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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 (Al4+2x Si2-2x O10-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 SiO2 -Al2 O3 phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.

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