OD Structures, — a Game and a Bit More

The notion of OD structures consisting of layers is explained, and visualization of its main features facilitated by a simple game: the player is asked to stack prefabricated layers periodic in 2 dimensions, which are all of the same kind or of a small number of different kinds, in accordance with some rules which correspond to the vicinity condition (VC). As shown, important features of the sequences of layers depend only on their symmetry (i.e. layer groups) and on geometrical features of any of the kinds of pairs, especially the layer group of any of the pairs. Table 1 shows that OD crystals consisting of layers occur amongst the most diverse chemical substances. In Tables 2 and 3 some examples of OD crystals with a variety of relations between crystallochemical entities and OD layers are listed. In the Appendix and Table 4 new and simplified formulae for the number Z_v'(v) of possible positions of a certain layer L_v′ relative to the fixed position of its predecessor (or successor) L_v are given.     

Polytypes of the system Fe1−xS

The structures of Fe_1−xS (0 < x < 0.135) are members of a family of derivative structures in the sense of Megaw. The NiAs structure as aristotype is the simplest and most symmetrical member of this family. The other polytypes of Fe_1−xS may be derived as hettotypes by lowering the symmetry. The loss of symmetry in changing from the aristotype to the hettotype may be of various kinds: small displacements of Fe and S atoms from the NiAs positions and/or Fe vacancies in some atomic planes occur. The structures of the system Fe_1−xS are interpreted as OD structures consisting of OD layers. The symmetry relations of the structures of FeS and Fe₇S₈ are described by OD groupoid families. Polymorphism, twinning and stacking faults are explained on this basis.     

OD approach to the polytypism in CdP2

The structures of CdP₂ are described as stacking sequences of layers of CdP₄ tetrahedra. On the basis of the OD theory of Dornberger-Schiff, the stacking possibilities are derived and convenient stacking notations proposed. The idealized layer structure is given, the percentage of α-CdP₂ for any stacking sequence defined. The symbol of the OD groupoid family is P11(n)2m · (4) x, y with parameters x = y = 1/2 and (4⁺), (4⁻) as the two alternative transformations from layer to layer. The net constants are a = b ≈ 5.29 Å; the “thickness” of a layer is c₀ ≈ 4.95 Å.     

Prediction of the structures in the family of La(IO<Subscript>3</Subscript>)<Subscript>3</Subscript> iodates based on topology and symmetry analysis within the OD theory

Topology and symmetry analysis of the structures of the La (IO₃)₃ family is performed within the Dornberger-Schiff OD theory. Two-dimensional periodic blocks (“layers”) of two types are found in the monoclinic La (IO₃)₃ iodate; the local symmetry of one of these blocks is higher than the symmetry of the structure as a whole. This feature defines the possibility of varying the relative position of the pairs of “layers” and the existence of structures other than the structure studied. Three hypothetical polytypes with the maximum degree of ordering that belong to different crystal systems (triclinic, monoclinic, and trigonal) and disordered structures are predicted by the OD theory. This example demonstrates the possibilities of the OD theory for predicting structures.     

OD Interpretation of Pyroxenes

The structures of pyroxenes are interpreted as OD structures consisting of layers. The symmetry relations of the idealized structures of “high pyroxenes”, consisting of only one kind of silicate sheets are described by the OD groupoid family: In this case the tetrahedral layers (OD layers) are identical with silicate sheets and the octahedral layers (OD layers) are identical with the chemical octahedral sheets, apart from the fact, that the O atoms are considered to belong partly to one and partly to the other idealized layer. In the idealized pyroxene structures, which are called in this paper “low pyroxenes”, every second silicate sheet is of lower symmetry. A silicate sheet of higher symmetry is considered as an OD layer, called tetrahedral layer. An OD layer of the other kind, called compound layer, consists of one silicate sheet of lower symmetry with an octahedral sheet attached to it on either side. With this definition of the two kinds of layers, the OD groupoid family has the following symbol: Polymorphism, disorder, twinning and parallel intergrowth are explained on this basis.     

Brownmillerites as members of the unified OD family with two-dimensional disorder: A topology and symmetry analysis,the prediction of structures,and the properties of crystals

A topology and symmetry analysis of the structures of the brownmillerite family is performed within the OD theory. Blocks of two types with two-dimensional periodicity (“layers”) are revealed in two main structural types with Ibm2 and Pcmn symmetry. The high local symmetry of one layer is not characteristic of the other layer or of the structure as a whole. This feature determines the possibility of varying the arrangement of pairs of layers and the existence of one-dimensional disorder, as well as of structures with a maximum degree of order, periodic structures, and disordered structures. A symmetry analysis allows one to reveal the second direction of disordering (two-dimensional disorder), which is comparatively uncommon. The structure law of the family, which allows the systematic predicting of commensurate structural models without applying the fourth dimension, is described. Structure-property relationships are considered.     

