Special directions in momentum space. III. Practical applications

This paper complements two previous papers devoted to Special directions in momentum space. I. Cubic and II. Hexagonal, tetragonal and trigonal symmetries [Kontrym-Sznajd & Samsel-Czekala (2011). J. Appl. Cryst.44, 1246-1254; Kontrym-Sznajd & Samsel-Czekala (2012). J. Appl. Cryst.45, 1254-1260], in which sets of special directions (SDs) were proposed. Such directions, employing the full symmetry of the Brillouin zone, allow for constructing in the whole space anisotropic quantities from their known values along a few directions. SDs also define which spectra, measured in, for example, Compton scattering experiments, are the most efficient for reconstructing three-dimensional densities from their one-dimensional projections. This paper, in which new sets of special directions (SDs) for cubic structures are proposed, is devoted mainly to practical applications of SDs. Taking into account experimental uncertainty, an optimal strategy for experimental investigations is discussed.