Volume 139, Issue 3-5

Natural jordanite from Binnatal, Switzerland is monoclinic, space group P 2 1 / m , with a = 8.918(1), b = 31,899(4), c = 8.462(1) Å and β = 117.79(1)°. The unit cell is approximately halved along both the a and c axes. Starting from the one-fourth substructure, the complete structure was solved by a kind of minimum residual method (the method of key shifts), and was refined by ordinary Fourier and least-squares methods ( R = 7.0%). The structure of jordanite is a deformed PbS-type structure. The unit cell contains 40 metal and 46 sulfur atom sites. The twelve independent metal sites are distributed on three layers at y ≈ 0.05, ≈ 0.15 and ≈ 0.25 (the mirror plane), with four metal sites, 3 Pb + As, on each layer. These metal layers are interleaved by sulfur layers; three additional S atoms are added to the third metal layer to form a metal-sulfur mixed layer. Some of the sites have statistical nature; one Pb site on the first layer is occupied by 0.50 Pb + 0.50 As, another Pb site on the third layer is occupied by 0.88 Pb. Thus, the unit-cell content is Pb 27.8 As 12.0 S 45.8 , with the ideal formula Pb 28 As 12 S 46 . The fully occupied Pb atoms on the first, second and the third layers are coordinated with six (average Pb–S = 3.01 Å), seven (3.04 Å) and eight (3.08 Å) S atoms, respectively. The sulfur coordinations about the As atoms are ordinary trigonal pyramids with an average As–S = 2.25 Å. The AsS 3 pyramids are isolated from each other (type I.c 1 of the classification of N owacki ).

The zeolite Li-A(BW) was first reported by B arrer and W hite (1951) and given the approximate formula, LiAlSiO 4 · 2H 2 O. A recent examination of their specimens has resulted in the determination of the orthorhombic unit cell with a = 10.31, b = 8.18, c = 5.00 Å, and the proposal of a structure based on Pna 2 1 . The x-ray analysis was based on 78 intensity data from powder, and refined to R = 0.13. The aluminosilicate framework consists of 4-, 6- and 8-membered rings, the 4-membered rings linking to form ribbons running lengthwise along the fibrous crystals, while the 8-membered rings enclose channels of about 3.2 Å free diameter running likewise. A column of water molecules is situated centrally in the channel adjacent to Li cations which are located each side of the 6-membered rings. Use is described in determining the space group and the ratio Al/(Si + Al), of a program which refines distances to prescribed values. Evidence of ordering of Si and Al atoms is also found. Li-A(BW) shows much similarity to bikitaite and cancrinite.

The crystal structure of a mica, which was synthesized from talc and potassium carbonate under a hydrothermal condition, was determined by least-squares methods. The mica is a Mg-rich free from Al ions, with Mg ions substituting for Si, and with some vacant positions in the octahedral sites. This mica is intermediate between the trioctahedral and dioctahedral types and agrees with a Mg-rich mica first reported by S eifert and S chreyer (1971). The lattice parameters are: a = 5.321(2), b = 9.238(1), c = 10.287(1) Å and β = 100.06°(1). The space group is C 2/ m with Z = 1. The final residual is R = 9.2% using anisotropic temperature factors. The refinement gave the structural formula: K 2.00 (Mg 5.60 □ 0.40 )(Si 7.32 Mg 0.68 )O 20 (OH) 4 , where □ means a vacant position. In the light of this result, the structural formula may be shown from the chemical composition as: (K 1.92 Na 0.07 )(Mg 5.68 □ 0.32 )(Si 7.26 Mg 0.6l Fe 0.07 Al 0.06 )O 20 (OH) 4 , where small amounts of Al and Fe ions are included in the tetrahedral sites. (Si,Mg)–O distance, 1.649 ± 0.006 Å in average, suggests 8.5% substitution of Mg ions in the tetrahedral sites, which is close to 7.6% in the above formula. The difference between the mean basal O–O distance and the mean basal-apical O–O distance is small (0.018 Å). Inner and outer K–O distances are 3.010 Å and 3.346 Å in average respectively. The observed tetrahedral rotation angle (7.10°) is close to the value calculated by the equations previously reported.

Cinnamic acid pyrrolidid crystallizes in the orthorhombic space group Pbca having parameters a = 24.884 Å, b = 7.477 Å and c = 11.747 Å. The crystal structure was found by phase assignement with the symbolic-addition procedure. The refinement by the block-diagonal-matrix least squares led to an R value of 0.11 using 1410 observed reflections. A short discussion of the structure is given.

PbCO 3 is isotypic with aragonite and crystallizes in tlie space group Pmcn with lattice constants: a = 5.1800 Å; b = 8.492 Å; c = 6.134 Å. The structure was refined from x-ray data with the least-squares method ( R = 0.072). The configuration of the CO 3 group is discussed in relation to the structures of aragonite, strontianite and witherite.

