**Abstract**

Complete 3D electron diffraction can be collected by rotation electron diffraction (RED) for single-crystal powder-sized samples, i.e., <0.1 μm, in all dimensions. Data collection takes about 1 h and data processing takes another hour. The crystal structures are solved by standard crystallographic techniques. X-ray crystallography requires crystals several micrometers big. For nanometer-sized crystals, electron diffraction and electron microscopy (EM) are the only possibilities. Two methods have been developed for collecting complete (except for a missing cone) three-dimensional (3D) electron diffraction data: the rotation electron diffraction and automated electron diffraction tomography (ADT). By collecting 1000–2000 electron diffraction patterns, a complete 3D data set is obtained. The geometry in RED is analogous to the rotation method in X-ray crystallography; the sample is rotated continuously along one rotation axis. In recent years, large number of crystal structures has been solved by RED. These include the most complex zeolites ever solved and quasicrystal approximants, such as the pseudo-decagonal approximants PD2 and PD1 in Al-Co-Ni. In this chapter, the results of our recent studies on the structure analysis of complex pseudo-decagonal (PD) quasicrystal approximants PD2 (*a* = 23.2, *b* = 32.3, *c* = 4.1 Å) and PD1 (*a* = 37.3, *b* = 38.8, *c* = 4.1 Å) by RED have been discussed. These are known to be the most complicated approximant structures ever solved to atomic resolution by electron crystallography. PD2 and PD1 are built of characteristic 2 nm wheel clusters with fivefold rotational symmetry, which agrees with other approximants in the PD series as well as with the results from high-resolution electron microscopy images.

**Keywords:** electron crystallography, rotation electron diffraction, quasicrystal, approximant
