Statistical Descriptors in Crystallography

Defects in the model [Index]

Identifying the origin of systematic error and improving the model is far more difficult. Beu and his collaborators (Beu, Musil & Whitney, 1962, 1963; Beu & Whitney, 1967; see also Mitra, Ahmed & Das Gupta, 1985; Mandel, 1980) achieved a major improvement in the precise and accurate determination of lattice parameters by careful tests and corrections for remaining systematic errors based on maximum likelihood. They assumed a normal distribution of errors, and their refinement technique was therefore equivalent to least squares (Wilson, 1980b). The modelling of electron density distributions with aspherical-atom formalisms (Stewart, 1976; Hirshfeld, 1977), and of atomic thermal-displacement probability density functions with anharmonic contributions (Johnson & Levy, 1974; Kuhs, 1983) has shown considerable success, but has not had a significant impact on standard crystal-structure determination, which in its present form answers the needs of chemical crystallographers and will continue to be an increasingly automated analytical technique. A thorough study of intensity measurement and data-reduction procedures might indicate more generally applicable improvements.

[Next], [Previous], [Index], [Glossary]

Copyright © 1997 International Union of Crystallography