Volume 226, Issue 8 -

The orthorhombic phase BaGe 5 (Pearson symbol oP 60; also called Ba 10 Ge 50 ) was resolved by crystal chemical analogy and was found to be related to the cubic clathrate II. An orthorhombic structure model for BaGe 5 was obtained from a cluster-filled clathrate II derivative. The structure refinement (Rietveld method), based on X-ray diffraction powder data, resulted in a defect-rich clathrate II structure with Ba and Ge vacancies. Further analysis shows that BaGe 5 can be derived from the clathrate I Ba 8 Ge 43 by constructive crystallographic shear. The relationship to clathrate IX Ba 6 Ge 25 is also discussed.

The general building principle of the commensurate subset of mixed valent sodium cuprates Na 1+ x CuO 2 (0 ≤ x ≤ 1) has been revealed. Starting from parent ­NaCuO 2 , spin doping of the chain of edge sharing CuO 4 plaquettes requires to incorporate further sodium ions for charge compensation. The accessible space needed for this purpose is generated by elongating the NaO 6 octahedra present in NaCuO 2 . In this way, from one octahedron two square pyramidal and two tetrahedral sites result, out of which at best one each tetrahedral and square pyramidal site per original octahedron can be occupied, excluding combinations of electrostatically blocked sites. This general building principle has been employed to predict further structure candidates of this series ( x = 1/4, 1/3, 2/3, 5/7, 3/4, 1). Density functional calculations ( x = 0, 5/7, 3/4, 1) confirm the predicted charge ordering as well as the related structural features. The structure candidates are identified as local minima on the energy landscape.

The title compounds Sr 2 [BN 2 ]Br ( 1 ), Eu 2 [BN 2 ]Br ( 2 ) and Eu 2 [BN 2 ]I ( 3 ) were obtained from reactions of mixtures of Sr 3 [BN 2 ] 2 and SrBr 2 ( 1 ) and the binaries EuN, h-BN and Eu X 2 ( X = Br, I) ( 2 , 3 ), respectively. The crystal structure of Sr 2 [BN 2 ]Br was solved from X-ray powder diffraction data and those of the europium compounds from X-ray single crystal data. Sr 2 [BN 2 ]Br and Eu 2 [BN 2 ]Br are isotypic crystallizing in the rhombohedral space group R -3 m (No. 166, Pearson code: hR 18; Z = 3; a = 4.11692(2) Å, c = 26.4611(2) Å ( 1 ); a = 4.0728(3) Å, c = 26.589(3) Å ( 2 )). The crystal structures are built up by layers of condensed edge-sharing [B—N—B]@Eu 6 and [Br]@Eu 6 trigonal antiprisms, which are alternately stacked along [001]. Eu 2 [BN 2 ]I – isotypic to Sr 2 [BN 2 ]I – crystallizes in the monoclinic space group P 2 1 / m (No. 11, Pearson code: mP 24; Z = 4; a = 10.2548(6) Å, b = 4.1587(3) Å, c = 13.1234(9) Å, β = 91.215(4)°). The crystal structure is characterized by slightly puckered layers formed by condensed edge sharing I@Eu 6 octahedra which are separated by isolated [BN 2 ] 3– units. The bond lengths for the strictly linear [BN 2 ] 3– anions in (1) and (2) are d (B—N) = 1.351(4) Å and 1.356(8) Å, respectively. In Eu 2 [BN 2 ]I two crystallograhically distinct [BN 2 ] 3– anions are present with d (B1—N) = 1.32(4) Å, 1.37(4) Å and d (B2—N) = 1.30(4) Å, 1.34(4) Å, respectively. Their bond angles vary slightly: ∠(N—B1—N) = 179(3)° and ∠(N—B2—N) = 177(3)°. The magnetic susceptibility data of the europium compounds ( 2 ) and ( 3 ) indicate that the Eu ions are divalent with 4 f 7 configuration. Vibrational spectra were measured and interpreted based on the D ∞ h symmetry of the discrete linear [N—B—N] 3– moieties, considering the site symmetry reduction and the presence of two distinct [BN 2 ] 3– groups in ( 3 ).

Crystal structures of TiI 3 were determined and refined at selected temperatures between 4 and 340 K against neutron powder diffraction data. On heating, thermal expansion is found to increase abruptly at the phase transition at T c = 323 K. Most prominently, linear thermal expansion is highly anisotropic and small along c ( i.e. along chains of Ti atoms) in the low-temperature phase, while above T c it is much larger along c . An order parameter is defined by the ratio between the long and the short Ti—Ti distances on the metal chains. The temperature dependence of the order parameter indicates the transition to be of first order.

A series of rare-earth metal disulfides Ln S 2 and diselenides Ln Se 2 ( Ln = Sm, Gd, Tb, Dy, Ho, Er and Tm has been prepared by high-pressure high-temperature synthesis at 8(1) GPa. The dichalcogenides LnX 2 ( X = S, Se) are found to crystallize in the α -LaS 2 type with the monoclinic space group P 12 1 / a 1 (no. 14). The crystal structure is a twofold superstructure of the ZrSSi aristotype and consists of puckered cationic [ LnX ] + double slabs which are sandwiched by planar chalcogen sheets containing X 2 2– dumbbells.

