Volume 142, Issue 1-2

A theory of polycolor symmetry is derived from elementary considerations. It is shown that each color group is characterized by a symmetry group G , and a subgroup H which determines a homomorphism from G to a group Γ of color permutations. Various ways in which the properties of H can affect the color groups are discussed. The 32 crystallographic point groups are classified in a new way which facilitates the determination of subgroups and hence of color groups. Several treatments of color symmetry that have appeared in the literature are discussed. They seem to differ in their assumptions and conclusions; it is shown that most of these differences can be traced to implicit or explicit requirements which the authors have placed on the groups H or Γ .

Dipotassium-tetrazidozincate, K 2 Zn(N 3 ) 4 , crystallizes in space group Pbca − D 2 h 15 with the following cell dimensions: a = 14.40, b = 11.70, c = 11.29 Å, Z = 8. The crystal structure was solved using three-dimensional x-ray data by interpretation of Patterson and Fourier functions. The refinement by block-diagonal-matrix least squares led to an R value of 8.7%. The structure consists of isolated Zn(N 3 ) 4 tetrahedra. Two potassium ions are surrounded by eight azide groups. The azide groups are linear and symmetric, the mean N–N distances are 1.184 Å.

The crystal structure of bis(diethylcarbamoyl)mercury, [(C 2 H 5 ) 2 NCO] 2 Hg, has been determined by x-ray diffraction. Due to twinning of the crystals, the analysis had to be based on reflections having h + k even, and packing considerations. The crystals are monoclinic, with cell dimensions a = 15.014(8) Å, b = 11.930(9) Å, c = 4.082(2) Å, β = 115.13(3)°. The space group is either P 2 1 / a , P 2 1 or Pa , with two molecules per unit cell. The C–Hg bond length is 2.13(2) Å. No intermolceular coordination to the Hg atom is observed; the intermolecular distances are Hg…N, 3.67(3) Å, and Hg…O, 3.40(3) Å.

The temperature dependence of the < u 2 > ½ 's was studied in the temperature range 22 to 500°C for the individual atomic species of NaCl, NaF, KCl and KBr. An initial set of values computed by polynomial extrapolation according to the model by B uyers and S mith (1968) was corrected for quasi-harmonic effects. The results are in excellent agreement with experimental data on NaCl. Specifically the experimental ratios of 〈 u 2 〉 ½ for Na 18° + to Na 227°c + and Cl 18° − to Cl 227°c − c are 1.30 versus the value 1.32 here reported.

The crystal structure of three addition compounds of glycine, viz., bisglycine barium(II) dichloride monohydrate, (NH 3 + CH 2 COO − ) 2 Ba ++ Cl 2 − · H 2 O; bisglycine strontium(II) dichloride trihydrate, (NH 3 + CH 2 COO − ) 2 Sr ++ Cl 2 − · 3H 2 O;and bisglycine manganese(II) dichloride, (NH 3 +CH 2 COO − ) 2 Mn ++ Cl 2 − , hereafter refered as GlycBa, GtycSr and GlycMn, respectively, were solved by single-crystal x-ray diffraction methods and refined to R values of 0.034, 0.058 and 0.074, respectively, using visually estimated and counter measured intensity data. GlycBa and GlycSr crystallize in the orthorhombic system of space group Pbcn , with four formula units per unit cell of dimensions a = 8.31, b = 14.84 and c = 9.32 Å; and a = 16.42, b = 9.35 and c = 8.26 Å, respectively, and GlycMn crystallizes in the triclinic system of space group P [unk], with one formula unit per unit cell of dimensions a = 4.97, b = 7.92 and c = 6.98 Å, α = 107.4, β = 115.9 and γ = 87.0°. The glycine molecule is almost planar except for the nitrogen atom, which deviates by 0.145, 0.113 and 0.677 Å. The conformation of the glycine molecule is synplanar with conformation angle of 5.8, 6.7 and 29.2° and the molecule exists in zwitterion configuration in these structures. Nitrogen, chlorine and water-oxygen atoms take part in the hydrogen-bond formation and only one of the carboxyl-oxygen atoms is acceptor of an hydrogen bond in GlycBa and GlycSr whereas both the carboxyl-oxygen atoms are acceptors of hydrogen bonds in GlycMn. The average values of N…O, N…Cl, OCl and O…O bonds are 2.86, 3.21, 3.23 and 2.84 Å, respectively. The coordination number is 9 in GlycBa and GlycSr and is 6 in GlycMn. Oxygen and chlorine atoms are coordinated to the metal ion in GlycBa and GlycMn and chlorine atoms do not enter into coordination with the metal ion in GlycSr. The coordination polyhedron around Ba ion can be visualized as a distorted antiprism with an extra atom and around Sr ion as a distorted antiprism with an extra atom or as a distorted regular prism and around Mn ion as an octahedron. Glycine residue acts as a bidentate, forming four-membered chelate rings with metal ions in GlycBa and GlycSr and acts as an unidentate in GlycMn.

