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There are three major steps in order to determine the structure of an unknown material. First of all the shape and size of the unit cell are deduced from the angular positions of the diffraction lines. Then the number of atoms per unit cell computed from the shape and size of the unit cell, the chemical composition of the specimen, and its measured density. Finally, the position of the atoms within the unit cell is deduced from the relative intensities of the diffraction lines.
The process of finding the position of the atoms within the unit cell is generally the most difficult and there are many structures which are known only incompletely, in the sense that this final step has not yet been made.
The first step in which size and shape of the material is measured is same as the indexing of powder diffraction pattern which involves the accurate determination of peak positions, determination of the unit cell parameters from the peak positions such as Bragg's Law, inter planar d-spacing, and systematic absences.
In Bragg's Law when x-rays are scattered from a crystal lattice, peaks of scattered intensity are observed which corresponds to the two conditions. First condition is that the angle of incidence is equal to the angle of scattering, and the second is that the path length difference is equal to an integer number of wavelengths. The condition for maximum intensity helps to calculate details about the crystal structure, or if the crystal structure is know, to determine the wavelength of the x-rays incident upon the crystal.
Remember that crystals possess a regular, repetitive internal structure. The concept of symmetry describes the repetition of structural features. Symmetries are most frequently used to classify the different crystal structures. In general one can generate 14 basic crystal structures through symmetries. These fourteen basic crystal structures are called Bravais Lattices. Any crystal structure can be reduced to one of these 14 Bravais Lattices.
As it is mentioned above that the indexing is the process of determining the unit cell parameters from the peak positions. To index a powder diffraction pattern it is necessary to assign Miller indices, hkl, to each peak. Note that a diffraction pattern can not be analyzed until it has been indexed. It is always the first step in analysis. Unfortunately it is not just the simple reverse of calculating peak positions from the unit cell dimensions and wavelength.
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