The energetics of interaction between oxygen vacancies in sillimanite: A model for the mullite structure

A microscopic model is introduced to discuss the modulated structure of mullite. The oxygen vacancies of this aluminosilicate are known to play a central role. In particular, a single vacancy strongly orders its surrounding Al/Si tetrahedral sites. It is shown in this work that if two oxygen vacancies approach too closely to one another, their Al/Si dressing overlap. This situation results in repulsive interaction. The field of interaction between the vacancies is estimated with the use of an atomistic computer simulation. We use a Bragg-Williams type of theory to dicuss the ordering pattern of the vacancies. Due to frustration between the two dominant repulsive interactions, our model predicts a modulated phase transition in agreement with observation.