Oxygen vacancy ordering and the incommensurate structure of mullite

Abstract

A description of the disordered arrangement of oxygen vacancies in a 2(Al2O3)·SiO2 mullite is presented. This description is consistent with the incommensurate diffraction maxima observed in the 1/2 c* reciprocal section and with many broader diffuse diffraction features that have been measured in other reciprocal sections. The structure was modelled using Monte Carlo techniques where the oxygen vacancies were allowed to interact via a set of pair energies. Cations in adjacent tetrahedrally coordinated sites were given displacements that depended only on the local arrangement of these oxygen vacancies. In addition to the 1/2〈110〉 and [110] repulsive interactions which are required to satisfy cation bonding requirements, it was found that unequal vacancy repulsive interactions were required along 〈100〉 and 〈010〉. Attractive vacancy-vacancy interactions along 1/2〈112〉 and 〈001〉 were also necessary but in the latter case the magnitude of the interaction is such that the probability of having an 〈001〉 vacancy pair was near that of a random vacancy distribution.