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September 2016 issue
Cover illustration: Miniaturized X-ray beamsplitters based on lithographic waveguide channels [Hoffmann-Urlaub and Salditt (2016). Acta Cryst. A72, 515-522] pave the way to `X-ray optics on a chip'. At the intersection of the resulting beams, intricate phase discontinuities such as that marked by the arrow lead to phase vortices. The scale bar represents 0.1 µm.
advances
research papers
Miniaturized X-ray beamsplitters based on lithographic waveguide channels have been fabricated and tested. Numerical simulations of beam propagation and splitting by finite difference calculations have been confirmed by near-field reconstructions from the measured far-field interference pattern, using an error reduction algorithm. The device enables novel nano-interferometric and off-axis holography applications.
foundations
research papers
Alternative settings of space groups are explored: what they are, why they can be useful and how to obtain them.
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An iterative transform algorithm is proposed to improve the conventional molecular-replacement method for solving the phase problem in X-ray crystallography. Several examples of successful trial calculations carried out with real diffraction data are presented.
Vectorial parameterizations of proper rotations in three-dimensional space are generalized so the parameters are directly linked to non-orthonormal bases of crystal lattices or to frames with redundant crystallographic axes.
The indirect Fourier transform is discussed in the context of complementary statistical inference frameworks in order to determine a solution objectively, which then allows one to automate model-free analysis of small-angle scattering data. Modern machine-learning methods are used to obtain the most robust solution.
The diamond cubic grid is one of the usual cubic crystal structures. The Voronoi cells are triakis truncated tetrahedra having four hexagon and 12 triangle faces, 30 edges and 16 vertices. A symmetric coordinate system is presented that addresses not only the voxels, but also the faces, edges and vertices between them. In this way, not only volumes, but also surfaces, or paths containing edges can be easily described and visualized.
short communications
A method is suggested to build a digital name for any convex polyhedron by using the adjacency matrix of its edge graph and vice versa. Thus, the problem of how to discern and order the overwhelming majority of combinatorially asymmetric (i.e. primitive triclinic) polyhedra is solved.
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