Analysis of diffuse scattering of single crystals using Monte Carlo methods

While conventional crystal structure analysis using Bragg intensities revea ls only information about the average structure of the crystal, diffuse sca ttering contains additional information about the disorder, i.e. departure from the average structure, of the studied material. Two different approach es to the analysis of diffuse scattering based on Monte Carlo methods are d escribed in this paper: the direct Monte Carlo (MC) simulation technique an d the Reverse Monte Carlo (RMC) method. The MC method requires the construc tion of a model for the disorder based on physical and chemical considerati ons and the selection of a set of near-neighbour interactions. The given mo del is realized by minimizing the total energy of the crystal via MC simula tions. Next, the corresponding diffraction pattern is calculated and compar ed with the experimental data. By adjusting the near-neighbour interaction and repeating the process, a qualitative "match" between observed and calcu lated diffuse scattering is obtained. In contrast, the RMC method minimizes the difference between observed and calculated diffuse scattering intensit ies directly. This method leads to one real space structure consistent with the observed diffuse scattering but does not automatically result in a che mically sensible structure or further insight into the particular disorder problem. The first example given in this paper demonstrates the viability of the RMC method by refining diffuse scattering data calculated from simulated struc tures with known disorder parameters. These structures were generated using the MC technique. As a second example MC and RMC simulations of the diffus e scattering of stabilized zirconias (CSZ) are shown, modelling occupationa l disorder as well as displacements.