The analysis of incommensurate structures in terms of full space group theory, and the application of the method to melilite

This paper deals with the application of full group theoretical methods to the elucidation of the symmetry and structure of an incommensurate phase. The analysis shows that the full symmetry and structure of the incommensurate phase can be determined unequivocably where certain minimal symmetry data are available. The theory is compared with existing methods used in the study of incommensurate structures, and is applied to the elucidation of the incommensurate structure of melilite. The analysis demonstrates that there are two symmetrically distinct distortions of the Z tetrahedral site in melilite which, when it contains Fe, is responsible for two quite independent MÖssbauer signatures.