On the crystal symmetry of diamond and its X-ray reflections

Abstract

The problem of the symmetry of the diamond structure in relation to its X-ray behaviour is considered in a formal manner. It is shown that the presence or absence of the 200 or the 222 reflection cannot uniquely decide whether the symmetry is tetrahedral or octahedral. The 200 reflection is shown to be absent if the structure is either completely symmetric or antisymmetric with respect to the centre of inversion at 1/8, 1/8, 1/8 or if the two distributions are superposed in any arbitrary ratio. The 222 reflection is, however, absent only in the fully antisymmetric case. Making use of these results, the nature of the structures that are possible for the tetrahedral and the octahedral modifications of diamond are discussed.