Incommensurate systems show long‐range order, but lack translational periodicity. They cannot be described within the three‐dimensional lattice space groups. In these systems a local atomic property is modulated with a period that is incommensurate with the underlying lattice as the wavelength of the modulation is not an integral multiple of the unit‐cell edge. Here, we describe the dielectric and polarization properties as well as neutron, X‐ray scattering and NMR features of incommensurate systems. The elementary excitations of incommensurate systems, i.e. phasons and amplitudons, are discussed as well. In addition to plane wave also soliton structures appear in the ground state. One‐, two‐ and three‐dimensional modulated structures are treated. The basic theoretical understanding of incommensurate systems is discussed.
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