Band 147, Heft 1-2

A series of topographs is rendered which might make clearly evident some of the laws of dynamic interaction in X-ray diffraction by perfect crystals.

The transformation of malachite into tenorite has been studied by x-ray diffraction, differential thermal analysis and thermogravimetric methods. The transformation, topotactic in nature, was partial when malachite was heated at 220°C for about 70 hours and was complete on further heating at 350°C for 7 hours. The orientational relationship between the two phases was found to be [100] mal //[001] ten , [001] mal //[110] ten and [010] mal nearly parallel to [[unk]l0] ten . The mechanism involved consisted in complete expulsion of CO3 groups and protons from malachite structure and readjustment of oxygen and copper ions within the lattice.

Point complexes, row complexes and net complexes in three-dimensional space are defined–by analogy to lattice complexes–as sets of point configurations in crystallographic point groups, rod groups and layer groups, respectively. For this the point configurations are united stepwise via point-positions and configuration-sets. With subperiodic groups, however, affine isomorphisms and affine automorphisms rather than isomorphisms and automorphisms of groups have to be used as equivalence relations. The assignment of all the configurationsets of crystallographic point groups, rod groups and layer groups to point complexes, row complexes and net complexes, respectively, is given explicitly by tables.

Statistics of data of space filling polyhedra lead to an upper limit of about 26 faces. In agreement with this a plausibility-reasoning renders the value 3 n —1 faces for the n dimensional space. Presuppositions regarding the shape of the polyhedra must be made, otherwise the number of faces is unlimited.

K -space symmetry rules are used to elucidate the nature of possible ordering behaviour in a single crystal. These rules are then applied to the observed behaviour in the intermediate plagioclase feldspars. Group theoretical analysis of the possible ordering behaviour in a solid solution indicates that, at arbitrary points in k -space it is possible to have an interaction between two different ordering schemes associated with the development of the same superlattice. This interaction corresponds to a structural resonance and leads to the lowering of the energy for the ordered states at the point of accidental degeneracy in the Brillouin zone of the ordering single crystal. The effect is only likely in the case of a non-equilibrium cooling cycle. The structural and other implications of the group-theoretical model are tested against the available experimental and structural data for the intermediate plagioclase feldspars, and shown to be satisfactory.

Compounds of the type (RE) 2 M 3 [BO 3 ] 4 with RE = La…Lu (except Ce), and M = Ca were prepared. Their x-ray and IR data are remarkably similar to those of Yb 2 aCa 3 [BO 3 ]4, space group P 2 1 cn , suggesting that they form an isomorphous series. For comparison, analogous compounds of the “Pr 2 Sr 3 [BO 3 ] 4 type” with RE = La, Gd, Yb, and M = Sr, as well as RE = La, Gd, and M = Ba were also prepared. Again there is a strong similarity of all data available to those of the RE—Ca-borates, suggesting that all compounds referred to probably form, with certain limitations, an isostructural group.

Potassium strontium azidehyclrate forms a series of solid solutions. Crystals with the composition defined in the title have been investigated using three-dimensional photographic x-ray data. The crystals are orthorhombic, a = 6.398 Å, b = 10.915 Å, c = 6.263 Å. The structure was solved by Patterson and Fourier techniques, and refined by least-squares method based on 291 independent X-ray reflections to an R value of 0.085. The cations are not equally distributed among the twofold positions 000 and ½0½ within the space group C 222. Each cation position has eight neighbours which form a non regular antiprism. The coordination polyhedra contain N atoms and water which are distributed at random. The azicle ions are linear and symmetric, N—N = 1.175Å.

The product crystallizes in space group P 2 1 / c with the lattice constants a = 6.168(3) Å, b = 14.245(8) Å, c = 17.683(14) Å, β = 106.24(4)°. Both phenyl-rings are cis -orientated on the oxaphospholane-ring and so the cyclopropane-ring and the oxygen atom 1 are in the cis position of the five-membered heterocycle. The methyl group is fixed in the endo position over the heterocyclic ring.

The crystal and molecular structure of C. I. Pigment Red 3, 4-methyl-2-nitrophenylazo-2-naphthol has been determined by x-ray diffraction techniques. It crystallises in the monoclinic system with cell parameters a = 16.316 ± 0.038 Å, b = 12.860 ± 0.033 Å, c = 6.960 ± 0.018 Å, β = 102.00 ± 0.05°. The space group is P 2 1 / a 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, 1601 reflections (Cu K α radiation). The hydrogen atoms have been found and included but not refined. The final residual is 7.8%. The molecule exists as the hydrazone tautomer and intramolecular hydrogen bonds keep the molecules approximately planar; the slight deviations from planarity are explained by packing considerations. The molecules are packed in columns with alternate molecules antiparallel and are linked by van der Waals forces.

The possible ways of eliminating the factors which affect the measurement of cell dimensions in the case of single crystals in general are illustrated by actual application to the triclinic crystal para nitro-phenoxy acetic acid.

The crystal structure of LiScSiO 4 olivine ( Pbnm ; a = 4.8214(7), b = 10.444(1), c = 5.9729(9) Å) has been determined and refined with anisotropic thermal parameters to an unweighted disagreement factor of 0.016. Lithium occupies the M1 site and Sc the M2 site. A comparison with isotopic Mg g SiO 4 allows recognition of structure modifications due primarily to a change of the formal charge on the octahedral cations. Important features are (1) large changes in tetrahedral geometry due to interaction of Sc 3+ and Si across a shared adge; (2) uniform increase in Li—O distances compared to Mg—O distances in the M1 site due to larger Li 1+ ; (3) both increases and decreases of bond distances of the M2 octahedron relative to those in Mg 2 SiO 4 .

The crystal structure of ktenasite from Miniera Trentin (space group P 2 1 / c , a = 5.589, b = 6.166, c = 23.751 Å, β = 95.55°) was determined by Patterson and Fourier methods and refined to a final R value of 0.058. The structure is characterized by corrugated sheets ∞ 2 [(Cu, Zn) 2 (OH) 3 O] − of distorted copper-zinc polyhedra. Sulphate groups are connected to both sides of the octahedral sheet by corner sharing. The resultant composite tetrahedraloctahedral layers are connected each other by [Zn(H 2 O) 6 ] +2 octahedra through a system of hydrogen bonds. The crystal chemical formula for ktenasite from Miniera Trentin is Zn 2 (Cu 5.2 Zn 2.8 )(SO 4 ) 4 (OH) 12 · 12H 2 O. The relations of ktenasite with other minerals are remarked and discussed.

Electrostatic site-potentials can be calculated using the Madelung method in which the crystal structure is divided into parallel slices d hkl . Each slice is divided into a set of parallel identical ionic chains [ uvw ]. Site-potentials calculated for the same ( hkl ) but different [ uvw ] have the same values. However, site-potentials calculated for the same [ uvw ] but different ( hkl ) give inconsistent values. They become consistent when an empirical correction term is added. The corrected site-potentials agree with those calculated by the Ewald method. Examples are given for fluorite and rutile.

Crystals of charge-transfer complex of tetrachlorophthalic anhydride and hexamethylobenzene belong to the monoclinic system. The possible space group is P 2 1 , P m , or P 2/ m . The unit-cell dimensions at 293°K are a = 9.266 Å, b = 13.63 Å, c = 8.955 Å, β = 119.4° and at 120°K are a = 9.197 Å, b = 13.30 Å, c = 8.824 Å, β = 118.74°.