Band 126, Heft 5-6

A large number of perfect (001) cleavages were obtained by cleaving natural apophyllite crystals. By etching such cleavages in ammonium bifluoride solution it is established that the pits indicate the sites of dislocations in the crystals. This is further confirmed by comparing the etch patterns on matched cleavage surfaces. Eccentricity of the pits has been attributed to the inclined nature of dislocations. Existence of parallel dislocations seems to be due to the purity of the crystal. These observations are verified by comparing etch patterns produced on opposite faces of a thin flake (0.032 mm thick) and also by successive etching and polishing a cleavage surface.

The transformation of lithiophorite during thermal treatment has been studied by single crystal x-ray diffraction methods. Lithiophorite was found to transform at 550°C into a spinel phase of γ -Fe 2 O 3 or γ -Al 2 O 3 type structure and the orientational relationships between the two phases have been established. The mechanism of transformation has been explained from a structural view-point by the migration of cations through the lattice. It was found that the [010], [100] and c * directions of lithiophorite became respectively the [1[unk]0], [11[unk]] and [111] directions of the transformed phase.

Bragg's law, in the usual form, is applicable to very precise x-ray measurements only if refraction will be taken into account. Therefore a more comprehensive diffraction law has been derived on the basis of the kinematic interference theory for the general case of asymmetric back reflection. This law is also valid for light-optical diffraction phenomena in or on crystals which contain superperiodic modulations.

We have examined, as a function of atomic number or outer-electron concentration: (1) atomic volumes of the elemental transition (T) metals and succeeding B -group elements, (2) atomic volumes of mutual solid solutions of the T metals and, (3) apparent atomic volumes of 3 d T-metal solutes in T-metal solvents, pointing out features of interest and concern. Secondly, we examine, as a function of the number of d electrons, the radii of ‘divalent’, ‘trivalent’ and ‘tetravalent’ T metals in octahedral anion coordination, derived from compounds with the group-V and -VI elements, P, As, Sb, S, Se and Te. The observed T-metal radii in these pnictides and chalcogenides (both metallic and semiconducting) depend on the number and configuration of the d electrons, and on the symmetry of the anion coordination polyhedron in a manner similar to that observed by others for ionic oxides and halides. No single, simple system of T-metal radii can be suitable for deriving bond numbers in such compounds.

The crystal-structural data of cadmium mercuric thiocyanate have been given as follows: tetragonal system, unit-cell dimensions: a = 11.48 Å, c = 4.33 Å; space group: I [unk]( S 4 2 ).

The paper deals with the use of the higher moments of the product of the normalized intensities (denoted by z x ) from a pair of crystals in testing the isomorphism of the pair. The expressions for the general p th moment of z x are first worked out for isomorphous and non-isomorphous pairs of crystals and from these the explicit expressions for the first three moments of z x are deduced. Both centrosymmetric and non-centrosymmetric crystals are considered and in each type of crystal the expressions for the first three moments of z x are given for isomorphous and non-isomorphous pairs of crystals, depending on the number of atoms in the replaceable group. The theoretical results have been tested using suitable two-dimensional hypothetical models.

Gaylussite, Na 2 Ca(CO 3 ) 2 · 5H 2 O, is shown by single crystal x-ray studies to be monoclinic with space group Cc or C 2/ c and unit-cell dimensions a = 14.34, b = 7.777, c = 11.58 Å, β = 130.2°. Indexed powder data are also given.

It is shown that the unit-cell (factor group) analysis of the infra-red and Raman spectra of the isomorphous anhydrous nitrates of barium and strontium is superior to that of the site-group method and that it is also in favour of the non-centrosymmetric space group T 4 – P 2 1 x 3 which was recently proposed by B irnstock . An analysis of the combination and overtone modes of Ba(NO 3 ) 2 and Sr(NO 3 ) 2 is also given in terms of the B irnstock space group.

Explicit formulae are given for calculating image-seeking functions by the summation method. These are compared with weighting schemes for Fourier syntheses which have been proposed from probability considerations. In the case when only a small part of the structure is known some of these superposition functions are shown to be equal to the weighted syntheses of W oolfson , and of S im , and to be similar to those of V and and P epinsky , of M azumdar , and of R amachandran and R aman .

The electron-density distribution in any structure can be split up into two parts, one of which is symmetric, the other antisymmetric about any selected point. The corresponding self convolutions of these functions are simply related to the coordinates of the selected point and the intensities of the diffraction maxima and are readily calculable. These functions contain within themselves information on the symmetry and lack of symmetry of the electron density about the selected point.

Using a three-dimensional set of 267 independent structure factors estimated from Weissenberg films, the structure of Zn 5 (OH) 8 Cl 2 · 1H 2 O has been refined. Space group R [unk] m , a = 6.34, c = 23.64 Å, Z = 3. A three-dimensional Fouriersynthesis showed that the water molecules statistically occupy one of six possible sites about 0.4 Å off the ideal position in 0 0 ½. The structure consists of brucite-like main layers [Zn 3 (OH) 8 ] 2− with ¼ unoccupied octahedral sites [Zn–O = 2.08 and 2.17 Å, O–O = 2.82 (shared edge), 3.04, 3.10, and 3.18 Å], and of interlayers [2Cl · 1H 2 O] 2− (Cl–Cl = 3.66, Cl–H 2 O between 3.28 and 4.05 Å). The remaining zinc atoms are situated in tetrahedral sites between these two layers, above and below the empty octahedral sites of the main layer (Zn–O = 1.94, Zn–Cl = 2.31 Å, O–O = 3.24, O–Cl = 3.38 Å). The R value dropped to 14.0%. With exception of the bonds to H 2 O (±0.12 Å), the accuracy of all bond lengths is about ±0.02 Å.

The atomic scattering factor for two-electron ions is developed as a compact, analytic function of the nuclear charge, Z . Form-factor values calculated from this expression are shown to be in good agreement with those obtained from more elaborate representations. A possible application of this function in the x-ray analysis of crystals is suggested.

Vauquelinite, Pb 2 Cu[CrO 4 PO 4 OH], is monoclinic, with a = 13.754, b = 5.806, c = 9.563 Å, β = 94°34′, space group P 2 1 / n . The crystal analysis of the mineral was determined by the trial-and-error method starting from the atomic positions found in fornacite. The refinement carried out by the least-squares method gave a final discrepancy index R of 0.089. The atomic packing in vauquelinite is very similar to that in fornacite. Some differences occur in coordination around lead ions and in the arrangement of symmetry elements in the two minerals.

Crystals of silicon carbide are often structurally inhomogeneous, consisting of a number of domains of different structures or polytypes. By the application of x-ray diffraction topography it is possible both to identify the polytypes present in a crystal and to determine the configuration of their domains. This method is illustrated by application to a crystal with epitaxial growth and a crystal with laminar domains of different polytypes.