**Principal Investigator**
T Richard Welberry **Project** p05

Research School of Chemistry **Machine** VP

**Co-Investigators** Sheridan
C. Mayo, Andrew G. Christy, Thomas Proffen, Aidan P. Heerdegen,
Research School of Chemistry.

**Computation of W-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. Conventional crystal structure analysis of disordered materials using the sharp Bragg diffraction data reveals only average one-body structural information, such as atomic positions, thermal ellipsoids and site occupancies. Diffuse scattering, on the other hand, gives two-body information and is thus potentially a rich source of information of how atoms and molecules interact with each other.

Traditionally there have been two major mathematical
approaches employed to describe and understand this diffuse part
of the diffraction pattern - a reciprocal space (modulation-wave)
approach and a real-space (correlation) approach. Either of these
approaches may be employed to obtain sets of physical parameters
which describe quite accurately the observed diffuse intensities.
The ultimate goal of such studies, however, is not simply to find
a set of mathematical correlation parameters that can describe
the diffraction pattern but to obtain a realistic model of the
how the material is organized and that is consistent with the
observed scattering. Although such models can be derived *a
posteriori* from the mathematical fit to the data, this approach
can all too often lead to misinterpretation and unrealistic models
for the disorder. This possibility can often be reduced if the
normal order of analysis is reversed such that the investigation
begins not with a mathematical description but with the models
themselves. The idea is to develop a model which first satisfies
any known physical/chemical constraints and then iteratively adjust
the simulation until the diffraction pattern from the computer
model matches the measured intensities. By turning the usual
analysis procedure around the physical organization of the material
is given the greatest emphasis and many possible, but unlikely
or non-physical, configurations that are consistent with the diffraction
data will thus be eliminated from consideration.

**What are the basic questions addressed?**

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?

**What are the results to date and 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.

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. Substantial progress has been made during 1995 in modelling a urea/hexadecane inclusion compound and further related examples are being studied.

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.

**What computational techniques are used and why
is a supercomputer required?**

We use mainly Monte Carlo simulation for the modelling. This part of the work is not generally performed on the VP since it does not vectorise well. The main part of the work carried out on the VP is obtaining the three dimensional diffraction patterns from the simulation results. This involves direct Fourier transformation for which we have developed a highly vectorised algorithm. For disordered crystals, large sample sizes are necessary in order to obtain statistically useful spatial information. In addition the diffraction patterns need to be computed on a fine grid of points in three dimensions. Because of the large amounts of CPU time which would be required, lesser classes of computer allow only the crudest models to be explored.

**Publications**

*A paracrystalline description of defect distributions
in wüstite, Fe 1-xO,* T.R. Welberry
and A.G. Christy Journal of Solid State Chemistry

*A Modulation Wave Approach to Understanding the
Disordered Structure of Cubic Stabilised Zirconias (CSZ's)*
T.R. Welberry, R.L. Withers and S.C. Mayo, J. Solid State Chem.,
**115**, 43-54 (1995).

*A computer-simulation study of the 'white-line
effect' in diffraction patterns of mixed charge-transfer salts*,
T.R. Welberry and N.J. Fox. J. Appl. Crystallography, **28**,
611-614 (1995).

*Diffuse X-ray Scattering from Disordered Crystals,
*T.R. Welberry and B.D. Butler, Chemical
Reviews. **95**, 2369-2403 (1995).