An ambiguity in indexing Renninger diagrams and the distinction between some opposite directions in cubic crystals

In the course of a discussion of the nature of an ambiguity in the indexing of Renninger peaks the possibility was discovered of distinguishing some opposite directions in a cubic crystal without recourse to anomalous scattering. A multiple-diffraction experiment performed on a (111) Ge plate rotated about [222] enabled distinction between the [10] and [01] directions to be made. The azimuthal angles counted from alternative zero meridians containing [10] or [01] are the same, but give rise to peaks indexed hkl and 2 - l,2 - h,2 - k respectively. However, dynamically equivalent situations 222, hkl/(2 - h,2 - k,2 - l) and 222, (2 - l,2 - h,2 - k)/lhk are geometrically different, being distinguished as Bragg-Laue and Bragg-Bragg, respectively, or vice versa.