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

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 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)

(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).

Although the long-term aim of the research is to enable this iteration process to be automatic, this goal is still some years away from being feasible, and decisions made in step (4) at present require manual intervention.


Thomas Proffen

Andrew Christy

Sheridan Mayo

Aidan Heerdegen

Research School of Chemistry


p05 - 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. One major on-going project is involved with trying to understand the disorder in cubic stabilized zirconias (CSZ's) which have commercial importance as "cubic zirconia" gems. A second system which continues to be of interest is Mullite which is a major component of nearly all aluminosilicate ceramics. A third system is that of the non-stoichiometric iron oxide, wüstite Fe1-xO, which is thought to be a major constituent of the Earth's lower mantle. Here defect clusters consist of both vacancies in the Fe sub-lattice and interstitial Fe ions. 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. Systems of most recent interest have been various guest/host systems such as the urea inclusion compounds, where the flexible frame-work of hydrogen-bonded urea molecules encapsulate various long-chain alkane molecules to produce disordered structures exhibiting a large number of different diffraction

effects. Here it has been necessary to model the ordering of the alkane orientations, but also their interaction with the host urea lattice. We have also recently commenced work on thallium antimonyl germanate which is a non-linear optical material in which it is thought that the disordered cation sites influence the optical behaviour

The methods have also been applied to a number of organic molecular crystal systems which exhibit disorder. This area possibly presents the most promise of realising a quantitative interpretation of observed diffuse scattering, thereby yielding valuable detailed information about intermolecular interactions.

Our methods are now established as a viable means of interpreting and studying disorder in a whole range of different materials. The diffraction calculation algorithm will continue to be used as a routine tool in the process, while our simulation and model building techniques continue to develop.

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 while the calculation of the diffraction pattern, stage (3), is highly vectorized (>97%) and ideal for VPP. This latter calculation uses the software algorithm developed by Dr. Brent Butler some years ago.

At present for each cycle of the iteration stage (2) may take up to several hours of SGI cpu while typical times for stage (3) are ~15-30 minutes of VPP cpu time. In a given project numerous different models must be tested and a relatively small proportion of our runs can be said to be production runs. It is essential that the turn-around on the above iterative process is as short as possible, particularly the stage (3). The results of one iteration must be properly assessed before the next iteration is commenced. It is virtually impossible to manage this kind of interactive iteration in the normal queue modes.


Welberry, T.R., Butler, B.D., Local Structural Information of Mullite Obtained from Diffuse X-ray Scattering. , Journal of European Ceramic Soc., 16, 1996, 187-193

Welberry, T.R., Christy, A.G., Defect distribution and the diffuse X-ray diffraction pattern of wüstite, Fe1-xO, Physics and Chemistry of Minerals, 1996, in the press

Welberry, T.R., Mayo, S.C., Diffuse X-ray scattering and Monte-Carlo study of guest-host interactions in urea inclusion compounds, Journal of Applied Crystallography, 29, 1996, 353-364

Welberry, T.R., Mayo, S.C., Diffuse X-ray Scattering and Short-range Order in Thallium Antimonyl Germanate, TlSbOGeO4, Journal of Applied Crystallography, 1997, submitted

- Appendix A