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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. [ABSTRACT FROM AUTHOR]

Philipsburgite, Cu5Zn((As,P)O4)2(OH)6·H2O, from the Middle Pit, Gold Hill Mine, Tooele Co., Utah, USA, was studied by single-crystal X-ray diffraction and scanning electron microscopy. The empirical formula of the studied sample is (Cu4.69Zn1.23)(As0.86P0.18O4)2(OH)5.61·H2O, which agrees well with the previous reports on the mineral. Philipsburgite is monoclinic, P21/c, a = 12.385(6), b = 9.261(4), c = 10.770(5) Å, β = 97.10(1)o, V = 1225.7(9) Å3 (at 100 K), and Z = 4. The crystal structure was refined to R1 = 0.046 for 2563 unique observed reflections with |Fo| ≥ 4σF. The crystal structure of philipsburgite is isotypic to that of kipushite and can be considered as a complex three-dimensional framework consisting of two types of layers stacked parallel to the a-axis. The A-type layer is formed by the edge-sharing Jahn-Teller-distorted Cuφ6 octahedra [φ = O2−, (OH)−, H2O]. Two adjacent octahedral layers are linked via (As2O4) tetrahedra. The B-type layer is built by corner-sharing (ZnO4) and (As1O4) tetrahedra and is formed by the four- and eight-membered tetrahedral rings. The A:B ratio of the A and B layers is equal to 2:1. The hydrogen bonding network in philipsburgite is rather complex and consists of two- and three-center hydrogen bonds. The As1 site accommodates ca. 18% of P and is a preferable position for the P substitution in philipsburgite. The observed selectivity of the As1 site for P may indicate that, for the intermediate compositions with the P:As ratios close to 1:1, there is a fully ordered species with P prevalent at the As1 site and As prevalent at the As2 site. The intermediate composition would, therefore, be Cu5Zn(AsO4)(PO4)(OH)6·H2O and such a mineral can be considered as a separate species, according to the rules of the International Mineralogical Association (IMA). Philipsburgite should be considered as structurally complex with the Shannon information contents of 4.954 bits/atom and 614.320 bits/cell. The obvious reason for the structural complexity of the mineral is its modularity, i.e., the presence of two structurally distinct modules, the octahedral-tetrahedral (A) and tetrahedral (B) layers. [ABSTRACT FROM AUTHOR]

Phase formation in the mixed sulfate-selenate aqueous system of uranyl nitrate and cesium nitrate has been investigated. Two types of crystalline compounds have been obtained and characterized using a number of experimental (single crystal XRD, FTIR, SEM) and theoretical (information-based complexity calculations, topological analysis) techniques. No miscibility gaps have been observed for Cs 2 [(UO 2 ) 2 ( T O 4 ) 3 ] ( T = S, Se), which crystallizes in tetragonal system, P -42 1 m , a =9.616(1)–9.856(2), c =8.105(1)–8.159(1) Å, V =749.6(2)–792.5(3) Å 3 . Nine phases with variable amount of S and Se have been structurally characterized. The structures of the Cs 2 [(UO 2 ) 2 ( T O 4 ) 3 ] ( T = S, Se) compounds are based upon the [(UO 2 ) 2 ( T O 4 ) 3 ] 2- layers of corner-sharing uranyl pentagonal bipyramids and T O 4 tetrahedra. The layers contain two types of tetrahedral sites: T 1 (3-connected, i.e. having three O atoms shared by adjacent uranyl polyhedra) and T 2 (4-connected). The Se-for-S substitution in tetrahedral sites is highly selective with smaller S 6+ cation showing a strong preference for the more tightly bonded T 2 site. Crystallization in the pure Se system starts with the formation of Cs 2 [(UO 2 )(SeO 4 ) 2 (H 2 O)](H 2 O) crystals, its subsequent dissolution and formation of Cs 2 [(UO 2 ) 2 (SeO 4 ) 3 ]. The information-based structural complexity calculations for these two phases support the rule that more topologically complex structures form at the latest stages of crystallization. [ABSTRACT FROM AUTHOR]

Three novel uranyl selenate and sulfate oxysalts templated by protonated azetidine molecules, [ Az H] + , and its ring-opened counterpart 1-azetidinepropanamine, [ Az H(CH 2 ) 3 NH 3 ] 2+ , have been prepared and studied by X-ray structural analysis. Conformations of azetidinium cations were analysed by means of infrared vibrational assignments supported by the DFT calculations. Crystallization of [ Az H] 2 [(UO 2 ) 2 (SeO 4 ) 3 (H 2 O)] ( I ) from highly acidic solutions suggests that low pH does not necessarily result in the opening of azetidine ring. [ Az H(CH 2 ) 3 NH 3 ][(UO 2 ) 2 (SeO 4 ) 3 (H 2 O)](H 2 O) ( II ) and [ Az H(CH 2 ) 3 NH 3 ](H 5 O 2 )[(UO 2 ) 2 (SO 4 ) 3 (HSO 4 )] ( III ) are the first structurally characterized crystalline compounds bearing isolated ring-opened azetidine moiety. [ABSTRACT FROM AUTHOR]

Crystals of the title compound are prepared by evaporation of aqueous solutions of Na2SO4 and NaF at 25 °C. [ABSTRACT FROM AUTHOR]

Yellow-green prismatic crystals of the title compound are obtained from an aqueous solution containing UO2(NO3)2, K2C2O4, H2SeO4, and 15-crown-5 by evaporation at room temperature. [ABSTRACT FROM AUTHOR]