Analysis of single-crystal diffuse X-ray scattering via automatic refinement of a Monte Carlo model

In this paper, the feasibility of automatic least-squares refinement of a Monte Carlo model of a disordered structure by quantitative comparison of its calculated diffraction pattern with observed diffuse scattering data is demonstrated. At each stage of the refinement, the goodness-of fit parameter chi(2) is used as a quantitative measure of the agreement of the model with the observed data. Numerical estimates of the differentials of chi(2) with respect to the model parameters are calculated and these are used to provide automatic updating of the parameters via a least-squares algorithm. The method has been applied to the material Fe-3(CO)(12) which shows strong diffuse scattering caused by the fact that the triangular Fe-3 group can occupy a given molecular site, in either of two different orientations. A model has been refined involving 16 independent parameters that describe both the correlation of neighbouring occupancy variables and local orientational and centre-of-mass translational relaxation displacements. Although the method still presents a formidable computational task even for the fastest of modern computers, the work described represents a significant first step towards the ultimate goal of allowing routine analysis of diffuse scattering data.