Scattering and diffraction. Optical
diffraction diagrams
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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 2dimensional 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 2dimensional object. 

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

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 figure on the right side shows the same projection of the electron density of this molecule. 