The crystal structure of K 2 Cu(C 2 O 4 ) a · 2H 2 O was refined by the least-squares method using three-dimensional diffractometer data. The final R value is 3.6%. One of the two independent Oxalate ions is non-planar; the carboxyl groups are twisted against each other by an angle of 9°. Each of the two non-equivalent potassium atoms is surrounded by eight oxygen atoms which form a distorted squared antiprism. The oxygen polyhedra around the octahedrally coordinated copper atoms Cu(1) and Cu(2) are chain-like linked by the non-planar Oxalate ions parallel to the b axis. The octahedron chains are held together by hydrogen bonds and potassium oxygen bonds. Potassium copper Oxalate dihydrate may be twinned after [210].

The crystal structure of Cs 2 Cu(C 2 O 4 ) 2 · 2H 2 O has been determined by x-ray methods. The compound belongs to the space group P [unk]. There are two formula units in the unit cell of dimensions a = 9.2980 ± 7 Å, b = 9.1167 ± 6 Å, c = 7.1316 ± 4 Å, α = 97.524 ± 5°, β = 97.410 ± 4° and γ = 107.522 ± 4°. The R factor of the three-dimensional structure determination is 0.065. The copper atoms occupy special positions and possess octahedral coordination. There is no definite coordination for the caesium atoms. One Oxalate ion is twisted by 5.4°.

A historical review shows that the term “Gitterkomplex” (lattice complex) has been used in different meanings, without being defined explicitly. Hints on possible symbolisms are given.

An algebraic definition of “point position” is given by means of triples of linear polynomials and the concept of “lattice complex” is formulated such that the point positions can be attached to their lattice complexes by a simple algorithm.

Using some concepts of set theory and of group theory a lattice complex (Gitterkomplex) is defined as a set of point configurations. For this the difference between space groups and classes of space groups has to be considered. In order to define lattice complexes point configurations are combined stepwise to form sets of equivalent points, “Konfigurationslagen”, and classes of these. Some properties of lattice complexes are explained and possibilities of using this concept of lattice complexes are discussed.

X-ray diffraction patterns of most of the graphite-FeCl 3 compounds show line shifts and line broadenings incompatible with the simple model of structure, the model of “stages”, used as a basis for investigations up to now. Instead of starting from the old model with its periodic stacking of layers, we now assume a one-dimensional disorder of composition, i.e. a disturbance in the sequence of the layers of graphite and FeCl 3 . The intensity distribution along the 00 l axis in reciprocal space has been computed. Shifts in the position of the reflections and different broadening of the various lines have been obtained from the calculations as functions of the type and extent of the disorder in graphite-FeCl 3 samples. It is shown by some examples, that the computed and the measured 00 l -intensity distributions possess the same features. Thus it is possible to identify the type and extent of the disorder in graphite-FeCl 3 samples.

At present improved experimental techniques permit precise collection of intensity data at elevated temperatures, thus allowing a quantitative study of the temperature dependence of the structural parameters. However, our understanding of the process of thermal expansion is still poor, due to lack of precise data on the behavior of the vibrational properties of atoms. This is discussed by correlating concepts of crystal dynamics with modern theories of chemical bonding. The role of transverse vibrations in bridging-oxygen atoms is emphasized, by studying an ideal isolated Si–O–Si system at its equilibrium position and considering cation-anion interactions which obey Hooke's elasticity law. The resultant changes in the value of the Si–O–Si angle are interpreted in terms of redistribution of energy modes which are considered responsible for preferential expansion of a crystal structure. Such concepts are applied to the study of the thermal behavior of a number of silicates (diopside, tremolite, beryl). Particular emphasis is given to the relationship between the thermal expansion of low and high quartz.

Raman signals given by single crystals of ferroelectric KIO 3 are strongly dependent on the directions of phonon-propagation. The anti-Stokes frequencies, measured using different experimental arrangements, are correlated with the optical indicatrix. The ferroelectric phase transitions at 72.5°C and 212°C are accompanied by a “soft-mode” behaviour of some transversal modes, as predicted earlier. The temperature dependencies of the valence constants of I–O and K–O bonds thus calculated, show that the biggest differences in the bond energies of the ferroelectric β and γ phases must be attributed to K–O interaction. Moreover, the bonds of the IO 6 -complex are weakened during the transition in the high-temperature phase. The interatomic distances, estimated using the method of central-field approximation and the coordinates of normal modes given by S alje (1973), agree with the structural data. The phonon spectra of the phases α , β , and γ are compatible with the point group symmetries R [unk] m , Pm and P 1 with 2, 4 and 4 molecules in their respective unit cell. A decrease in the scattering frequencies is observed in Raman experiments in which a small quasi-momentum transfer is involved. This is due to polariton dispersion. The coupling parameters, calculated using polariton frequencies, indicate strong photon-phonon interactions for all wave vectors near the origin of the Brillouin zone.

Crystals of plumbagin C 11 H 8 O 3 are monoclinic with space group Pc and 8 molecules in the unit cell. The cell parameters are a = 7.10, b = 13.35, c = 20.22 Å, β = 110°.