Volume 145, Issue 3-4

Germanium dibromide (GeBr 2 ) is monoclinic, P 2 1 / c , with a = 11.68, b = 9.12, c = 7.02 Å, β = 101.9°, and eight formula weights per cell. The crystal structure as determined by x-ray diffraction consists of layers of edge-sharing distorted GeBr 6 octahedra parallel to {100} with bromine bridges linking the layers. Distortion of the octahedra gives rise to chains of vertex-sharing GeBr 3 trigonal pyramids within the octahedral layers. The octahedral distortion in GeBr 2 and other germanium halides may be an example of the second-order Jahn-Teller effect.

All twelve independent components d ijkl = ½[unk]( εij components of strain tensor, E k components of electric field) of the quadratic electrostrictive tensor of rhombic calcium formate have been determined employing an improved method for measuring extremely small thickness variations. These variations are transformed into a frequency modulation of a 100 MHz oscillator and compensated with the aid of an auxiliary crystal of known linear electrostriction. The constants exhibit a similar behaviour as those of alkali halides of rocksalt type: the response on an electric field is a longitudinal contraction and a transversal dilatation. The observed distinct anisotropy is correlated with the elastic and dielectric behaviour.

There have been taken high-temperature photographs from powders of the high-temperature phase Fe 2 Si. From a 1062 ± 10°C photograph the positions of the diffraction lines could be calculated with the hexagonal constants a = 4.052 ± 0.002 Å, c = 5.085 5 ± 0.002 5 Å, c / a = 1.255, which are equivalent to the rhombohedral values a = 8.667 Å = 3 × 2.889 Å, ϱ = 89.06Å. Calculations of diffraction intensities prove a lattice which is in close relation with the states of order in the α -(Fe,Si) mixed-crystal series with the filled NiAs type and with the Fe 5 Si 3 structure. After quenching one finds a D 0 3 type with a = 5.61 ± 0.02 Å = 2 × (2.80 5 ± 0.01) Å showing a short range period of τ = 8.51 ± 0.17 Å = 3 × (2.84 ± 0.06) Å. At high temperatures the Fe 2 Si phase demands more space than those α -(Fe,Si) crystals with slightly lower silicon concentrations. At room temperature on the contrary a contraction is found.

Conditions under which the product of the three structure factors forming a triplet would be positive are discussed in a special case when the diffracted intensities are predominantly influenced by the low number of atoms in the unit cell.

The theoretical basis for an iterative procedure for adjoining antiidentity operations to point groups is presented. The theory is stated in a general context and is then applied to point groups yielding the crystallographic point groups from the proper crystallographic point groups and yielding the antisymmetry groups (including the magnetic point groups) from the crystallographic point groups. A method for constructing point groups that describe the symmetry of an object having a number of two-mode properties (positive-negative, black-white etc.) is discussed. Finally, a physical interpretation of the crystallographic point groups involved in the construction of a given magnetic point group is presented.

The crystal structure of clinoptilolite has been worked out, based on C2/ m , using two crystals from two different localities: one from Kuruma Pass, Japan, a = 17.660(4) Å, b = 17.963(5) Å, c = 7.400(3) Å, β = 116.47(3)°, and the other from Agoura, U. S. A., a = 17.662(4) Å, b = 17.911(5) Å, c = 7.407(3) Å, β = 116.40(3)°. In the tetrahedral framework of the heulandite type there are recognized four kinds of main cation positions, M(l), M(2), M(3), and M(4). At M(l) and M(2), which have so far been known as cation positions in the heulandite structure, Na and C'a are located ; M(l) tends to accommodate more Na than M(2). The new position, M(3), which is specific for K, is located almost at the center of the eight-membered ring of the channel parallel to a . This position is coordinated by six framework oxygen atoms and three water molecules. At M(4), which is octahedrally coordinated by six water molecules, Mg is located. It is very likely that these four positions are characteristic of all members of the heulandite-group zeolites. The difference between clinoptilolite and heulandite is primarily in the difference of site content: for clinoptilolite, M(l) and M(2) are rich in Na, while for heulandite, they are rich in Ca. The occupancy of K at M(3) in clinoptilolite is, in general, higher than that of heulandite. The location and coordination of K explain the evidence that the presence of K in the structure is one of the controlling factors of the thermal behaviour of the heulandite-group zeolites.

The chiral isomers of di[ethylene-l,2-bis(methylphenylphosphme)]ruthenium(II)-chloride crystallize in the space group I 4 with a = 22.14 Å, c = 14.00 Å and Z = 8. The structure has been determined by x-ray diffraction methods and was refined to an R value of 6.6%. The absolute configuration has been established by measuring a suitable collection of Friedel pairs. The complex molecules have almost the symmetry 222, and are situated with respect to the c axis in such a way, that the structure is nearly nonpolar. The absolute configurations of the asymmetric P-Atoms is R in the (+)-isomer and S in the (−)-isomer.

