Noncrystallographic twofold axes and their detection*

Abstract

Abstract Noncrystallographic symmetry is defined, as the symmetry property associated with the crystallographic unit. The mathematical formulation for detecting a noncrystallographic axis of symmetry in a crystal has been made and the effect of symmetry on the intensity statistics has been systematically deduced. The theoretical results obtained have been tested on a hypothetical structure. Fairly good agreement was found between the theoretical results and those computed from the hypothetical structure. A study of the variance and the higher moments of the intensity distribution will be a useful test in dealing with such symmetries. A method is suggested for detecting such symmetries present in a crystal.