Analysing the PDF and total scattering data

Whilst it is straightforward to achieve a qualitative understanding of the information provided by a PDF, producing accurate structural models is more involved. Traditionally, analysis of total scattering data involved visual inspection of the scattering functions and the use of peak fitting to obtain information about the arrangement of the first few coordination shells. It is also common to use molecular dynamics or Monte Carlo to obtain structural models, from which theoretical total scattering functions can be calculated and compared with the observed data. Only if the two are found to be in good agreement can the models provide useful information about the system. The tuning of initial potentials to create a structural model that more accurately reflects the data is theoretically possible, but the direct effect of the potentials on the diffuse scattering is often difficult to quantify and the process of fine-tuning is laborious. Recently, the analysis of total scattering in the literature has become separated into two distinct methods: small and large box modelling. 

Small box modelling, or real-space Rietveld as it is sometimes referred, uses the refinement of a crystallographic unit cell to fit input total scattering functions. An initial structure for a material is proposed and a pair distribution function of the structure calculated. This is done by assuming infinite translational symmetry, as in a traditional Rietveld refinement. The delta functions produced by the structure are convoluted with Gaussian functions to model thermal oscillations in the system. A least squares minimisation is then applied to a series of refineable parameters (e.g. cell size, atomic position, site occupancy, instrumental parameters, thermal displacements etc) to obtain the best fit to the system. 

Figure 5.5: Flowchart of the RMC algorithm.