Space Group Data Research Articles

Relations between dense sphere packings

A survey is made of periodic three-dimensional assemblies of equal spheres in which each sphere has from 6 to 11 nearest neighbors. Space group data are derived for 34 of the more dense sphere packings formed by stacking planar layers of three kinds. The relation of the density of sphere packings to coordination number and the “symmetry-equivalence” of spheres are briefly discussed.

Cation ordering in the tetrahedral sites of the thiospinel FeIn 2S 4 (indite)

Recent X-ray and electron diffraction studies have substantiated earlier indications, based on dielectric behavior, e.s.r. studies, elastic constants, magnetic measurements, specific heat and spectral data, that in many cases the cubic spinel structure exhibits a small deviation from Fd3 m symmetry. This discrepancy has been associated with a small displacement (less than 0.10Å) of the octahedrally coordinated metal atom along [111] in space group F4̄3 m but has not hitherto been tested using precise single crystal X-ray diffraction data. Although more than thirty hk0 reflections of the type h + k = 4 n + 2, structurally forbidden for the space group Fd3 m, are clearly visible in diffraction patterns from the thiospinel indite ( FeIn 2S 4; a = 10.618(3) A ̊ ), a refinement in space group Fd3 m using 412 unique X-ray data ( u = 0.25907(7); inversion parameter = 0.947(7); R = 0.048) indicates that the structure may be satisfactorily described in terms of the conventional symmetry. A refinement of the data in space group F4̄3 m shows that the displacement, if present, is not detectable within experimental error but allows a rationalization of the observed diffraction symmetry in terms of an unequal distribution of In atoms over the two nonequivalent tetrahedral sites in F4̄3 m (100 and 83 ± 1% In, respectively) and the presence of a nonspherical distribution of residual electron density about the octahedral site.

Crystal and molecular structure of tetraphenylarsonium tetranitratomanganate(II) and X-ray study of other M(NO3)4 2? ions (M = Ni, Cu, or Zn)

Tetraphenylarsonium tetranitratomanganate(II), (Ph4As)2Mn(NO3)4 forms monoclinic crystals, space group C2/c, with a= 23·35, b= 11·37, c= 18·36 Aβ= 107·0° and is isomorphous and nearly isostructural with the corresponding cobalt complex. The eight co-ordination polyhedron in the anion is of approximate D2d(dodecahedral) symmetry. The bidentate nitrate ions are co-ordinated to the metal in a more symmetrical fashion than in the cobalt analogue, the bonds defining the elongated bisphenoid averaging 2·27 A(2·08) and those defining the flattened bisphenoid averaging 2·34 A(2·45)[values for Co(NO3)42– in parentheses]. These differences apparently reflect the change in central metal-atom radius and the d-electron configuration.Unit-cell and space-group data indicate that the Zn(NO3)42– ion is also eight co-ordinate but that the corresponding copper complex is not.

Unit Cell and Space Group Data on Certain Pyranose Sugars.

Unit Cell and Space Group Data on Certain Pyranose Sugars.

A preliminary crystallographic investigation of 1-phenylhydantoin and three derivatives of uracil

A preliminary investigation has been made of the crystallographic data of 4-methyl-5-ethyluracil (I), 4-methyluracil-5-acetic acid (II), 4-methyl-5-methylaminouracil (III), and 1-phenyLhydantoin (IV). The lattice constants and space-group data were obtained from rotation and Weissenberg photographs; the determinations were made on the basis of one crystal setting for each species, and the measurements were corrected for film shrinkage. The angular constants of the direct cells were determined by the method of angular lag (Buerger, 1942): from measurements on (1) an equi-inclination photograph of the first layer in monoclinic cases, (2) a composite anti-equi-inclination photograph (of the zero and first layers, respectively) in triclinic cases. The crystal densities were determined by flotation. The errors are estimated to be about ± 0.05 A for the linear constants and about ± 0 ° 20' for the angular constants.