Abstract
For a long time solid state systems were considered as either crystalline, i.e. lattice periodic and with space group symmetry, or amorphous. In the former case the diffraction peaks are infinitely sharp for a perfect infinite crystal, in the latter there are no sharp peaks. The presence of some disorder does not eliminate sharp Bragg peaks as long as long-range order is preserved. Moreover, the sharp Bragg peaks lie on a lattice, the reciprocal lattice, such that each peak can be labelled with three integer coefficients. It was also known that sometimes additional peaks appear, satellites. For example, a crystalline material with magnetic moments may show an ordering of the moments that can be described as a helix. If the period of this helix is not a period of the underlying lattice, the total system consisting of crystal and magnetic moments does not have lattice periodicity. This was not a problem as long as one did not want to describe the symmetries of crystal and magnetic system simultaneously. Moreover, for a long period it was not clear whether there was a common (super)lattice for crystal and magnetic moments, or not.
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Janssen, T. (1995). From Quasiperiodic to More Complex Systems. In: Axel, F., Gratias, D. (eds) Beyond Quasicrystals. Centre de Physique des Houches, vol 3. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03130-8_5
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DOI: https://doi.org/10.1007/978-3-662-03130-8_5
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