The Order-Disorder Structure of Carbamazepine Dihydrate: 5 H-Dibenz [b,f] azepine-5-carboxamide Dihydrate,C15H12N2O · 2 H2O

The crystal structure of the title compound has been determined by X-ray diffraction techniques. The structure was solved by MULTAN-82 using the space group Aba2. The atomic parameters were refined by full-matrix least-squares calculations in Abam to the conventional R-value of 0.105, but it is impossible to interpret the results with normal space group symmetry as the title compound is an order-disorder (OD) structure consisting of two kind of layers. The OD-groupoid family is Ab2₁A1 [1/4·0].     

KNa2Tm[Si8O19] · 4H2O,a new layered silicate related to rhodezite-shlykovite-delhayelite-umbrianite-guenterblassite-hilleshaymite: Topology-symmetry analysis of the OD-family and structure prediction

Crystals of a new silicate KNa₂Tm[Si₈O₁₉] · 4H₂O, space group P12/m1 (the chemical formula was determined in the course of structure solution), are obtained under hydrothermal conditions. KNa₂Tm[Si₈O₁₉] · 4H₂O is the first synthetic representative of the family, which contains the following well-known and recently discovered minerals: rhodezite, delhayelite (fivegite, hydrodelhayelite), mountainite, shlykovite (cryptofillite), and guenterblassite (umbrianite, hilleshaymite). A crystal chemical analysis within the extended OD theory revealed the similarity of the structures of the family, including the new simplest representative and the factors responsible for structural diversity, namely, different symmetry of sheets of octahedra connected with layers of tetrahedra, which are distinguished in all the structures, and different patterns of symmetry relation between the sheets. Hypothetic structures with a higher degree of disordering are deduced. Crystals with these structures can be found in nature or obtained synthetically.     

Structure and nonlinear optical properties of the family of lead and barium nonaborates with a zeolite-like framework

The structures of new nonaborates, (Pb,Ba)₃(OH)[B₉O₁₆][B(OH)₃] (space group P31c) and Ba₃Na(OH)[B₉O₁₆][B(OH)₄] (space group P1), synthesized under hydrothermal conditions, have been investigated. These structures differ from the structure of the previously studied nonaborate Pb₃(OH)[B₉O₁₆][B(OH)₃] (space group P31c) in the occupation of the zeolite nonaframework, which, in the case of the (Ba,Na) borate, contains a larger number of cations and OH groups. Despite this difference, all the structures have a high trigonal or pseudotrigonal symmetry, which suggests the existence of the structure type or the family of nonaborates. The structural similarity is violated by the presence of B(OH)₄¹⁻ tetrahedra instead of neutral trigonal groups B(OH)₃ in channels of the (Ba,Na) borate. The latter polyhedra are characterized by a pseudomonoclinic arrangement that corresponds to the space group Cc with the true triclinic group P1. The ability of nonaborates to generate the optical second harmonic as a function of the specific features of their crystal structures is discussed.     

OD interpretation of the crystal structure of lithium tellurite,Li2TeO3

The OD groupoid family of the structure of lithium tellurite, Li₂TeO₃, is characterized by the symbol: . The OD groupoid of the structure is deduced from the observed arrangement of points in reciprocal space, the symmetry of the intensity distribution and the systematic absences. The structure is built of OD layers of one kind. Any OD layer is idendical to a Li₂TeO₃ double sheet. The assumption of Folger that the structure is an OD structure has been found to be justified.     

On the Symmetry of the n=1 Ruddlesden‐Popper Phase Ca2FeO3Cl

Single crystals of Ca₂FeO₃Cl have been obtained as a by product during single crystal growth experiments of calcium ferrates from a CaCl₂ flux. The reddish‐brown optically uni‐axial crystals adopt the tetragonal space group P4/nmm with a = 3.8381(4) Å and c = 13.685(2) Å and Z = 2 formula units per cell. The structure has been determined from a single crystal diffraction data set collected at room conditions and refined to final residual R(|F|) = 0.053 for 163 observed independent reflections with I > 2σ(I). Ca₂FeO₃Cl belongs to the structure family of the Ruddlesden‐Popper series with n = 1, which is also referred to as the K₂NiF₄‐type. Main building units are layers of perovskite type corner connected FeO₅Cl‐octahedra perpendicular to [001]. The two crystallographically independent calcium ions are located between the octahedral layers and are coordinated by nine ligands each: Ca1 (4×O + 5×Cl) and Ca2 (9×O). Following prior studies Ca₂FeO₃Cl crystallizes in space group P4. However, the present investigation shows clearly that this assignment is incorrect and that the compound has been described in an unnecessarily low symmetry.     