The crystal structure of the inclusion complex of zeolite Na- A with NaNO 3 has been determined from powder data. The refinement in space group Pm 3 m was carried out by means of Fourier and least-squares methods, and led to an R value based on intensities of 0.17. The cubic pseudo-cell content was 12Na[12AlO 2 ,12SiO 2 ], 9.3NaNO 3 , 6.7H 2 O with a cell constant of 12.39 ± 0.02Å. All nitrate anions have their threefold axis in common with the similar axis present in the host structure. Two nitrates appear to be located inside the sodalite cage. Most of the nitrates, and also the water molecules incorporated during washing, occupy positions in the large cavity. The nitrate anions attached directly to the wall of the cavity lie in the plane formed by the nearest three cations. Consideration of the interatomic distances shows that one cannot strictly distinguish between cations belonging entirely to the framework and those entering with the included nitrate anions.

The crystal structure of 1,10-dithia-[2.2]metacyclophane, C 14 H 12 S 2 , has been determined by x-ray diffraction methods. The crystals are monoelinic with space group P 2 1 / n and cell dimensions a = 7.868, b = 27.269, c = 5.600 Å and β = 98.17°; Z = 4. The structure was solved by direct methods and refined by block-diagonal least-squares methods; R = 0.036 for the 1425 observed reflections. The molecule was found to be highly strained and the boat-shape deformation of both phenyl rings was observed.

The crystal structure of 8-nitro-1,10-dithia-[2.2]metacyclophane, C 14 H 11 O 2 NS 2 , has been determined by x-ray diffraction methods. The crystals are triclinic with space group P [unk] and cell dimensions a = 13.865, b = 7.626, c = 6.988 Å, α = 120.07°, β = 84.13° and γ = 94.44°; Z = 2. The structure was solved by direct methods and refined by block-diagonal least-squares methods; R = 0.053 for the 2277 observed reflections. The strain of the molecule and the boat shape deformation of both phenyl rings were found to be much increased by the introduction of a bulky nitro group. The best plane of the nitro group is inclined by 47° with respect to the plane of the adjacent phenyl group.

The cation distribution in the tetragonal spinel magnesium manganite has been determined by neutron diffraction. The degree of inversion has been found to be about 20 per cent. The values of the oxygen parameters as well as the interionic distances have also been calculated.

Crystal structures of seven new cadmium iodide polytypes 10 H 3 , 10 H 4 , 12 H 7 , 12 H 8 , 16 H 7 , 24 H 2 , 28 H 4 have been worked out. The structures are represented as 22(11) 3 , 21111211, 22(11) 4 , 2112(11) 3 , 12322222, 221(22) 4 3 and (22) 2 (11) 4 22(11) 4 respectively, in Zhdanov symbols. They all belong to the space group P 3 m 1.