Scattering and diffraction. Optical diffraction diagrams
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In the book Atlas of Optical Transforms (G. Harburn, CA Taylor, TR Welberry, Ed G. Bell & Sons, London 1975) several optical analogues are shown which can help in order to interpret X-ray diffraction patterns. Of the nearly 400 examples provided, we have selected a few which can help illustrate what has been shown in this chapter.

In each figure, the diagrams on the top row represent the system where the light is diffracted, and the lower row shows the diffraction produced. The exception is the final figure, which shows the diffraction patterns at the top and the objects obtained from the diffraction at the bottom.

We present here the simplest object (a circle) and the combination of two simple circles, showing the effect of the distance (spacing) between them. As this spacing increases, the number the diffraction fringes also increases and they appear much closer (that is the "reciprocal" effect. See the reciprocal lattice)

When the object is combined into lines, the corresponding diffraction fringes occur perpendicular to the original line. If the object  forms a 2-dimensional lattice (figure on the right), the diffraction pattern produces another lattice, reciprocal of the original. The variations in intensity in the latter are due to the finite size of the 2-dimensional object. 

The original object is getting slightly complicated. It can be seen as an idealized representation of several chemical molecules: benzene, toluene and nitro-benzene.

The same molecule can show polymorphic structures, ie different crystal structures. The diffraction diagrams apparently show different distributions of intensities, but in both cases one can discover how the diffraction pattern reveals (somehow) the diffracting object, in this case a molecule of benzene.

Distortions of the periodicity in the direct lattice (figures at the top) are transformed into the diffraction patterns as blurred lines.

If the crystal is composed of a set of discontinuous mosaics (left), the diffraction maxima on the diagrams become wider and diffuse. When the mosaics also change their orientation, the diffraction diagrams show emergent circles. Taken to the limit, this would result in a complete circle diagram, typical of microcrystalline powder.

If the sample contains two or more orientations in the lattice (twins), the maxima on the diffraction pattern split, and if the size of the twin components are small, the split maxima can appear as lines.

The two figures in the lower row show the corresponding images of a molecule (rhodium - phthalocyanine) as obtained from their diffraction patterns (upper row). The molecular image is more or less recognizable depending on the amount of information contained in the corresponding diffraction patterns. The two figures on the right column show the projection of the electron density of this molecule, as well as a two-dimensional scheme of it.

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