for a Delone set $X$ to be a regular or multi-regular system. One of the main goals is to estimate the regularity radius $\hat{\rho}_d$ for Delone sets $X$ in terms of the radius $R$ of the largest "empty ball" for $X$. The present paper establishes the lower bound $\hat{\rho_d}\geq 2dR$ for all $d$, which is linear in $d$. The best previously known lower bound had been $\hat{\rho}_d\geq 4R$ for $d\geq 2$. The proof of the new lower bound is accomplished through explicit constructions of Delone sets with mutually equivalent $(2dR-\varepsilon)$-clusters, which are not regular systems

Chiral open-framework uranyl molybdates. 2. Flexibility of the U:Mo = 6:7 frameworks: syntheses and crystal structures of (UO 2 ) 0.82 [C 8 H 20 N] 0.36 [(UO 2 ) 6 (MoO 4 ) 7 (H 2 O) 2 ](H 2 O) n and [C 6 H 14 N 2 ][(UO 2 ) 6 (MoO 4 ) 7 (H 2 O) 2 ](H 2 O)

Abstract Two new chiral open-framework uranyl molybdates, (UO 2 ) 0.82 [C 8 H 2