DIFFRACTION FROM POINTS, PLANES, MOLECULES, AND CRYSTALS

DIFFRACTION FROM POINTS, PLANES, MOLECULES, AND CRYSTALS 

Two basic questions we encounter in understanding X-ray crystallography are how do crystals diffract X rays, and how can we describe that process in mathematical terms These questions may be addressed in a number of ways, but the approach we choose here is divide and conquer. Diffraction from a crystal can be deconstructed into two problems, each worked out separately, and finally, their solutions combined. 

The reader probably has it branded indelibly upon his/her mind by now that Fourier transform and diffraction pattern are mathematical and physical correlates. Hence the point will be belabored no more, and only one or the other will be used. The questions now become specific. How does a collection of atoms diffract X-rays, and how does a point lattice diffract X-rays  

Introduction to Macromolecular Crystallography, Second Edition By Alexander McPherson Copyright 2009 John Wiley Sons, Inc. 

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The nature of the relation which exists between the symmetry of diffraction effects and that of the crystal may be gathered by consideration of the hkO intensities of two simple tetragonal crystals—urea (0---C(NH2)2), whose point-group symmetry is 42m, and penta-erythritol (C(CH2OH)4), belonging to class 4. For urea (see Fig. 144), the intensity of 310 is the same as that of 310, as is obvious from the relation of the molecules to the traces of these planes the equality... 

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