New layer megaborate Sm3[B13O22(OH)3](OH) · 3H2O and its place in the structural systematics

Crystals of a new aqueous rare earth borate Sm₃[B₁₃O₂₂(OH)₃](OH) · 3H₂O, space group P2/c, are obtained under hydrothermal conditions. The structure is determined by the heavy-atom method without preliminary knowledge of the chemical formula. The anionic radical is a boron-oxygen sheet in which two corrugated layers are related by centers of inversion. An independent layer is akin to pentaborate layers; it differs from the layer in (Nd_0.925Na_0.075)Nd[B₉O₁₅(OH)₂]Cl_0.85 · 2.65H₂O by an additional branch in the form of a 4: (3[2?? + 1T] + 1??) group. The intersheet space and large holes of the sheet accommodate Sm atoms, (OH) groups, and water molecules. The new Sm-borate and the related Nd-borate are polyborates (megaborates) with complex anionic radicals. In the Sm-borate, the new two-dimensional [B₁₃O₂₂(OH)₃]_??? complex anionic radical of the 13{(4: [2T + 2??])_?? + (5: [3T + 2??] + 4: (3[2?? + 1T] +1??))_??}_??? formula is built of three different blocks, unlike the [B₉O₁₅(OH)₂]_??? radical of the 9{(4: [2T + 2??])_?? + (5: [3T + 2??])_??}_??? formula in the Nd-borate, which consists of two blocks. The rule of the inverse relationship between the polymerization degrees of the boron-oxygen radical and rare earth polyhedra holds for both borates.     

The OD Structure of Dinitrosylcobalt Chloride, [Co(NO)2Cl]2

The OD groupoid family of the structure of dinitrosylcobalt chloride, [Co(NO)₂Cl]₂, is characterized by the symbol: The OD groupoid family of the structure is deduced from the observed arrangement of points in reciprocal space, the symmetry of the intensity distribution and the systematic absences. The structure is built of OD layers of one kind. The determination of the structure of the ordered orthorhombic form (MDO₂) has been determined from Weissenberg data obtained by JAGNER and VANNERBERG refined with OD full-matrix least-squares methods, based on a total of 150 reflections and anisotropic temperature coefficients. An R value of 0.13 has been obtained. The assumption of JAGNER that the structure is composed of dimers has been found to be justified.     

Cluster self-organization of intermetallic systems: Quasi-spherical nanocluster precursors with internal Friauf polyhedra (A-172) and icosahedra (B-137) in the Li19Na8Ba15 (hP842) crystal structure

A combinatorial and topological analysis of Li₁₉Na₈Ba₁₅ (hP842, a = 20 ?, c = 93 ?, V = 33552 ?³, P $ \bar 3 $ \bar 3 ) has been performed using computer methods (the TOPOS program package). Two types of crystal-forming quasi-spherical nanoclusters about 20 ? in diameter with internal Friauf polyhedra (A-172) and icosahedra (B-137) have been established by the complete decomposition of the 3D factor graph of the structure into cluster substructures. Each type of nanoclusters forms close-packed 2D layers 3⁶, which alternate along the c axis. The B-137 and A-172 nanoclusters are composed of three layers and have shell compositions (1 + 12 + 32 + 92) and (1 + 16 + 59 + 103) with local symmetries 3 and $ \bar 3 $ \bar 3 , respectively; they were revealed for the first time in crystal structures as cluster precursors. The icosahedral B-137 nanocluster contains a 104-atom quasicrystal approximant (Samson cluster).     

