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The structures of -Ba₃RAl₂O_7.5 and -Ba₃RM₂O_7.5 (R = rare-earth elements, M = Al, Ga) complex oxides have been studied by X-ray diffraction, electron diffraction and high-resolution electron microscopy. The order-disorder phase transition between the orthorhombic high-temperature form and the monoclinic low-temperature form results from sequential migration of oxygen atoms along the strings of vertex-sharing tetrahedral Al₂O₇ pairs.

Using examples of anion-deficient perovskites modulated by periodic crystallographic shear planes, it is demonstrated what kind of local structural information can be obtained using various transmission electron microscopy techniques and how this information can be implemented in the crystal structure refinement against the powder diffraction data.

A novel operando electrochemical cell with single-crystal sapphire X-ray windows has been designed for and successfully applied to the investigation of phase transformations and the valence states of the cations in high-power and high-voltage cathode materials for Li-ion batteries.

Electron diffraction tomography is optimally suited to determine the crystal structure of metal-ion battery cathode materials at different states of charge. Here the possibilities, hurdles and advantages compared to other techniques are discussed.

Oxidation/reduction reactions in three-dimensional or layered manganites and cuprates are accompanied by the formation of domain structures. The microstructure of several representatives was studied by means of electron diffraction and high-resolution electron microscopy.

An overview is given to recent advances in the field of modulated molecular and inorganic crystals. The importance of detailed knowledge of the modulated structure to understand crystal chemistry and the functional properties of the modulated phases is outlined.