Analysis of diffuse scattering of single crystals using monte carlo methods

Abstract

While conventional crystal structure analysis using Bragg intensities reveals only information about the average structure of the crystal, diffuse scattering contains additional information about the disorder, i.e. departure from the average structure, of the studied material. Two different approaches to the analysis of diffuse scattering based on Monte Carlo methods are described in this paper: the direct Monte Carlo (MC) simulation technique and the Reverse Monte Carlo (RMC) method. The MC method requires the construction of a model for the disorder based on physical and chemical considerations and the selection of a set of near-neighbour interactions. The given model is realized by minimizing the total energy of the crystal via MC simulations. Next, the corresponding diffraction pattern is calculated and compared with the experimental data. By adjusting the near-neighbour interaction and repeating the process, a qualitative “match” between observed and calculated diffuse scattering is obtained. In contrast, the RMC method minimizes the difference between observed and calculated diffuse scattering intensities directly. This method leads to one real space structure consistent with the observed diffuse scattering but does not automatically result in a chemically 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 structures with known disorder parameters. These structures were generated using the MC technique. As a second example MC and RMC simulations of the diffuse scattering of stabilized zirconias (CSZ) are shown, modelling occupational disorder as well as displacements.