Volume 222, Issue 10

In this paper, we obtain the list of all color groups associated with a coloring of a square or hexagonal lattice Λ arising from sublattices of Λ. The results are obtained using a canonical representation of a sublattice L of Λ by a 2 × 2 matrix and no restriction on whether L is compatible or not with Λ is imposed.

The crystal structure of the intermetallic compound HfPdGe is investigated by means of X-ray single crystal and high-resolution synchrotron powder diffraction in combination with light microscopy. Investigated specimens exhibit twinning which can be described by a six-domain model of a monoclinic basic structure. The crystal structure of HfPdGe (space group P 2 1 / m , Pearson symbol mP 18, a = 6.6573(1) Å, b = 3.9359(1) Å, c = 11.4411(2) Å, β = 90.102(1)°, Z = 6) comprises a three-dimensional polyanion of alternating palladium and germanium atoms with Pd—Ge distances varying between 2.499(2) Å and 2.647(3) Å. The structural motif of HfPdGe contains fragments of the TiNiSi and the ZrNiAl structure types.

The new monodiphosphate Li 9 Cr 3 (P 2 O 7 ) 3 (PO 4 ) 2 was synthesized and analyzed by single-crystal X-ray diffraction, infrared and Raman spectroscopy. It crystallizes in the trigonal space group P -3 c 1 with the following unit cell constants: a = b = 9.684(1) Å, c = 13.605(1) Å, V = 1104.9(2) Å 3 . The three-dimensional framework is made up of [(CrP 2 O 7 ) 3 (PO 4 ) 2 ] 9– layers, with CrO 6 octahedra sharing vertices and edges with mono- and diphosphate groups. Li cations, spread over three different sites, fill up the remaining cavities, stabilizing the framework via Li—O bonds, making up tetrahedral arrangements at Li(2) and Li(3), and a complex hexacoordination at Li(1). IR and Raman spectra of Li 9 Cr 3 (P 2 O 7 ) 3 (PO 4 ) 3 confirm the centrosymmetric structure and the bent configuration of the POP bridge of the diphosphate group.

It was shown by quantum chemical calculations (TB-LMTO-ASA) for the compounds of the system aluminium—platinum that the Bader's atomic volumes and charges of platinum and aluminium atoms change with the concentration. This behaviour is in contrast to Vegard 's approach which assumes constant volume increments of the constituents in the whole concentration region. Introduc ing the variation of the atomic volume with the composition extends the Vegard 's approach and allows non-linear and even non-monotonic slope of the atomic volume vs concentration dependency, which is observed experimentally in several systems.

A series of crystal structures of tris( N , N -di-isobutyldithiocarbamato)bismuth(III), Bi{S 2 CN(iBu 2 )} 3 ( 1 ), tris( N , N -tetramethylenedithiocarbamato)bismuth(III), Bi{S 2 CN(CH 2 ) 4 } 3 ( 2 ), tris( N , N -hexamethylenedithiocarbamato)bismuth(III) chloroform solvate, Bi(S 2 CN(CH 2 ) 6 ) 3 · CHCl 3 ( 3 ), and tris( N -methyl, N -phenyldithiocarbamato)-bismuth(III) hemi acetonitrile solvate, Bi(S 2 CN · (Me)Ph) 3 · 0.5 CH 3 CN ( 4 ) has been determined and each structure shows the presence of three chelating dithiocarbamate ligands as well as two (in ( 1 ) and ( 2 )) or one (in ( 3 ) and ( 4 )) intermolecular Bi … S interactions leading to the formation spherical dimeric aggregates. The conclusion of this structural study is that regardless of the size of the dithiocarbamate-bound R groups, intermolecular Bi … S interactions dominate the crystal packing in Bi(S 2 CNR 2 ) 3 .

The compound C 36 H 26 N 4 O 4 , a derivative of Pigment Yellow 101, is one of the few organic pigments that show fluorescence in the solid state. Since single crystals could not be grown, the structure was determined from powder data. The X-ray powder pattern could be indexed with an orthorhombic unit cell. The space group remained ambiguous. The crystal structure was solved by lattice energy minimisation in different space groups using the program CRYSCA. Subsequently, the structure was refined by the Rietveld method using restraints. The compound crystallises in a herringbone pattern in Pbcn with a = 30.117(1) Å, b = 9.723(2) Å, c = 9.511(3) Å, Z = 4 with the molecule on an inversion centre. The insolubility and the solid-state fluorescence can be explained from the crystal structure.

The crystal structure of C 70 ·Se 8 ·CS 2 was determined from single crystal X-ray diffraction data at 100 K. Due to some peculiarities of the space group Pca 2 1 and the presence of local centres of symmetry, the crystal structure refinement turned out to be problematic. Instead of stabilizing the refinement procedure by means of a very high number of restraints about direct neighbour distances and -angles, and the shape of the probability density function of the carbon atoms of the fullerene molecules, the molecular structure of the C 70 molecules was treated as a rigid body applying a local symmetry restraint in a local coordinate framework, and the TLS-formalism, using the JANA2000 program.The crystal structure may be derived from the NiAs structure type, with the fullerene molecules forming a highly distorted hexagonal closed packing. In order to enable lone-pair-p-interactions between the fullerene and the chalcogene molecules, the Se 8 -rings are shifted from the centres of the octahedral voids towards the triangular faces.

Single crystals of TPA-ZSM-5 were synthesized using KOH as a mineralizer instead of NaOH. The size of the TPA-ZSM-5 crystals after 120 h was approximately 100 μm. When KOH was used, the quantity of TPA-ZSM-5 crystals formed was increased, and Al distribution in the crystal was uniform. The form and quality of these crystals were suitable for single crystal X-ray diffraction. Nucleation of the analcime by-product, which is formed in the presence of NaOH, is inhibited when KOH is used, because the potassium ion does not act as a template for the analcime structure. Instead, zeolite W was observed as a by-product. However, compared to analcime, the amount of zeolite W was lower, and it was easier to separate from TPA-ZSM-5. Thus, potassium ions play an important role in the production of large quantities of high-quality ZSM-5 with a uniform Al distribution.

Geometry of hydrogen bonds in 2-amino-3-hydroxymethyl-1,3-propane diol (TRIS) was accurately determined by single crystal TOF neutron diffraction at 30 K, 100 K and 170 K. The structure of TRIS can be formally described as a structure formed by layers of molecules stacked along the b -axis. Within layers the molecules are coupled by O—H … O'/N hydrogen bonds, while the adjacent layers are linked by weaker N—H … O bonds. Weak intramolecular C—H … O contacts stabilize the molecule. Refined anisotropic displacement parameters are analyzed using the TLS approach at each temperature. Frequencies of translational and librational modes are compared to those obtained by solid state calculations. Molecular DFT calculations with simulated crystal environment were used to reveal the influence of hydrogen bonds on molecule's geometry. The shape the molecule has in crystal is not optimal under the absence of external forces and in the structure is maintained at the expense of ∼33 kcal/mol. Comparison of molecular and solid state DFT frequency calculations predicts red shifts of O—H stretching frequencies due to formation of hydrogen bonds.

Having started the discussion on “What is a crystal?” and having carefully read all contributions to it, I feel obliged to summarize and draw some (interim) conclusions. Even though written and printed, I consider this to be a round-table discussion. Hence, I shall refrain from mentioning names and acknowledging credit unless that cannot be avoided.