In usual arrangements for measuring quadratic electrooptic effects the electrostatic attraction of the electrodes produces piezooptic effects, which are of the same order of magnitude as the intrinsic effects. Employing auxiliary electrodes, a full compensation of these stresses within the crystal can be achieved. By these means also the determination of piezooptic constants is possible. The method is tested with several crystals comparing the measured piezooptic constants with literature values.

Tables are presented which allow rapid derivation of the relationships which determine the probability of the positive sign of a structure factor according to the Σ 1 relationship for triclinic, monoclinic and orthorhombic space groups.

The crystal and molecular structure of C.I. Pigment Red 6, 4-chloro-2-nitrophenylazo-2-naphthol has been determined by x-ray diffraction techniques. It crystallizes in the monoclinic system with cell parameters a = 12.293 ± 0.005 Å, b = 6.958 ± 0.003 Å, c = 15.780 ± 0.005 Å, β = 94.22 ± 0.10° The space group is P 2 1 / c and there are four molecules per unit cell. The structure was solved using direct methods and least-squares refinement has been completed on three-dimensional data with θ less than 55° (Cu Kα radiation) The hydrogen atoms have been found and included but not refined The molecule exists as the hydrazone tautomer and intramolecular hydrogen bonds keep the molecules approximately planar; the slight deviations from planarity are, in the main, explained by packing considerations. The molecules are packed in columns with alternate molecules antiparallel and are linked by van der Waals forces.

Madelung constants were computed for a number of millerite (= lowtemperature NiS) type and high-pressure GeP-type structures, mainly for idealized representatives with all five A–B distances in the AB 5 polyhedra made equal. The millerite type proves to be electrostatically less favourable than a theoretical A [5] B [5] structure with symmetry P 6 3 / mmc described previously, The same holds for the majority of the representatives of the high-pressure GeP type, notably also for the representative in which the AB 5 polyhedron has the same shape as the electrostatically optimal isolated AB 5 group of tetragonal symmetry: only models that are very close to the NaCl type are electrostatically more favourable. The results of the computations agree with the experience that A [5] B [5] structures do not occur for predominantly ionic compounds.

On rhombohedral strontium monouranate which is metastable below ca . 770°C ( α -phase) and stable above ca . 1230°C ( γ -phase) in air, x-ray powder diffraction study was made with the samples of three different compositions, i.e . SrUO 3.948(1) , SrUO 3.597(1) and SrUO 3.777(1) . Their structures were essentially identical with that of Z achariasen (1948) on SrUO 4 with space group R [unk] m , Z = 1; 1 U in (000), 1 Sr in (½½½),2 O(1) in ±( uuu ) and 2 O(2) in ± ( vvv ), and no more discrepancies were observed in the cell and the oxygen parameters between α and γ phases than those resulted from the oxygen non-stoichiometry: SrUO 3.948(1) a = 6.551(3) Å, α = 34.82(2)°, u = 0.112(2), v = 0.357(2) SrUO 3.597(1) a = 6.587(3) Å, α = 35.30(2)°, u = 0.110(2), v = 0.340(2) SrUO 3.777<1) a = 6.542(3) Å, α = 35.54(2)°, u = 0.113(2), v = 0.340(2). In oxygen deficient crystals, oxygen vacancies were found to be formed in O(2) position but not in O(1). The U–O(2) bond length 2.30(1) ∼ 2.31(1) Å is reasonably consistent with the other alkali and alkaline-earth uranates, whereas the U–O(1) bond length lies in the range 2.04(4) ∼ 2.08(4) Å which is longer than the usual uranyl bond length of 1.8 ∼ 1.9 Å.

From the information contained in one powder photograph obtained in a Guinier-Hägg camera the crystal structure of (NH 4 ) 4 [(MoO 2 ) 4 O 3 ] (C 4 H 3 O 5 ) 2 · H 2 O, only known in microcrystalline form, has been determined and refined to a moderate degree of accuracy. The work has comprised step-scanning measurement of the intensity profile, indexing with a trial-and-error program, determination of the Mo positions from an incomplete Patterson function derived from resolved integrated intensities, and finally localization of light non-hydrogen atoms and structure refinement by a series of Fourier calculations and profile analyses. The material crystallizes in the monoclinic system, space group C 2, with two formula units in a cell of dimensions a = 14.572(2) Å, b = 10.114(2) Å, c = 11.461(2) Å and β = 121.45(1)°. Since as many as 51 parameters are involved the atomic coordinates obtained are approximate, but the main features of the structure are established. The structure contains discrete [(MoO 2 ) 4 O 3 (C 4 H 3 O 5 ) 2 ] 4− ions having a twofold axis through an oxygen atom.