Use of Monte Carlo (MC) and Reverse Monte Carlo (RMC) Simulation of 3DModel Systems for Analysing Diffuse X-ray Scattering.

Principal Investigator

T. Richard Welberry

Research School of Chemistry

The aim of our project is modelling the disorder that occurs in crystals of some organic molecules,
inorganic materials and mineral systems, which we observe in our diffuse X-ray diffraction experiments. We address the question: can we, by using a detailed potential model of the systems under investigation, describe the short-range order properties of the materials sufficiently well that we mayobtain computed diffuse diffraction patterns which are in substantive agreement with observed X-ray diffraction patterns? The process is an iterative one involving several stages of computation.
(1) A model is first set-up in terms of basic inter-atomic or inter-molecular interactions.

(2) A computer realisation of the model is obtained via computer simulation (usually Monte Carlo (MC) simulation).

(3) The diffraction pattern of the model system is calculated and compared to the observed data.

(4) The model is adjusted as a result of the findings in step (3) and the process is repeated from (1).

A quite different approach to the analysis of diffuse scattering, the so-called Reverse Monte Carlo (RMC) method, is also under investigation.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 atom sites within the crystal.




Thomas Proffen

Andrew Christy

Sheridan Mayo

Aidan Heerdegen

Research School of Chemistry



p05, v51 - VPP, PC



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

The method has been used to study disorder in a number of quite diverse systems. Major on-going projects are involved with trying to understand the disorder in cubic stabilized zirconias, CSZ's, (these have commercial importance as "cubic zirconia" gems); in Mullite (a major component of nearly all aluminosilicate ceramics); and the non-stoichiometric iron oxide, wüstite Fe1-xO (a major constituent of the Earth's lower mantle). For each of these systems three dimensional models of the way in which vacancies order, and the way in which the rest of the structure relaxes around the defects, have been established but require further development

- Appendix A


and refinement. Systems of more recent interest have been various guest/host systems such as the family of urea inclusion compounds; thalliumantimonyl germanate which is a non-linear optical material; B8-type alloys which involve interstitial transition metal ordering and the transitionmetal compound Fe3(CO)12 in which the Fe3 moiety is disordered.

In these studies the final atomic coordinates from a model Monte Carlo simulation are used to calculate diffraction patterns for comparison with the observed X-ray patterns. Although convincing results have been obtained by this method the crucial step of comparing the observed and calculated patterns has, to date, been performed visually and adjustment of the system parameters has relied heavily on an accumulation of experience, gained over a number of years. In 1997 we have made our first attempts to perform this iterative MC methodology solely by computer, using quantitative rather than visual comparison of observed and calculated diffraction patterns and automatic updating of model parameters, using a least-squares algorithm. This represents a formidable computational task, which is only feasible with state-of-the-art computational facilities. Despite the necessity at this stage of making a number of quite drastic approximations, the results so far obtained convincingly demonstrate the viability of this numerical approach. We believe this will be increasingly more powerful and widely used as computers become even faster.

Further investigations have been carried out on the viability of using the Reverse Monte Carlo (RMC) method to analyse single crystal diffuse scattering data. Although a series of test RMC simulations demonstrated that the RMC method is capable of analysing defect structures even containing occupational and displacement disorder in combination, the subsequent refinement of 'real' experimental data has revealed a problem regarding the size of the model crystal. A large size results in a satisfactory fit to the data, but this appears to be achieved by unrealistic adjustment of the many longer range correlations in the structure rather than the few shorter range correlations which are chemically significant. A small crystal size on the other hand restricts the simulation to a more 'local' scale, but then the resulting lattice averages have large statistical errors and the calculated diffuse scattering is too noisy to obtain a goodfit. In view of these problems with RMC we expect the emphasis of our work to shift to the direct MC method.

What computational techniques are used?

At present, the Monte Carlo simulation, stage (2) above, is not generally well vectorized and is better performed on the SGI while the calculation of the diffraction pattern, stage (3), is highly vectorized (>97%) and ideal for the VPP. This latter calculation uses the software algorithm DIFFUSE developed by Dr. Brent Butler some years ago.

The RMC simulation software was written as a segment of the diffuse scattering and defect structure simulation program DISCUS to give thehighest 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

Appendix A -


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.


T. R. Welberry, A. G. Christy, Defect distribution and the diffuse X-ray diffraction pattern of wüstite, Fe1-xO., Phys Chem Minerals., 24, 1997, 24-38.

T. Proffen, T. R. Welberry, An Improved Method for Analyzing Single Crystal Diffuse Scattering using the Reverse Monte Carlo Technique , Z. für Krist., 212, 1997, 764-768.

T. Proffen, T. R. Welberry, Analysis of Diffuse Scattering via Reverse Monte Carlo Technique: a Systematic Investigation . Acta Cryst.,A53, 1997, 202-216.

T. Proffen, R. B. Neder, DISCUS, a Program for Diffuse Scattering and Defect Structure Simulations. J. Appl. Cryst., 30, 1997, 171-175.

A. G. Christy, E. S. Grew, S. C. Mayo, M. G. Yates, D. I. Belakovsky, Hyalotekite, (Ba, Pb,K)4(Ca,Y)2(B,Be,Si)4 Si8O28F, a tectosilicate related to scapolite: new structure refinement, possible phase transitions and a short-range ordered 3b superstructure.Mineral. Mag., 61, 1998, 77-92.

T. R. Welberry, S. C. Mayo, Diffuse X-ray Scattering and Short-range Order in Thallium Antimonyl Germanate, TlSbOGeO4. J. Appl. Cryst., (in press)

T. R. Welberry , Diffuse Scattering In Aperiodic Crystals. Proceedings of the Conference on Aperiodic Crystals, (in press).

T. R. Welberry, TheRecording and InterpretationofDiffuseX-rayScattering Proceedings of the Conference on Local Structure from Diffraction, (in press).

A. G. Christy, A. K. Larsson. Computer simulation of modulated structures and diffuse scattering in B8-type (Co,Ni,Cu)1+x(Ge,Sn) phases . J. Solid State Chem. (in press)

T. Proffen, Analysis of the diffuse neutron and X-ray scattering of stabilized zirconia using the Reverse Monte Carlo method. Physica B, (in press).

T. Proffen, , T. R.Welberry, Analysis of Diffuse Scattering of Single Crystals using Monte Carlo Methods. Phase Trans., (in press).

T. R. Welberry, T. Proffen, Analysis of Diffuse Scattering from Single Crystals via Reverse Monte Carlo Technique: I. Comparison with Direct Monte Carlo J. Appl. Cryst., (in press)

T. Proffen, T. R. Welberry, Analysis of Diffuse Scatteringfrom Single Crystals via Reverse Monte Carlo Technique: II. The Defect Structure of Calcium Stabilised Zirconia. J. Appl. Cryst., (in press)

- Appendix A