A method for verifying that coordinate systems are conserved while performing texture analysis using MAUD is demonstrated for neutron diffraction data of a quartz single crystal.

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.

Full pattern analyses of small-angle X-ray and neutron scattering data with both discrete reflections and central diffuse scattering are presented. Data with both equatorial streaks and two- and four-point reflections can be fitted in elliptical coordinates with relatively few parameters.

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.

This article explores widely used approaches for two-time correlation calculations and common methods for extracting relevant information from correlation functions. The results are applicable to a wide range of processes including growth and coarsening.

Quaternion methods for obtaining solutions to the problem of finding global rotations that optimally align pairs of corresponding lists of 3D spatial and/or orientation data are critically studied. The existence of multiple literatures and historical contexts is pointed out, and the algebraic solutions of the quaternion approach to the classic 3D spatial problem are emphasized. The treatment is extended to novel quaternion-based solutions to the alignment problems for 4D spatial and orientation data.

Exact analytic descriptions of parabolic, paraboloidal, and parabolic cylindrical X-ray mirrors in a mirror-centered coordinate system for design, modeling, fabrication, and testing are given.

Using K₄[Pt₂(P₂O₅H₂)₄]·2H₂O as a test case, we present newly developed serial femtosecond crystallography data reduction software for small-unit-cell systems featuring sparse indexing, seed-skewness integration, an overlap-based combined Ewald sphere width and partiality correction, and a sophisticated post-refinement and merging procedure.

An indirect two-trace method to determine interfaces between two crystals with a uniquely defined interface plane is proposed. It involves preparation of only one sample surface, instead of the two perpendicular sample surfaces required by the traditional two-trace method.