Computation of X-ray Diffraction Patterns for 3D Model Systems



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 may obtain 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, has also been investigated. 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.


Principal Investigator

T. Richard Welberry

Research School of Chemistry


Thomas Proffen

Andrew Christy

Sheridan Mayo

Aidan Heerdegen

Research School of Chemistry


p05 - VPP, PC


Appendix A -



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 and refinement. Systems of more recent interest have been various guest/host systems such as the family of urea inclusion compounds; thallium antimonyl germanate which is a non-linear optical material; B8-type alloys whic involve interstitial transition metal ordering and the transition metal 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.

We expect the emphasis of our work to shift almost entirely towards this automated MC approach. Because of the need to perform basically independent calculations at a large number of parameter state positions the problem is a highly parallel one. Although initial work was performed on the SGI using a single processor we have more recently been using a cluster of 5 PC's so that the elapsed time cycle time can be considerably reduced. As the methodology develops we expect to utilize whatever is the most efficient computational resource available.

What computational techniques are used?

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

Although the newly developed automatic refinement of a MC model requires long production runs, a substantial proportion of our work involves development and testing of suitable MC models. In doing this testing it is essential that the turn-around is as short as possible and a substantial fraction of our usage is required in the high and express queues.


Proffen, Th., Analysis of the diffuse neutron and X-ray scattering of stabilized zirconia using the Reverse Monte Carlo method. Physica B, 241, 1997, 281-288.
- Appendix A



Christy, A.G., Grew, E.S., Mayo, S.C., Yates, M.G., Belakovsky, D.I., 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.

Welberry, T.R., Mayo, S.C. Diffuse X-ray Scattering and Short-range Order in Thallium Antimonyl Germanate, TlSbOGeO4. J. Appl. Cryst., 31, 1998, 154-162.

Welberry T.R., TheRecording and InterpretationofDiffuseX-rayScattering Proceedings of the Conference on Local Structure from Diffraction, (Fundamental Materials Research, Eds. S.J.L.Billinge and M.F.Thorpe) pp 35-58, Plenum Press, New York and London (1998).

Christy, A.G., Larsson A.K., Computer simulation of modulated structures and diffuse scattering in B8-type (Co,Ni,Cu)1+x(Ge,Sn) phases . J. Solid State Chem., 135, 1998, 269-281.

Christy, A.G., Larsson A.K., Simulation of Sinusoidal Diffuse Scattering Loci in the Non-Stoichiometric B8-type Alloy Phases (Co,Ni,Cu)1+x(Ge,Sn) phases . J. Solid State Chem., 140, 1998, 402-416.

Proffen, Th., Welberry, T.R. Analysis of Diffuse Scattering of Single Crystals using Monte Carlo Methods. Phase Trans., 67, 1998, 373-397.

Welberry, T.R., Proffen, Th. Analysis of Diffuse Scattering from Single Crystals via Reverse Monte Carlo Technique: I. Comparison with Direct Monte Carlo J. Appl. Cryst., 31, 1998, 309-317.

Proffen, Th., Welberry, T.R. Analysis of Diffuse Scattering from Single Crystals via Reverse Monte Carlo Technique: II. The Defect Structure of Calcium Stabilised Zirconia. J. Appl. Cryst., 31, 1998, 318-326.

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

Welberry, T.R. and Christy, A.G., About short- and long-range orderings in wüstites, Fe1-xO: reply to comments of C. Carel and J.R. Gavarri. Physics and Chem istry of Minerals (in press)

Mayo, S.C., Proffen, Th., Bown, M. and Welberry, T.R., Diffuse Scattering and Monte Carlo Simulations of Cyclohexane-Perhydrotriphenylene (PHTP) Inclusion Compounds, C6H12/C18H30 . Journal of Solid State Chemistry (in press).

Withers, R.L., Proffen, Th. and Welberry, T.R., Inter-sublattice Correlations and Locus Approach to Localized Diffuse Scattering. Philosophical Magazine A (in press).

Appendix A -