Robert Crispin Evans (1909–2005)

Interpenetration of homogeneous sphere packings and of two-periodic layers of spheres

74 types of interpenetrating sphere packings and 4 types of interpenetrating layers of spheres exist that occur with highest symmetry in the cubic, hexagonal or tetragonal crystal family. The patterns of the interpenetration are analysed.

Spectral decomposition of the linear elastic tensor for trigonal symmetry; classification of symmetry restrictions for arbitrary point groups

Eigenvalues and eigenvectors of the linear compliance tensor for trigonal symmetry have been expressed in terms of the seven parameters of the corresponding Voigt matrix; conditions on these parameters guaranteeing positive strain energy have been derived.

Multiple diffraction in the kinematical approach

The expressions derived for the calculation of multiple diffraction patterns for a perfect crystal in the framework of the kinematical theory are compared with the relevant result of the kinematical power-transfer equation deduced for a mosaic crystal. Furthermore, it is shown that the interference term can be deduced from kinematical wavefields.

Enumeration of polytypes MX and MX₂ through the use of the symmetry of the Zhdanov symbol

The number of possible close-packed polytypes MX and MX₂ for repeat P have been calculated through elementary combinatorics for each possible space group.

Zhdanov's rules work both ways

The mapping between the possible space-group symmetry of a periodic stacking of layers of close-packed balls and the possible two-dimensional two-color point-group symmetry of the cyclical representation of its Zhdanov symbol is shown to be a bijection.

Precise measurement of local strain fields with energy-unfiltered convergent-beam electron diffraction

Convergent-beam electron diffraction was employed to measure local strain on the nanometre scale in semiconductors. Radon transformation, the subtraction of background intensity, and analytical strain determination were used to overcome the challenges presented by energy-unfiltered CBED.

Theoretical structure factors for selected oxides and their effects in high-resolution electron-microscope (HREM) images

Structure-factor (X-ray and electron) calculations and high-resolution electron-microscope image simulations are used to evaluate charge redistribution effects.

Invarioms for improved absolute structure determination of light-atom crystal structures

The determination of molecular absolute configuration from an X-ray analysis of structures that contain only light elements can be difficult owing to the weak anomalous dispersion signal. It is shown that the invariom approach can improve the precision and standard uncertainty of the Flack x parameter and thus also the reliability of deducing the molecular chirality in an absolute structure determination.

Finding optimal radial-function parameters for S atoms in the Hansen–Coppens multipole model through refinement of theoretical densities

The multipolar model of the valence-electron-density distribution for sulfur has been optimized based on theoretical structure factors for six organic molecules. It is shown that: (a) the ratio of the n(l) values for different l is more important than their absolute values, and (b) the (2,4,6,8) set of n(l) with κ′ refined as a single value is an optimal choice of radial function parameters for S atoms.

On a simple tiling of Deza and Shtogrin

Some properties of an exceptional simple tiling by fullerenes, first described by Deza and Shtogrin, are presented.

On the symmetry of simple 16-hedra

The symmetry point group statistics for all combinatorially non-isomorphic convex simple 16-hedra (17490241 in total) are contributed in the paper for the first time. The most symmetrical polyhedra with 6 to 56 automorphism group orders (165 in total) are drawn in Schlegel diagrams and characterized by facet symbols and symmetry point groups.