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.

Principal Investigator

T Richard Welberry
Research School of Chemistry
Australian National University



Facilities Used



Darren Goossens
Matthias Honal
Research School of Chemistry
Australian National University

RFCD Codes

240202, 250105, 260101, 291302


Significant Achievements, Anticipated Outcomes and Future Work

The method has been used to study disorder in a number of quite diverse systems. Major projects have been 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. 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 which involve interstitial transition metal ordering and the transition metal compound Fe3(CO)12 in which the Fe3 moiety is disordered.

In 1997 we developed algorithms to perform this iterative MC methodology solely by computer, using quantitative 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. We believe this methodology will become increasingly powerful and more widely used as computers become even faster, allowing increasingly complex systems to be studied.


Computational Techniques Used

(1) A simulation model is first set-up in terms of basic inter-atomic or inter-molecular interactions.

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

(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 step (1).

Approximately equal amounts of time are spent on steps (2) and (3) above. The latter calculation uses the software algorithm DIFFUSE developed by Dr. Brent Butler at RSC some years ago (this was highly vectorised code). The newly developed methodology for automatic refinement of a MC model requires long production runs. A substantial proportion of the work involves parallel computations in which basically the same calculation is carried out with different sets of model parameters. The methodology is thus ideally suited to a parallel processing environment. Since 1999 and before the advent of the SC machine, virtually all our work has been carried out on a local cluster of 12 Pentium II/III workstations. At present we are carrying out work to implement the methodology on the SC machine.


Publications, Awards and External Funding

M. Honal, T.R. Welberry, Monte Carlo Study of the Quasicrystal-to-Crystal Transformation Using an Approach Based on the Gummelt Covering, Zeitschrift für Kristallographie, (in press).