Abstract: Aperiodic crystals are crystalline materials with atomic structures that lack translational symmetry. This book gives a comprehensive account of the superspace theory for the description of the crystal structures, and symmetries of incommensurately modulated crystals and composite crystals. It also gives a brief introduction to quasicrystals, thus providing the necessary background for understanding the distinctive features of aperiodic crystals, and it provides the tools for the application of quantitative methods from the realms of crystallography, solid state chemistry, and solid state physics to aperiodic crystal structures. The second half of the book is devoted to crystallographic methods of structural analysis of incommensurate crystals. Thorough accounts are given of the diffraction by incommensurate crystals, the choice of parameters in structure refinements, and the use of superspace in analysing crystal structures. The presentation of methods of structure determination includes direct methods, Fourier methods, Patterson function methods, the maximum entropy method (MEM), and charge flipping. So-called t-plots are introduced as a versatile method for the crystal chemical analysis of incommensurately modulated structures and composite crystals.

Keywords: aperiodic crystal, charge flipping, composite crystal, diffraction, direct methods, Fourier methods, incommensurately modulated crystal, maximum entropy method, Patterson function, quasicrystal