A full reciprocal-space volume of diffuse scattering data was collected from a single crystal of mullite, Al2(Al2.8Si1.2)O9.6. These data were then analyzed, using least-squares techniques, by deriving an equation for diffuse scattering that involved only local order between vacancies on specific O sites. The effect of the large, but predictable, cation shifts upon the diffuse intensity was accounted for in the coefficients of the O-vacancy short-range order intensities. This analysis showed that the vacancies were negatively correlated at the near-neighbor ½<110>, [110], <001> and <011> interatomic vectors and were positively correlated along the <010>, <101>, ½<112> and ½<310> vectors. Monte Carlo modelling of the structure which was based upon these local-order parameters demonstrated that the structure of mullite was dominated by effective near-neighbor vacancy-vacancy repulsive interactions. A real-space model of mullite was presented that was approximately consistent with the measured local-order parameters.

B.D.Butler, T.R.Welberry: Journal of Applied Crystallography, 1994, 27[5], 742-54