The meaning of occupancy

In any situation where there is substitutional disorder of any kind in a crystal the diffraction pattern consists of two parts the diffraction pattern of the averaged structure, which is confined to the Bragg reflections and whose analysis in terms of occupancy I have discussed and superimposed on this the diffraction pattern of the difference structure i.e. a distribution of electron density everywhere equal to the difference between the average and the actual structure. Even in the case of complete disorder this will be non-zero, but its diffraction pattern will be very weak everywhere because it will be diffused over all diffraction directions. Only if there is some kind of ordering on subsets of the crystallographic sites, which subsets define a superlattice of the crystal lattice, will the intensity of the difference pattern concentrate into definite directions and be easily detectable and interpretable. However if such a superlattice regularity is confined to 1 or 2 dimensions or to very small 3-dimensional domains then the difference diffraction will be smeared out. It may then be difficult to detect, and even when detected it can be difficult to interpret unambiguously. 

So far as is known such a result has not yet been seen in a silicate. However sub-unit cell structure has been resolved in amphiboles (Hutchison, Irusteta and Whittaker, 1975) which can be associated with the form of the amphibole double chain. This has permitted the direct observation of an intercalated layer of triple chains in some thin crystals. From a compositional point of view such an intercalation corresponds to a small amount of solid solution of talc in amphibole, so that we have in this case a direct 

Bancroft, G.M., JfiJssbauer Spectroscopy (book) p. 206, McGraw-Hill. London (1973). 

America, Abstracts with Programs. 

Hawthorne, F.C., The Crystal Chemistry of the Clino-Amphiboles Ph.D. Thesis. McMaster University (1973). 

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