On simple and double diffraction enhancement of symmetry

Under special circumstances, the diffraction symmetry of a crystal may be higher than that corresponding to the crystal Laue class. The phenomenon has been termed 'diffraction enhancement of symmetry'. Iwasaki [Acta Cryst. (1972), A28, 253-260] is responsible for the first systematic attempt to develop a comprehensive theory of this phenomenon. In this paper, a more general formulation has been developed which leads to enhancement conditions more compact and easier to use than Iwasaki's. By use of these conditions, several new cases of enhancement have been found, in addition to all the cases previously published. Several theorems are enunciated and proved which strongly limit the possible cases of enhancement. The formulation includes also the so-called 'double enhancement'. A set of double-enhancement cases has been found and tabulated. The extension of some of the theorems proved for simple enhancement provide limitations to the possible cases of double enhancement.