Partial structure factors from disordered materials diffraction data: An approach using empirical potential structure refinement

Neutron and x-ray diffraction are widely used to measure the structure of liquids and disordered solids. Using techniques such as isotope substitution or anomalous dispersion or combining neutron and x-ray data, it is sometimes possible to invert the total diffraction patterns from these materials into a set of partial structure factors, which describe the correlations between specific atom types in the material. However, even in situations where the matrix for performing this inversion appears well determined, there are significant uncertainties in the process and it is rarely possible to achieve a unique set of partial structure factors in practice. Based on the much earlier method of F. G. Edwards and J. E. Enderby [J. Phys. C 8, 3483 (1975)] and extending the reverse Monte Carlo method of McGreevy [J. Phys.: Condens. Matter 13, R877 (2001)] and others, a modified approach is developed here that allows possible atomic distribution functions, which are consistent with the measured data to be explored. The basis of the present approach is that any solution to the inversion process must be derivable from a distribution of nonoverlapping atoms or molecules as in the physical system under investigation. Solutions to the problem of inverting the measured differential cross sections to partial structure factors are then extracted assuming different levels of confidence in the data, confidence being represented by a feedback factor on a scale of 0-1. These different solutions serve to identify where ambiguities exist in the derived partial structure factors, particularly when a particular partial structure factor contributes only weakly to the total diffraction pattern. The method is illustrated using some old diffraction data on molten zinc chloride that have significant uncertainties associated with them, but that have been used extensively as the basis for a number of computer simulations of this material.