Band 141, Heft 1-2

The structure of mercury(II)phosphate, Hg 3 (PO 4 ) 2 , has been determined by symbolic addition and Fourier methods and refined to an R value of 0.043 on the basis of 1491 independent counter intensities. The crystals are monoclinic, space group P 2 1 / c , with four formula units in a unit cell of the dimensions a = 9.737(2), b = 11.466(2), c = 6.406(1) Å and β = 99.51(2)°. The mercury atoms are two-coordinated in a nearly linear way; the mercury to oxygen distances vary between 2.06(1) and 2.13(1) Å, and the O–Hg–O angles between 163.4(4) and 169.9(5)°. All oxygen atoms belong to phosphate tetrahedra. Each mercury atom is bonded to one oxygen atom of each of two phosphate tetrahedra and each phosphate group is bonded to three mercury atoms.

The orthorhombic aragonite structure can be described by a pseudohexagonal cell with a = 9.38, c = 5.74 Å and γ = 117°, the base of which resembles that of apatite ( a = 9.43, c = 6.88, γ = 120°) closely. In addition, there exists a rough two-dimensional structural relation which is schematically represented by the formula aragonite Ca 8 □ 2 (CO 3 ) 6 (CO 3 ) 2 = 8 CaCO 3 apatite Ca 10 (PO 4 ) 6 (OH) 2 i.e . the CO 3 triangles of aragonite correspond to the PO 4 tetrahedra and OH ions in apatite, and two Ca sites of the apatite structure are not occupied in aragonite. The two-dimensional relationship is the basis of a topotactic reaction aragonite→apatite if aragonite crystals are treated hydrothermally with phosphate solutions. Starting from aragonite single crystals, it is shown that the apatite formed is not a single crystal but consists of fibers with the fiber axis parallel to c . In addition, most fibers also have parallel a axes, i.e . they are completely parallel. This is in agreement with the structural relations. The rest of the fibers is randomly rotated around c . This is obviously necessary to compensate the differences between the cell bases of both phases.

The linear electrooptical constants of orthorhombic single crystals of strontium formate, strontium formate dihydrate, and barium formate have been determined for He-Ne LASER radiation at 6328 Å. In order to obtain the absolute signs of the electrooptical constants the chirality of the crystals as characterized by optical activity, morphology, and piezoelectric effects was respected. Electrooptical and piezoelectric constants exhibit a highly anisotropic behaviour, which is connected with the preferential orientation of the strongest ionic bond chains parallel to the [001] axis.

The G and F matrix method lias been applied to the study of the force field of scheelite. The splitting of the intramolecular vibration bands and the lattice vibrations have been clarified at the same time through the intermolecular atom-atom interactions. The obtained interatomic force constants of nonbonded oxygen pairs in scheelite follow roughly the Lennard-Jones 6-12 law. The normal modes of the intramolecular vibrations and the lattice vibrations have been fully discussed on the basis of the normal-coordinate treatment. For the tetrahedral ions ( T d symmetry) of the WO 4 2− , v 2 ( E ) is larger than v 4 ( F 2 ), representing an opposite relation to the usual order. This has been explained by calculating and comparing the normal vibration and the modes of vibration for several kinds of the tetrahedral ions such as SiO 4 4− , PO 4 3− , SO 4 2− , MoO 4 2− and WO 4 2− . The assignment of the vibrations has also been theoretically confirmed.

The crystal structure of a twelve-layered hexagonal polytype of lead iodide, grown by silica-gel method, has been worked out. The structure is represented as (11) 3 2112 in Zhdanov symbols, with space group as P 3 m 1. The polytype showed a phase transformation during growth, which has been discussed in terms of creation and ordering of stacking faults.

The crystal structures of six new polytypes, 20 H 4 , 20 H 5 , 20 H 6 , 30 H 2 , 30 H 3 and 30 H 4 , of cadmium iodide have been determined. The structures are represented as 2112(11) 7 , 222221122211, (22) 3 211211, 222221121122222211, (22) 7 11 and (22) 4 2112221111, in Zhdanov symbols, with space group P 3 m 1. The growth of these polytypes have been discussed in terms of the creation of periodic stacking faults in the basic structures.

The crystal structure of zinckenite, Pb 6 Sb 14 S 27 , has been refined to an R value of 0.13 with the aid of three-dimensional x-ray data. The intensities were measured by means of a Supper-Pace autodiffractometer, using Cu Kα radiation. The hexagonal unit cell, with a = 22.148(6) and c = 4.333(6) Å, contains 1½ formula units. Results of refinements in the space groups P 6 3 / m and P 6 3 are compared according to H amilton's R -ratio test. The latter space group is the correct one.

