Rigid units revisited

Rigid-unit modes, which allow coordination polyhedra to remain undistorted and hence cost little energy, provide a way of understanding many important physical properties. Campbell et al. [Acta Cryst. (2018). A74, 408–424] have developed an elegant new algebraic approach to finding these distortion modes.

An algebraic approach to cooperative rotations in networks of interconnected rigid units

This article presents an algebraic approach to the analysis of cooperative rotations in networks of interconnected rigid units wherein the geometric constraints of connectedness reduce, in the small rotation-angle limit, to a homogeneous linear system of equations. The approach is illustrated by application to perovskites, to quartz, and to the hexagonal and tetragonal tungsten bronzes.

Measuring stress-induced martensite microstructures using far-field high-energy diffraction microscopy

A forward model algorithm is presented to analyze far-field high-energy diffraction microscopy (ff-HEDM) data sets for materials undergoing martensitic transformation, such as shape memory alloys. This approach is demonstrated on three single- and near-single-crystal NiTi data sets. The results demonstrate a new ability to identify martensite microstructures using ff-HEDM, as well as a need for improvements to the widely accepted maximum work criterion applied to the crystallographic theory of martensite for materials that do not strictly adhere to the fundamental assumptions of that theory.

Comments on A new theory for X-ray diffraction

Fewster [(2014), Acta Cryst. A70, 257–282] claimed that a new theory of X-ray diffraction is required, and that small crystallites will give rise to scattering at angles of exactly twice the Bragg angle, whatever their orientation. This article demonstrates that this theory is in error.

Response to Fraser & Wark's comments on A new theory for X-ray diffraction

In response to the comments by Fraser & Wark [(2018), Acta Cryst. A74, 447–456], experimental evidence and an explanation of the new theory in the context of a modified Ewald sphere construction are presented.

Structure evolution of h.c.p./c.c.p. metal oxide interfaces in solid-state reactions

The atomic structure of Al₂O₃/MgAl₂O₄ interfaces at different growth stages is revealed by scanning transmission electron microscopy. Partial dislocations in the hexagonal close-packed/cubic close-packed oxygen sublattices become increasingly dominant as the growth proceeds, suggesting a dislocation glide mechanism in the late growth stage.

Estimating the structure factors in X-ray diffraction

The meaning of the structure factor and how it impacts on the determination of structures are reassessed. A route to obtaining the structure factors is presented for several data collection methods and crystal qualities.

Explicit construction of the Voronoi and Delaunay cells of W(A_n) and W(D_n) lattices and their facets

Voronoi and Delaunay (Delone) cells of the root and weight lattices of the Coxeter–Weyl groups W(A_n) and W(D_n) are constructed. The face-centred cubic and body-centred cubic lattices are obtained in this context.

Incorporating particle symmetry into orientation determination in single-particle imaging

In coherent-diffraction-imaging experiments, the symmetry of the particle may complicate and facilitate the solution of the orientation problem and the structure at the same time. For symmetric particles, the correlation-maximization method can find the relative orientations of the diffraction patterns and determine the symmetry of the particle.

Variation of second-order piezo­electric coefficients with respect to a finite strain measure

Higher-order piezo­electric coefficients are finite strain measure dependent, and therefore consistency between the strain measure used in nonlinear constitutive modelling of piezo­electric materials and higher-order piezo­electric coefficients is required. A general transformation formula for the second-order piezo­electric tensor (elasto­striction) is derived, and additionally specific transformation formulae for the piezo­electric coefficients for the crystallographic and 6mm classes are presented. As an example, the piezo­electric coefficients are recalculated for GaN and GaAs crystals. The results show that typical variation is about 5%, but for some components it may reach a prominent 20%.

Fast analytical evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of the electron density. I. The Löwdin α-function method

The exact potential and multipole moment method for evaluation of intermolecular electrostatic interaction energies using the pseudoatom representation of electron densities is significantly improved in terms of both speed and accuracy by integrating the exact potential using a fully analytical technique.

The phase problem for two-dimensional crystals. II. Simulations

Phase retrieval using diffraction data from two-dimensional crystals and minimal molecular envelope information is examined by simulation. Practical considerations for application to X-ray free-electron laser data are discussed.

Specular reflection intensity modulated by grazing-incidence diffraction in a wide angular range

A theoretical description is given of the novel X-ray diffraction effect in single-crystal structures with a distorted crystal subsurface based on the dynamical theory of diffraction.

Application of differential resonant high-energy X-ray diffraction to three-dimensional structure studies of nanosized materials: A case study of Pt–Pd nanoalloy catalysts

Resonant high-energy X-ray diffraction is used to study the structure of materials with limited structural coherence.

X-ray reflectivity of chemically vapor-deposited diamond single crystals in the Laue geometry

The absolute X-ray reflectivity of chemically vapor-deposited (CVD) single-crystal diamond plates was measured in the Laue geometry. The results are interpreted in terms of solution of the Darwin–Hamilton equations describing radiation transfer in a crystal represented by an ensemble of uncorrelated misoriented blocks.

Energy flow of Bloch waves in X-ray dynamical diffraction in the Laue case for perfect crystals

The direction of energy flow for Bloch waves during X-ray dynamical diffraction in perfect crystals is investigated.

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface.

Experimental and theoretical investigations of an X-ray LLL interferometer with a wedge-shaped mirror plate

An X-ray LLL interferometer with a wedge-shaped mirror plate is experimentally and theoretically investigated.

Vertex collisions in 3-periodic nets of genus 4

A complete set of unstable 3-periodic nets of genus 4 is derived and fully described.

Intensive X-ray standing-wave-like fields localized near a surface of a crystalline superlattice

A resonantly enhanced X-ray standing-wave-like field localized in the vicinity of a surface of a crystalline superlattice is analytically shown to exist.

Calculation of absorption and secondary scattering of X-rays by spherical amorphous materials in an asymmetric transmission geometry. Corrigendum

Corrections to Table 2 in Bendert et al. [Acta Cryst. (2013). A69, 131–139] are reported.

Groups, Graphs and Random Walks