DISCREPANCY INDICES FOR USE IN CRYSTAL STRUCTURE ANALYSIS

Abstract

The use of discrepancy indices (i.e., R-indices) in crystal structure analysis as an indes for the correctness of trial structures in the structure completion stage and asn index indicationg the extent of refinement stage are well known. a number of R-indices have been suggested by various workers for those purposes. The results obtained from a systematic compartive study of the various normalised R-indices for following three crystallographic situations, namely (i) the structure completion process, (ii) refinement of an incomplete model and (iii) refinement of a complete model, are summarised after introducing the necessary nomenclature, notation and relevant crystallographic literature. The results obtained from a comparitive study of the normalised and unnormalised Booth type indices based on intensity carried out under differnt crystallographic situations for assessing the advantage of the normalisation procedure during the structure completion stage are also summarised. The necessity of taking into account the space group symmetry for the crystal in the evalution of R-indices is pointed out. General theoroetical expressions for the normalised Booth type index based on intensity which are useful to test the correctness of any type of model for crystals of the tridinic monoclinic and orthorhombic systems are given. These are valid even for crystals with any number and types of atoms in the unit cell. The expression which accounts for random errors in the intensity data is also given. Other uses of R-indices are indicated.