Restraints and constraints in Rietveld refinement

Abstract In the same year as Rietveld’s paper, ‘A Profile Refinement Method for Nuclear and Magnetic Structures’ appeared (Rietveld 1969), Meier and Villiger ( 1969) published an article, the German title of which could be translated as ‘A Distance Refinement Method for the Determination of Atomic Coordinates of Idealized Framework Structures’. The similarity is evident: both methods refine atomic coordinates by using a least-squares procedure. The only difference is the type of observation. Whereas the former uses diffraction data, the latter uses chemical or geometric observations in the form of known or expected interatomic distances. The distance least-squares program DLS-76 (Baerlocher et al. 1976) has been widely used for a variety of purposes: to calculate good starting parameters for structure refinement to screen structural models for unknown phases (e.g. Baur 1977; Meier et al. 1987), and to predict structural changes (e.g. under high pressure) in cases where diffraction data were unavailable (Dempsey and Strens 1976). Despite its simplistic approach, the results obtained are generally remarkably good.