Modulated Structures

Crystal structures typically exhibit periodicity in three-dimensional space that is generated by translational symmetry. The diffraction pattern of these crystals can easily be described with three dimensions. However, sometimes we encounter aperiodic crystals that exhibit long-range order without lattice translation symmetry. In these modulated structures, additional sharp Bragg reflections are produced that cannot be described with only three hkl indices and traditional methods for structure elucidation fail.

In this case, modulation refers to the variation of the atomic sites of an ideal average periodic structure. When the wavelength of the modulation is incommensurate with the average periodic lattice, it disrupts the long-range periodicity, which produces diffraction patterns with additional reflections.

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