PACS. 02.20.-a Group theory - 64.70.Rh Commensurate-incommensurate transitions - 75.40.Cx Static properties (order parameter, static susceptibility, heat capacities, critical exponents, etc.),

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The most important symmetry properties of the incommensurately modulated crystal structures are investigated by use of exact symmetry theory of quasi-one-dimensional systems in the framework of group theory. It is shown that typical characteristic formulae developed for the description of scattering cross sections of one-dimensionally modulated crystals can be directly derived by the line-group technique. A symmetry analysis of static soliton structures is performed, representing a new method for the investigation of elementary excitations of crystals modulated incommensurately. It leads to the description of symmetry breaking, to the selection rules and hints at the similarity of symmetry behaviour of static and dynamic solitons. The actual formulae for Debye-Waller factors in the case of incommensurately modulated crystals are calculated and tabulated by using generating elements of the line groups concerned.

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