Diffraction patterns reciprocal nature

In crystallography, the difiiraction of the individual atoms within the crystal interacts with the diffracted waves from the crystal, or reciprocal lattice. This lattice represents all the points in the crystal (x,y,z) as points in the reciprocal lattice (h,k,l). The result is that a crystal gives a diffraction pattern only at the lattice points of the crystal (actually the reciprocal lattice points) (O Figure 22-2). The positions of the spots or reflections on the image are determined hy the dimensions of the crystal lattice. The intensity of each spot is determined hy the nature and arrangement of the atoms with the smallest unit, the unit cell. Every diffracted beam that results in a reflection is made up of beams diffracted from all the atoms within the unit cell, and the intensity of each spot can be calculated from the sum of all the waves diffracted from all the atoms. Therefore, the intensity of each reflection contains information about the entire atomic structure within the unit cell. 

Polycrystal-type (rings) electron diffraction patterns (Fig.6) are especially valuable for precision studies - checking on the scattering law, identification of the nature of chemical bonding, and refinement of the chemical composition of the specimen - because these patterns allow the precision measurements of reflection intensities. The reciprocal lattice of a polycrystal is obtained by spherical rotation of the reciprocal lattice of a single crystal around a fixed 000 point it forms a system of spheres placed one inside the other and has the symmetry co oo.m. It is also important for structure... 

The powder diffraction experiment is the cornerstone of a truly basic materials characterization technique - diffraction analysis - and it has been used for many decades with exceptional success to provide accurate information about the structure of materials. Although powder data usually lack the three-dimensionality of a diffraction image, the fundamental nature of the method is easily appreciated from the fact that each powder diffraction pattern represents a one-dimensional snapshot of the three-dimensional reciprocal lattice of a crystal. The quality of the powder diffraction pattern is usually limited by the nature and the energy of the available radiation, by the resolution of the instrument, and by the physical and chemical conditions of the specimen. Since many materials can only be prepared in a polycrystalline form, the powder diffraction experiment becomes the only realistic option for a reliable determination of the crystal structure of such materials. 

Now you tell us You might be thinking, but do not despair. It is true that the translational components of symmetry elements are lost during transformation into reciprocal space and simply appear as the corresponding rotational symmetry element, that s the bad news. The good news is that the translational components of any symmetry element do leave cryptic evidence in the diffraction pattern of their presence in the crystal. Furthermore we know exactly the nature and form of that evidence, it is distinct and clear to the eye of the crystallographer, and we know exactly where to look for it. 

The lattice factor can be considered to sample the structure factor at different points in reciprocal space and the observed diffraction pattern is essentially a two-dimensional projection of the square of this sampling. For samples which are polycrystalline in nature (Le, the grains are randomly oriented) the diffraction patterns are of the Debye-Scherrer type consisting of concentric rings. When the structural units are oriented along a particular axis the rings give way to broad spots, the distribution of which can reveal the orientation of the specimen. ... 

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