A full reciprocal-space volume of diffuse scattering data from a single-crystal of the mineral mullite, Al2(Al2 + 2x
Si2 − 2x
)O10 − x
, x = 0.4, was collected. These data were analysed using least-squares techniques by writing an equation for the diffuse scattering that involves only the local order between vacancies on specific oxygen sites in the material. The effect of the large, but predictable, cation shifts on the diffuse intensity is taken account of in the coefficients of the oxygen-vacancy short-range-order intensities. This analysis shows that the vacancies are negatively correlated at the near-neighbour ½ 〈110〉, [110], 〈001〉 and 〈011〉 interatomic vectors and positively correlated along the 〈010〉, 〈101〉, ½ 〈112〉 and ½ 〈310〉 vectors. Subsequent Monte Carlo modelling of the structure based on these local-order parameters demonstrates that the structure of mullite is dominated by effective near-neighbour vacancy–vacancy repulsive interactions. A real-space model of mullite is presented that is approximately consistent with the measured local-order parameters.
Local order parameters for symmetry fractionalization
