Special directions in momentum space. II. Hexagonal, tetragonal and trigonal symmetries

Abstract

This paper is a continuation of a previous one,Special directions in momentum space. I. Cubic symmetries[Kontrym-Sznajd & Samsel-Czekała (2011).J. Appl. Cryst.44, 1246–1254], where new sets of special directions (SDs), having the full symmetry of the Brillouin zone, were proposed for cubic lattices. In the present paper, such directions are derived for structures with unique six-, four- and threefold axes,i.e.hexagonal, tetragonal and trigonal lattices, for both two- and three-dimensional space. The SDs presented here allow for construction, in the whole space, of anisotropic quantities from the knowledge of such quantities along a limited number of SDs. The task at hand is to determine as many anisotropic components as the number of available sampling directions. Also discussed is a way of dealing with data when the number of anisotropic components is restricted by a non-optimal set of SDs.