Reverse Monte Carlo Simulation for Analysing Diffuse X-ray Scattering


Principal Investigator

T. Richard Welberry

Research School of Chemistry

The aim of our project is the investigation of disorder within single crystals by analysing the diffuse scattering observed in X-ray and neutron scattering experiments. Whereas the Bragg scattering contains only information about the average crystal structure, diffuse scattering reveals additional information about static or thermal disorder within the crystal. One approach extensively used in our laboratory is the direct Monte Carlo (MC) simulation to model the disordered structure (see project p05). One drawback of the MC method is that although an automatic adjustment of the model is in principle possible, current computer resources allow only a "manual" refinement of the model limiting the method to a qualitative comparison of the calculated diffraction pattern with the experimental data.

A different approach to the analysis of diffuse scattering is the so-called Reverse Monte Carlo (RMC) method. This technique uses the same basic algorithm as the MC method, but rather than minimizing the total crystal energy the difference between calculated and observed diffuse scattering intensities is minimized as a function of the positions and occupancies of the atoms within the crystal. The RMC process starts with the calculation of the diffraction pattern for the starting configuration, e.g. the average structure of the crystal. The RMC simulation proceeds with the selection of a random atom site within the model crystal. The variables associated with that site, i.e. occupancy or displacements, are changed by a random amount, and the scattering intensity and a goodness-of-fit parameter are calculated. If the agreement of calculated and observed diffraction patterns improve, the new configuration is accepted, if the move worsens the fit, the new configuration is only accepted with a certain probability. The proportion of such "bad moves" that are accepted is an important modelling parameter and corresponds to the temperature T in the MC simulation technique.




Thomas Proffen

Research School of Chemistry



v51 - VPP, PC



However, although the RMC refinement method allows one to obtain a real space representation of a model crystal which is consistent with the observed diffuse scattering data, one has to be aware that the resulting structure might be unlikely from a chemical point of view. Special efforts have to be made to exclude those unlikely or even impossible configurations during the RMC refinement.


What are the results to date and the future of the work?

Of particular interest in our work are disordered systems which show occupational disorder, e.g. ordering of vacancies, and displacements. In a series of RMC refinements using simulated test structures as input, the viability of the RMC method for analysing such systems was shown. Since these test structures were mainly two-dimensional most of the simulations could be carried out on local workstations. It was evident, that three-dimensional model crystals combined with high resolution diffraction patterns measured on our position-sensitive detector (PSD) diffractometer system will require much more computer resources than available locally. The diffuse scattering simulation program DISCUS which includes the new RMC simulation segment was adapted to the VPP and PC computers (see next section).

After an initial program test phase the diffuse scattering of cubic stabilized zirconia (CSZ) and thallium antimonyl germanate (TlSbOGeO4) were studied using the RMC method. The work on those systems showed that using RMC to analyse the diffuse scattering of such complex systems is far from routine and the calculations are still in progress. Current and future work will focus on further understanding of the influence of different parameters (e.g. size of the model crystal) on the RMC process. Furthermore the use of the RMC techniques will be extended to systems previously investigated using our established direct MC simulation technique. The long term goal is the use of a combination of both MC and RMC methods to merge the advantages of both methods.

What computational techniques are used?

The RMC simulation software was written as a segment of the diffuse scattering and defect structure simulation program DISCUS to give the highest possible flexibility. This program runs now on both computers, PC and VPP. The work invested by our group in developing the highly vectorizing program DIFFUSE to calculate diffraction patterns from a crystal structure was used to optimize the RMC and Fourier transformation part of DISCUS for the use on the VPP. The algorithm used requires the storage of the complex structure factors corresponding to all experimental data points. Together with reasonably large model crystal sizes this requires large amounts of memory not available on local workstations. The use of supercomputer resources is an absolutely vital requirement for the successful exploration and use of this modern simulation technique.


- Appendix A




Proffen, Th., Neder, R.B., DISCUS, a Program for Diffuse Scattering and Defect Structure Simulations, Journal of Applied Crystallography, 1997, in the press

Proffen, Th., Welberry, T.R., Analysis of Diffuse Scattering via Reverse Monte Carlo Technique: a Systematic Investigation, Acta Crystallographica A, 53, 1997, 202-216