Polymeric metal‐organic octupolar NLO materials: lithium(I) and sodium(I) 3,5‐dinitrobenzoates

Lithium 3,5‐dinitrobenzoate (Li(dnb)) exhibits a 1D propeller chain structure of D ₃ point symmetry and the chains are trigonally assembled in the crystal under the chiral space group P 3₁21. Sodium 3,5‐dinitrobenzoate (Na(dnb)) also crystallizes in space group P 3₁21 and exhibits a 3D structure. The structure of Na(dnb) could be regarded to be similar to that of Li(dnb) if the weaker Na‐O(nitro) bonds were to be ignored. These two compounds represent rare examples of octupoles arranged in an octupolar environment and show modest powder SHG effects. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Synthesis,structure and photoluminescence of a 3D pillared heterometallic coordination polymer containing 2D inorganic cadmium‐potassium‐oxide layer subunits

Self‐assembly of Cd(NO₃)₂ with o ‐phthalic acid monopotassium salt (KHphth) in the presence of ethylenediamine (en) produced a new heterometallic coordination polymer [CdK₂(phth)₂(en)_0.5(H₂O)]_n ( 1 ). Single‐crystal X‐ray analyses reveal that it crystallizes in a monoclinic space group P 2₁/c. a = 11.6707(6) Å, b = 8.1019(4) Å, c = 20.9503(11) Å, β = 94.6640(10)^o. The complex displays an en‐pillared 3D framework, which is constructed from 2D [CdK₂(phth)₂(H₂O)]_n layers featuring uncommon inorganic cadmium‐potassium‐oxide layers containing potassium‐oxide layers. In the solid state, complex 1 shows photoluminescence with the maximum emission intensities at 355 nm upon excitation at 312 nm. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Symmetry and topological analysis of the OD nenadkevichite-labuntsovite-zorite family

The symmetry and topology of the structures of nenadkevichite, labuntsovite, and zorite minerals are analyzed within the Dornberger-Schiff OD theory. The common “layers,” their symmetry, and the symmetry variants of their stacking determining their diversity and close structural characteristics are considered, which allowed us to relate these minerals to one family. According to the fundamental theorem of the OD theory, the number Z of possible combinations of aperiodic blocks inserted between the layers in zorite equals two simultaneously along two axes of the structure, which explains the structural disorder. Some hypothetical structures are also considered.     

A new photoluminescent supramolecular inorganic‐organic hybrid zincophosphate complex pillared by carboxylate ligand through hydrogen bonding interactions

A new inorganic‐organic hybrid zincophosphate, [Zn(H₂O)₂(H₂PO₄)₂]·2PABA ( 1 ) (PABA = p‐aminobenzoic acid), pillared by PABA ligands through hydrogen bonding interactions, has been synthesized and characterized. Single‐crystal X‐ray diffraction reveals that 1 crystallizes in the monoclinic P 2₁/c space group. The geometric feature in 1 is the 3D supramolecular structure constructed from alternately arranged organic and inorganic layers that consist of infinite parallel inorganic chains. These chains are extended to a 2D inorganic layer through intermolecule hydrogen bonding interactions between N atoms (from PABA ligand) and two O atoms (from adjacent inorganic chains). 1 was characterized by IR spectroscopy, XRD, DSC/TGA. The fluorescent property for 1 in solid state was also investigated at room temperature. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Identification of crystal symmetry in Kramers and non‐Kramers ions by optical absorption: Divalent copper and nickel ions in diamagnetic lattices

The optical absorption spectra of Ni(II) doped hexaimidazole zinc(II) dichloride tetrahydrate (HZDT) and Cu(II) doped magnesium potassium phosphate hexahydrate (MPPH) have been studied at room temperature. Ni(II)/HZDT spectrum consists of three strong and one weak band. The calculated value of Dq is 1051 cm^‐1 and the interelectron repulsion parameters B and C are 854 and 3626 cm^‐1 respectively. The correlation of optical work with EPR has yielded the spin‐orbit interaction parameters λ and ξ as –225 and –450 cm^‐1 respectively. The symmetry around the Ni(II) ion is distorted octahedral, as suggested by EPR results. The estimated percentage covalency of the nickel‐nitrogen bond is around 30%. The optical absorption studies of Cu(II)/MPPH show three bands, which are identified as ²B_1g → ²A_1g, ²B_1g → ²B_2g and ²B_1g → ²E_g transitions. The octahedral field parameter Dq and the tetragonal field parameters have been evaluated from the observed adsorption bands. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

High temperature synthesis and crystal structure of new representatives of the huntite family

Single crystals of REE, Al borates, new and known representatives of huntite family are obtained by annealing of REEBO₃ on Al₂O₃ surface at 1100°C. Phase identification for REE=Pr, Eu, Tb, Tm, Ho, Yb has been carried out using unit cell parameter determination on single crystals. Crystal structures of C 2/c (PrAl₃(BO₃)₄) and C 2 (EuAl₃(BO₃)₄) ‐ two polytypic modifications, previously determined for other REE's have been studied. Formation of one or another polytype in similar thermodynamic conditions is probably dependent on electronic structure of rare earth ion. Crystal field stabilization energy in crystal fields of different symmetry is a possible factor of polytype stability (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)