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If, in a crystal structure, atoms lie in the neighbourhood of a set of planes H, as indicated in Fig. 1a, then reflection by planes H is strong and hence the intensity IH is large. Of course, the converse is also true: if one observes a large intensity IH, then the atoms lie near planes as indicated in Fig. 1a. This statement follows also from the structure-factor expression:
A large FH will be found if (hxj + kyj + lzj) mod 1 is approximately constant for all j; or, in other words, if all atoms lie near one of the planes H. The phase depends on the value of the constant and changes with the origin.
Conversely, a structure-factor magnitude |FH| is small, if the atoms are randomly distributed with respect to the planes H, as shown in Fig. 1b.
The electron density can be thought of as a superposition of density waves parallel to lattice planes, the amplitudes of which are the |FH|-values, the relative phases being given by the -values. We will see later that these density waves afford a physical picture of the phase relationships used in Direct Methods.
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