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(e) What complications are introduced by the fact that crystals are three dimensional?

This is a difficult question to answer systematically without drawing on a fairly full knowledge of crystallography. In practice however it can be said that the complications in the principles involved are relatively few: the computation becomes necessarily greatly increased.

The important point to realise is that the relative scale of wavelength-to- object-size is quite different for light and for X-rays. For most of the objects illustrated in the Atlas the significant dimensions are a few thousand wavelengths of light. In the X-ray case however typical dimensions (e.g. a carbon--carbon bond of 1.4 $\times$ 10-10m) are comparable with the wavelength (1.54 $\times$ 10-10m for Cu $K\alpha$ radiation). Thus in optics all the sigificant scattered information is contained within very small angles, whereas in X-ray diffraction we need to take in scattering angles of up to 180$^{\circ}$ in order to extract the maximum information. The complications therefore turn out to be experimental rather than theoretical and will be dealt with in later pamphlets in the series dealing with other aspects of the subject. At the moment it will suffice to say that there is no difference in principle that need concern us, though experimentally and computationally there are significant increases in complexity on moving from two to three dimensions.


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