The aperiodic nature of mullite

Zusammenfassung

Different methods were applied to investigate the vacancy and Al/Si order in mullite. At first the symmetry was analysed thoroughly to derive constraints on the vacancy distribution based on crystal chemical premises. On this basis a superspace model was developed that defines the polyhedra network consisting of octahedra, tetrahedral tricluster units and tetrahedral dicluster units as a function of the modulation wave vector and the vacancy concentration. Refinements of superspace models based on synchrotron single crystal X-ray diffraction measurements indicate that in the real structure the identified pattern is present, but with a decreased degree of order. Different samples exhibit different degrees of order suggesting that mainly disordered and fully ordered mullite crystals exist. The Al/Si ordering could not be derived from symmetry constraints and the occupancy of Si could not be refined. Nevertheless, an Al/Si ordering pattern could be identified from the analysis of the displacive modulation.The dependence of the satellite reflections on the chemical composition was studied with precession electron diffraction tomography and density functional theory. This allowed to characterise the structural modulation on a new level and reveal the fundamental ordering patterns that define the crystal structure of mullite in terms of vacancy, tricluster and Al/Si order. The understanding of the crystal structure forms a new basis for future research on the properties of mullite and related applications.