The crystal structure of Si(OCOCH 3 ) 4 has been determined from single-crystal x-ray analysis. The compound crystallizes in the tetragonal space group P [unk]2 1 c . The unit cell with lattice constants a = 7.42, c = 11.34 Å contains two molecules. The crystals are built up by isolated silicon(IV) acetate molecules. The silicon atom is tetrahedrally coordinated and the acetate group has a role of monodentate ligand. The oxygen atom coordinated to silicon is at 1.625 Å while the second oxygen atom of the same acetate is 2.927 Å apart from silicon atom.

Several modifications of TlInS 2 crystallize from melts of this composition with annealing at various temperature. Symmetries and lattice parameters determined by the x-ray precession method are as follows: I. ( = β ), monoclinic, a ∼ b = 7.76 ± 0.01 Å, c = 30.01 ± 0.02 Å, β = 90°10′ ± 5′, P 2 1 / m , Z = 16, D x = 5.64 g/cm 3 . II. monoclinic, a = 7.77 ± 0.01 Å, b = 7.74 ± 0.01 Å, c = 240 ± 1 Å, β = 90°15′ ± 5′, P 2 1 / m , Z = 128, D x = 5.64 g/cm 3 . III. triclinic, a = 7.70 ± 0.01 Å, b = 7.77 ± 0.01 Å, c = 122 ± 1 Å, α = 90°11′ ± 5′, β = 90°26′ ± 5′, γ = 90°6′ ± 5′, P [unk], Z = 64, D x = 5.59 g/cm 3 . IV. (= α ), hexagonal, a = 7.67 ± 0.05 Å, c = 14.98 ± 0.05 Å, P 6/ mcc or P 6 cc , Z = 8, D x = 6.73 g/cm 3 .

Madelung constants were computed for some tetragonal AB 2 structure types which can be described as stacking variations of the fluorite structure. In addition to the geometrically ideal types, those deformed along a fourfold axis were also considered. The results are in agreement with the crystal-chemistry experience that, among ionic compounds of this kind, only the fluorite-type structure is observed.

The crystal structure of CaNH 4 P 3 O 9 , determined by use of the Patterson method, is a monoclinic deformation of the orthorhombic form: MgNH 4 P 3 O 9 . Trimetaphosphate ring (P 3 O 9 ) 3− has a “cis” configuration. Crystallographic features are given for three condensed phosphates: CaKP 3 O 9 and CaCsP 3 O 9 isotypic with MgNH 4 P 3 O 9 and CaNH 4 P 3 O 9 · 3H 2 O isotypic with CaNaP 3 O 9 · 3H 2 O.

Integrated x-ray intensities have been measured for 21 reflections in the 2 θ range up to 150° of polycrystalline Ni 2 SiO 4 spinel (a quench product from 40 kbar, 900°C). Using the observed structure factors of these 21 reflections and the least-squares structure refinement computer program of F inger (1969), refinements were performed on the cation occupancy, the oxygen parameter, three temperature factors and the scale factor. The final R value is 0.069. In the unit cell of AB 2 O 4 spinel (space group Fd 3 m , Z = 8), tetrahedrally-coordinated cations occupy equipoint 8 a and octahedrally-coordinated cations occupy equipoint 16 d ; oxygen atoms occupy equipoint 32 e with coordinates x , x , x . The structure refinement shows that 8% ± 6% of the total silicon atoms in Ni 2 SiO 4 spinel are octahedrally coordinated. The cation-oxygen bond distance is 1.632 Å in tetrahedral sites (92% Si, 8% Ni), and 2.076 Å in octahedral sites (4% Si, 96% Ni). The refined oxygen parameter, x , is 0.242 ± 0.003, if a center of symmetry is chosen as the origin of coordinates. That parameter transforms to 0.367 ± 0.003, when the tetrahedral site 8 a is chosen as the origin as is usually done in the literature. The lattice parameter of Ni 2 SiO 4 spinel ( a = 8.0424 ± 0.0002) used in the structure refinement was determined by least-squares analysis of six high-angle reflections (with semiconductor grade silicon as an internal standard).

Relative interlayer-bond energies based on an ionic model have been calculated for a series of layer silicates. These energies are 32.2 for muscovite 2 M 1 , 21.4 and 22.4 for two different phlogopites, 4.18 for talc and 6.53 for pyrophyllite (units are kcal/mole). Interchanging F for OH in the calculations results in energies (same order as above) of 32.6, 27.2, 27.6, 4.13, and 6.59 kcal/mole. The differences in energy between the hydroxy and fluorophlogopites represent the destabilizing effect of the hydroxyl hydrogen due to its electrostatic interaction with the interlayer cation.

X-ray diffraction data from a disordered single crystal of 4PbO · PbSO 4 was used to determine the structural principle of this compound.

The crystal structure of potassium hydrogen mesaconate has been determined and refined to an R value of 10.4%. The crystals are triclinic with a = 6.23 Å, b = 7.33 Å, c = 3.97 Å, α = 87° 30′, β = 107° 6′, γ = 98° 57′ with Z = 1, space group P 1.