[en] X-ray scattering measurements have been made in situ on highly oriented pyrolytic graphite intercalated with FeCl₃ to stage 4 in a sealed glass tube at 620 K. It has been found that the FeCl₃ is in a two-dimensional liquid state at this temperature and that the stacking of the sets of ordered graphite layers (ABAB) that bound the intercalant is nearly random. Through a novel modeling of L scans for 10.L, 11.L, 20.L, 21.L, 30.L and 22.L, a good fit has been achieved by using 60% of a preferred (A-A) stacking of sets with a broad lateral distribution about the ordered position. The remaining 40% of the sets are stacked with complete translational randomness, without regard to the normal graphite crystallography. This sliding randomness remains compatible with Daumas-Herold domain formation. (orig.)

[en] To calculate high-resolution images it is necessary to convolute the wavefunction generated by scattering from the specimen with the microscope objective-lens wavefront aberration function. This is usually done by a multiplication of the transfer function and the specimen exit-surface wavefunction in reciprocal space followed by a numerical integration over all scattering wave vectors. Examination of the analytic behaviour of the wave-front aberration function in the complex plane shows that, for simple scattering functions, it is possible to perform the integral analytically using the method of stationary phase. Analytic results for the imaging of disordered planes of atoms are compared with fast fourier transform calculations as a function of defocus. The limitations of stationary-phase integration are also discussed. (orig.)

[en] Several possible aperiodic tetrahedrally bonded structures are investigated based on the concept of propagating local positional order. Local positional order (LPO) in a tetrahedrally bonded system is parametrized by the angle of relative rotation of tetrahedral coordinations of adjacent atoms, θ. By choosing θ appropriately we can have LPO which is incompatible with periodic translational order. Propagation of LPO is described here by rolling polytope {5, 3, 3} and polytope 240. Defects of LPO in a system filled with atoms by a rolling polytope are discussed. As an alternative model, a three-dimensional Penrose tiling with tetrahedral decoration is investigated. It is shown that the proposed decoration necessarily introduces atoms with a broken bond. (orig.)

[en] A characterization of crystallographic unit cells as vectors in a Euclidean six-dimensional space (E⁶ in the usual mathematical notation; here termed G⁶) is introduced, in which the non-triclinic Bravais lattice types form one-, two-, three- and four-dimensional linear subspaces. This formalism makes the determination of the 'best' Bravais lattice (or lattices) for a particular experimentally determined cell a process of determining Euclidean distances in G⁶ from the cell to its projections into the subspaces of the lattice types. The elements of vectors in the space are drawn from the Niggli matrix with the unsymmetrical elements doubled. A cell is first reduced and all its nearly Buerger-reduced cells are used in the distance determinations. Thus the smallest distance provides information about both the propriety of the lattice type selection and the instability of the cell reduction. (orig.)

[en] X-ray pleochroism is observed near the Se K absorption edge in a monoclinic crystal of selenolanthionine monohydrate using linearly polarized synchrotron radiation and is explained by a simple molecular-orbital model. The complex anomalous-scattering tensor of selenium, measured by diffraction in a tetragonal crystal of the anhydrous compound, exhibits anisotropy nearly 6 for f' and 7 for f'', the most yet found for a K edge. The crystal structure was determined for D-(-)-selenolanthionine, space group P4₃2₁2, a=6.651 (2), c=21.758 (5) A, Z=4, R=0.027 for 304 unique reflections. (orig.)

[en] The potential of high-resolution electron microscopy (HREM) is demonstrated by the investigation of complex oxides with a general formula [U_nM_mO]-[M_pO_3p+1], M = (Mo, W). The HREM structure images of β-UMo₂O₈ agree well with the model derived from X-ray data. It is found that the γ-U₃Mo₂₀O₆₄ sample considered earlier as a monophase appears in fact as a set of isostructural phases. The structure of these phases with MoO₃ octahedral block width varying within p=1-7 is derived from electron microscope images. Both regular and irregular substitution of cations and the formation of uranium vacancies in M-O rows are detected in γ-U₃Mo₂₀O₆₄. Interstitial sites in the structures are detected, which can be occupied by extra U and W cations. The electron microscope images of vacancy rows give evidence for the finite length of some M-O rows. In this case oxygen dangling bonds at the ends of rows are supposed to be saturated by interstitial tungsten atoms. (orig.)

[en] Strain, as determined by diffraction techniques, is calculated from its constituents. First, the fraction of the crystals that have the proper orientation for diffraction. One degree of freedom is present: the angle of rotation φ₂'' about the scattering vector that the diffracting crystals have in common. The proper orientations, expressed in Euler angles, lie on a line ('trace') in orientation space. The density along the trace is asserted to be known as a Fourier series in φ₂''. Second, the strain in the diffracting crystals. The simplest possible models are discussed: the Voigt and Reuss approximations. The symmetries of the crystal (m3 or m3m) and of the orientation distribution function (o.d.f.) are taken into account. The dilatation in spacing of the reflecting planes is found as a Fourier series in φ₂'' also. Only the zeroth, first and second harmonic (including phase angles: five parameters) play a part. The diffraction strain is the average over the angle φ₂'' of the dilatation, weighted with the product of the orientation density and the square of the structure factor. For each contributing trace, the corresponding Fourier coefficients have to be multiplied and added to obtain the diffraction strain. The symmetry of the diffraction pole figure is derived. (orig.)

[en] The crystallographic concepts of lattice and space group are extended to describe materials with crystallographically forbidden point groups, and a complete classification of all two-dimensional space groups with rotational order less than 23 is given. (orig.)

[en] The effect of granularity in powder X-ray diffraction is reviewed, and the shortcomings of previously developed models in explaining this effect are described. A new physical model encompassing all aspects of this phenomenon is proposed. Mathematical formulae based on the model are derived, and their limit cases are discussed. Values of the theoretical intensities from the model are compared with results from a specially designed experiment. (orig.)

[en] Figures of merit based on PSI0 and on strong triplets are often unreliable for structures with superstructure effects. Prior information on pseudotranslational symmetry is used in order to estimate one-phase seminvariants. These are used, together with quartet invariants, for finding the correct solution in a multisolution process. (orig.)