The importance of Multisite correlations
in disordered structures
T.R.Welberry and R.L.Withers
Research School of Chemistry, Australian National University, Canberra,
ACT 0200, Australia (welberry@rsc.anu.edu.au)
Conventional
crystal structure determination using Bragg reflections reveals only single-site properties of a structure (average atomic positions
mean-square atomic displacement amplitudes, site occupancies). Diffuse scattering, on the other hand,
being the Fourier transform of the pair correlation function contains
information about two-site
properties and gives direct information about the mutual behaviour of
(neighbouring) pairs of atoms. Since many theories of how atoms and molecules
interact involve pair interactions (e.g. Lennard Jones potential, Buckingham
potential etc.) it might be supposed that there will be a direct correspondence
between the observed diffuse scattering and the pair-interactions that may be
considered to be the fundamental parameters of the system. It should be noted,
however, that without any direct phase information the diffraction experiment
does not contain any information about multi-site correlations.
If a system has
properties which stem from multi-site interactions then, although diffuse
scattering effects may be observed, these arise only from the indirectly
generated pair correlations. In such circumstances there is no direct link
between the observed pair correlations and the fundamental inter-atomic
interactions and little purpose is served by trying to interpret the scattering
in terms of a model formulated in terms of pair-interactions. In this paper we
describe examples of real systems in which complex diffraction patterns can be
explained by extremely simple models involving multi-site atomic interactions.
The first of
these examples involves O/F ordering and associated Mo ion shifts in the system
K3MoO3F3. Monte Carlo modelling is used to show how the latter, when
coupled with an appropriate local crystal chemical constraint (a multi-site
interaction), can give rise to the observed highly structured diffuse scattering
patterns. Examples of different sections of the calculated diffraction pattern
are shown in Fig.1.
Fig. 1. Three example reciprocal sections (100, 113, 331) of the K3MoO3F3 system, calculated from a Monte Carlo model based on a simple chemical constraint.
A second example involves Bi/Zn cation
ordering in the cubic pyrochlore (Bi1.5Zn0.5)(Zn0.5Nb1.5)O7. Here too a multi-site interaction based
on a simple chemical constraint is required to explain the observed diffraction
patterns.