The yttrium oxide chloride oxoselenate(IV) Y 3 O 2 Cl[SeO 3 ] 2 , doped with Eu 3+ at 3% mass percentage, can be obtained by common solid-state reactions from Y 2 O 3 , Eu 2 O 3 , YCl 3 and SeO 2 , and crystallizes isostrucäturally with the analogous terbium(III) compound Tb 3 O 2 Cl[SeO 3 ] 2 . The orthorhombic crystal structure ( Pnma , a = 548.24(4), b = 1457.92(9), c = 1102.83(7) pm and Z = 4 for undoped yttrium samples) was identified by single-crystal X-ray diffraction data and the purity of the product was checked with powder XRD methods. The presence of isolated pyramidal [SeO 3 ] 2– units could be confirmed by Raman spectroscopy. The optical band gap was determined by diffuse reflectance spectroscopy (DRS) applying the Kubelka-Munk function. Fluorescence spectroscopy measurements revealed the prominent f → f -transitions for Eu 3+ -doped compounds in both the excitation and the emission spectra of Y 3 O 2 Cl[SeO 3 ] 2 : Eu 3+ .

The antimonides Ce 2 Ir 3 Sb 4 , La 2 Ir 3 Sb 4 , and Ce 2 Rh 3 Sb 4 were synthesized by solid state reaction from the elements. The crystal structures of these compounds were determined from single crystal X-ray diffraction data. Ce 2 Ir 3 Sb 4 crystallises in a new structure type in the space group Pnma (no. 62) with a = 16.1510(8) Å, b = 4.5600(3) Å, c = 10.9463(5) Å. La 2 Ir 3 Sb 4 and Ce 2 Rh 3 Sb 4 crystallise in the Ce 2 Ir 3 Sb 4 structure type as well with a = 16.2659(10) Å, b = 4.5896(3) Å, c = 10.9996(7) Å) and a = 16.2293(8) Å, b = 4.5604(2) Å, c = 10.9804(5) Å, respectively. The four- and five-bonded transition metal atoms and three- and four-bounded Sb atoms form a 3D-network with the rare-earth metal embedded in its cavities, resembling the topology of Ca in the CaBe 2 Ge 2 or Th in ThCr 2 Si 2 type. Magnetic susceptibility and X-ray absorption near edge spectroscopy data indicate a stable trivalent state for Ce in the Ce 2 Ir 3 Sb 4 compound.

Simple rod packings of new kinds are used to circumscribe the Platonic and the Archimedean polyhedra. The geometry is chiral and describes a spherical propeller and differences in the Echoviruses 7 and 12 structures. A cubic version of such a chiral virus is discussed for the early evolution.

The reconstructive transition β -quartz to keatite is evaluated by employing symmetry-adapted hyperbolic surfaces, i.e. periodic equi-surfaces (PES) as structural trial models. The PES descriptors reveal a transition model very close to the one discussed by Li et al. We can show that this model is associated with only a small shift of the principal structure factors in reciprocal space. We derive an intermediate structure halfway between quartz and keatite of P2 1 symmetry through symmetry considerations and group-subgroup relations. Atomic shifts are given. It is shown that topological modeling of reconstructive phase transitions by means of periodic hyperbolic surface descriptors is a valuable extension to MD methods in exploring possible transition coordinates. As the PES-method works strictly under symmetry control along group-subgroup relations it allows for a rationalization of both global structural changes and local chemical variations. The whole transition is described by means of only one significant set of structure factors for quartz and two sets for keatite.

A continuous, genus-preserving transformation relating four minimal surfaces – P , G , D and H – was suggested within a common trigonal group-subgroup pair ( P -3 c 1– P 321). Periodic nodal surfaces (PNS) were used as approximants of minimal surfaces to illustrate the transition path. The mean and Gauss curvatures of PNS were calculated in order to quantify their similarity to minimal surfaces. The inhomogeneity of the Gauss curvature distributions on PNS was used to produce tilings directly on the surfaces. Such tilings on the P , G and D surfaces can be easily related to three-dimensional nets important in structural chemistry ( rhr , analcime, sodalite frameworks, respectively). A tiling on the H surface gave rise to a completely new 3,4-coordinated net.

Both, Periodic Nodal Surfaces (PNS) and exponential scale surfaces (ES), are suitable tools to investigate and describe the organisation of crystal structures. Therefore the mathematical relationship between ES and PNS is investigated. It is shown that the function cos ( x ) within the range 0 ≤ x ≤ 2π can be developed into a series in terms of orthogonal functions Φ n ( x ) = Σ k = 1 n c n k exp (cos (( k –1) x )). An orthonormal set of functions Φ n ( x ) has been evaluated using Gram-Schmidt orthonormalization. Series representation of cos ( x ) and sin ( x ) in terms of exp (sin (( k –1) x )) is impossible.

We are looking back on 30 years development of periodic space partitioners (PSP) and their relations to their periodic relatives, i.e. minimal surfaces (PMS), zero potential surfaces (P0PS), nodal surfaces (PNS), and exponential scale surfaces. Hans-Georg von Schnering and Sten Andersson have pioneered this field especially in terms of applications to crystal chemistry. This review relates the early attempts to approximate periodic minimal surfaces which established a systematic classification of all PSP in terms space group symmetry and consecutive applications in a variety of different fields. A consistent nomenclature is outlined and different methods for deriving PSP are described. Characteristic structure factor sets which solely define PNS by can be used to discriminate structure types of a given symmetry or even to determine complicated crystal structures. The concept of PSP relates space group symmetry, topology, and chemical bonding in an intriguing way and tessellations on PSP which can be generated in a straight forward way allow to predict new framework types. Through transformation of such continuous topological forms a new entry has been found for understanding and interpreting reconstructive phase transitions. Finally we indicate the importance of PSP models for soft matter science.