FUNDAMENTALS OF DIFFRACTION

In the previous chapter, we introduced basic concepts of symmetry and discussed the structure of crystals in terms of three-dimensional periodic arrays of atoms and/or molecules, sometimes perturbed by various modulation functions. In doing so, we implicitly assumed that this is indeed reality. Therefore, it is time to think about the problem from a different point of view how atoms or molecules can be observed - either directly or indirectly - and thus, how is it possible to determine the crystal structure of a material and verify the concepts of crystallographic symmetry  

Particles in motion, such as neutrons and electrons, may be used as an alternative to x-rays. They produce images of crystal structures in reciprocal space because of their dual nature as follows from quantum mechanics, 

Atomic radius may be calculated self-consistently or it may be determined from experimental structural data. Effective size of an atom varies as a function of its environment and nature of chemical bonding. Several different scales - covalent, ionic, metallic, and Van der Waals radii - are commonly used in crystallography. 

The process of transforming diffi-action patterns in order to reinstate the underlying crystal structures in the three-dimensional direct space is governed by the theory of diffiaction. The latter rests on several basic assumptions, yet it is accurate and practical. We have no intent to cover the comprehensive derivation of the x-ray diffraction theory since it is mainly of interest to experts, and can be found in many excellent books and reviews. Therefore, in this chapter we will discuss the nature and sources of radiation that are in common use today and consider the principles and fundamental laws of diffraction in general. We will also consider diffraction from a crystalline matter - specifically from polycrystalline materials - and describe diffraction pattern as a function of crystal symmetry, atomic structure and conditions of the experiment. 

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