There are three main steps in determining the structure of an unknown material. First, the shape and size of the unit cell are derived from the angular position of the diffraction line. The number of atoms per unit cell is then calculated based on the shape and size of the unit cell, the chemical composition of the sample, and the measured density. Finally, the position of the atoms in the unit cell is derived from the relative intensity of the diffraction line.
The process of finding the atomic position within a unit cell is usually the most difficult, and many structures are not completely known, and no final step has been taken in this sense.
The first step in measuring the size and shape of the material is the same as indexing the powder diffraction pattern, which involves accurately determining the peak position, determining unit cell parameters from the peak position, such as Bragg's law, inter-plane d-spacing, and system absence.
In Bragg's law, when X-rays are scattered from the crystal lattice, a peak of the scattering intensity is observed, which corresponds to two conditions. The first condition is that the angle of incidence is equal to the angle of scattering, and the second condition is that the difference in path length is equal to an integer number of wavelengths. The conditions of maximum intensity help to calculate the details of the crystal structure or, if the crystal structure is known, the wavelength of the X-rays incident on the crystal.
Remember that crystals have regular, repeating internal structures. The concept of symmetry describes the repetition of structural features. Symmetry is most commonly used to classify different crystal structures. Generally, 14 basic crystal structures can be produced by symmetry. These 14 basic crystal structures are called Bravais Lattices. Any crystal structure can be simplified to one of the 14 Bravais lattices.
As described above, the index is a process of determining a unit cell parameter from a peak position. To indicate the powder diffraction pattern, the Miller index hk1 must be assigned to each peak. Note that the diffraction pattern cannot be analyzed before being indexed. It is always the first step in the analysis. Unfortunately, it is not just a simple reversal of the peak position calculated from the cell size and wavelength.
Orignal From: Crystal structure determination and indexing
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