Characterizing modulated structures with first-principles calculations: a unified superspace scheme of ordering in mullite

The benefit of computational methods applying density functional theory for the description and understanding of modulated crystal structures is investigated. A method is presented which allows one to establish, improve and test superspace models including displacive and occupational modulation functions from first-principles calculations on commensurate structures. The total energies of different configurations allow one to distinguish stable and less stable structure models. The study is based on a series of geometrically optimized superstructures of mullite (Al(4+2x)Si(2−2x)O(10−x)) derived from the superspace group Pbam(α0½)0ss. Despite the disordered and structurally complex nature of mullite, the calculations on ordered superstructures are very useful for determining the ideal Al/Si ordering in mullite, extracting atomic modulation functions as well as understanding the SiO(2)–Al(2)O(3) phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.