Commensurate superlattice reflections

The diffraction pattern from a normal crystal is characterised by an array of spots separated by a distance /a = a that arise from the parent structure, together with a set of commensurate superlattice reflections that arise as a consequence of the additional ordering. In this case the spot spacing is 1 /na = a /n, where n is an integer, (Figure 8.21a, b). In modulated structures, the modulation might be in the position of the atoms, called a displacive modulation, (Figure 8.21c). Displacive modulations... 

When the modulation wavelength exactly fits a number of parent unit cells, (that is, is commensurate with it), it will be possible to index the reflections in terms of a normal superlattice. Recently a number of structures that were once described in this way have been restudied and found to be better described as modulated structures with commensurate modulation waves - commensurately modulated structures. 

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