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## Introduction: crystal structure analysis

The structure, i.e. the internal shape of a substance, is characteristic of its physical and chemical behavior. Therefore the knowledge about the structure of a substance is of great importance. There are various methods of crystal structure analysis. For example, the spatial arrangements of atoms in the crystal can be determined with the help of rays whose wavelengths correspond approximately to the atomic distances in the crystal lattice -, proton or neutron beams).

### Functionality

X-rays that hit the space lattice of a crystal are diffracted by it. The diffraction is specific to the crystal lattice, i.e. each lattice is assigned a certain diffraction pattern.

Bragg's equation provides the mathematical relationship: In order to identify the individual crystal lattices, the diffraction of X-rays on the individual particles is interpreted. The rays penetrate the inside of the crystal and are reflected on the atoms or molecules.

Bragg's law
The X-rays enter the first phase of the crystal. While a small part is reflected at the first atomic or molecular layer, the rest penetrates the interior of the crystal and is diffracted at the second, third or nth layer. The scatter at the individual centers is relatively small. However, they can be amplified by interference if the path difference (the distance $2d⋅sinα$) an integer multiple of the wavelength ($nλ$) is. This condition for the diffraction maxima only applies to certain angles of incidence ($α$).
nλ = 2 d sin $α$1)with n = 1, 2, 3, ...

In principle, the diffraction examinations can be carried out with electromagnetic rays (X-rays) or with corpuscular beams (particle beams), for example electron beams2) or neutron beams. Depending on the type of radiation used, the scattering centers are either the electron shells of the atoms (X-ray diffraction) or the atomic nuclei (neutron diffraction) themselves.

There are various methods for examining the crystal lattice using X-ray spectroscopy, which are based on Bragg's law. Some of them are

• the Laue process (single crystals)
• the Debye-Scherrer process (crystal powder)
• the electron density recordings

## Literature

Cool, O. (August 2012):General Chemistry. 1st edition Wiley-VCH Verlag GmbH & Co. KGaA, 220, ISBN: 978-3-527-33198-7
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