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ISSN: 2053-2733

September 2018 issue

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Cover illustration: Three-dimensional X-ray diffraction (3DXRD) data for a shape memory alloy (SMA) before and during deformation (red = austenite, green = martensite); the results reveal both strengths and weaknesses of long-accepted micromechanical theories of martensitic transformations [Bucsek et al. (2018). Acta Cryst. A74, 425-446]. The 3DXRD techniques and analyses presented in this work provide non-destructive means to study the mysteries of complicated microstructure evolution occurring underneath the surface of SMAs, as well as other crystalline materials.

advances

scientific commentaries


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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.

research papers


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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.

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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.

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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.

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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.

foundations

research papers


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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.

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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.

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

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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.

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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 {\bar 4}3m 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%.

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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.

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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.

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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.


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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.

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

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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.

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

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

short communications


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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.

addenda and errata


book reviews


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