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+2xSi2−2xO10−x) derived from the superspace groupPbam(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–Al2O3phase diagram. The results are compared with experimentally established models which confirm the validity and utility of the presented method.

中文翻译：

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用第一性原理计算表征调制结构：莫来石有序的统一超空间方案

研究了应用密度泛函理论的计算方法来描述和理解调制晶体结构的好处。提出了一种方法，允许人们根据相应结构的第一原理计算来建立、改进和测试超空间模型，包括位移和占据调制函数。不同构型的总能量允许人们区分稳定和不稳定的结构模型。该研究基于一系列几何优化的莫来石（Al4+2X硅2−2X氧10−X) 从超空间群导出巴姆(α0½)0SS。尽管莫来石具有无序且结构复杂的性质，但有序超结构的计算对于确定莫来石中理想的 Al/Si 排序、提取原子调制函数以及了解 SiO 非常有用2–铝2氧3相图。结果与实验建立的模型进行了比较，证实了该方法的有效性和实用性。