COMMENSURATE STRUCTURES DESCRIBABLE IN TERMS OF DEGENERATE IRREDUCIBLE REPRESENTATIONS. By A. David Rae, Research School of Chemistry, Australian National University, Canberra, ACT, Australia, 0200

When trying to understand problems in structure solution and refinement, many structures are best described as commensurate modulations of parent structures with a smaller unit cell. The diffraction pattern may then be described in terms of parent reflections g and satellite reflections g + k where k has a limited number of values, in the simplest case just one. The Fourier transform of the parent reflections describes a parent structure which is a disordered version of the true structure and is often quite easy to obtain, especially when the inherent disorder is recognised. The satellite reflections then define a modulation of the parent structure and possible resulting symmetries can be obtained from the irreducible representations associated with k. This approach is often more effective than using phase determination methods on structures where heavy atoms dominate reflections g but make effectively no contribution to reflections g + k. The increase in primitive cell volume by a factor N implies that, at most 1/N of each set of translationally related symmetry elements {R,t} of the parent structure survive, and a choice is often required. The behaviour of atoms on special positions of the parent structure can be informative, e.g. a heavy atom on an inversion centre in a parent P2₁/c structure may be on a general position in the modulated F-1. In some cases none of a set {R,t} survive or certain elements {R,t} and {R',t'} cannot coexist. This situation is associated with the existence of a degenerate irreducible representation. Disallowed symmetry operations create a different orientation of the true structure but may still describe a localised symmetry or be associated with twinning or disorder. When the equivalent point symmetry of the true structure is less than that of the parent structure, the parent symmetry is lowered and this may be detectable as absence conditions not quite holding, e.g. Pccn modulated to C112/d. Problems with refinement often exist in such structures and these are generally associated with atoms overlapped in the parent structure. Constrained refinement and the maintenance of the parent symmetry for thermal parameters is useful. A number of examples of structures solved using this approach will be given and the nature of the refinement problem detailed.