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.