7/31/2023 0 Comments X ray diffraction analysis![]() ![]() Schematics of X-ray* cameras for investigating single crystals: (a) camera for investigating stationary single crystals by the Laue method, (b) rotating camera, (c) camera for determining the dimensions and form of the unit cell (S) specimen, (GH) goniometric head, (7) graduated circle and axis of rotation of the goniometric head, (CL) collimator, (C) cassette containing photographic film PF, (CB) cassette for obtaining back-reflection photographs, (MR) mechanism for rotating or oscillating the specimen, (Φ) graduated circle and axis of oscillation of the specimen, (δ) arc guide for inclination of axis of the goniometric head. Important contributions to the development of Patterson methods and direct methods of X-ray diffraction analysis were made by a number of scientists, including N. The foundations of the direct methods of determining crystal structures were laid by the American scientists D. Patterson suggested that the structures of substances could be investigated by means of a function of interatomic vectors such functions are now called Patterson functions. The applicability of X-ray diffraction analysis to the investigation of a broad class of substances and industry’s need for such investigations stimulated the development of techniques for the analysis of structure. Guinier developed in 1938 the method of small-angle X-ray scattering for investigating the shapes and dimensions of inho-mogeneities in substances. ![]() Scherrer proposed that the structure of polycrystalline materials be investigated by means of X-ray diffraction. Bragg became the first to investigate the atomic structures of simple crystals by means of X-ray diffraction techniques. They showed that any diffracted beam can be regarded as a reflection of the incident beam from one of the systems of crystallographic planes (see BRAGG-VULT CONDITION). ![]() ![]() Vul’f proposed a simpler interpretation of the diffraction of X rays by a crystal: diffraction reflection. They require that in parallel beams the path difference between beams scattered by the atoms corresponding to neighboring lattice points be equal to an integral number of wavelengths. For a diffracted beam to appear, these three equations, which are known as the Laue conditions, must be satisfied. Where h, k, and l are integers called Miller indexes. Laue’s theory of X-ray diffraction by crystals yields the following relations between the wavelength λ of the radiation, the parameters a, b, and c of the unit cell of the crystal, and the angles of the incident (α 0, β 0, γ 0)and diffracted (α, β, γ) beams: An X-ray pattern obtained by this method is called a Laue pattern. They recorded on the photographic plate a diffraction pattern consisting of a large number of regularly arranged spots, each of which was the track of a diffracted beam scattered by the crystal. These investigators directed a narrow beam of X rays onto a stationary crystal, behind which a photographic plate was located. The diffraction of X rays by crystals was discovered in 1912 by the German physicists M. X-ray diffraction analysis has been used most successfully to establish the atomic structure of crystalline substances because crystals have a rigid periodicity of structure and constitute naturally produced diffraction gratings for X rays. The methods of X-ray diffraction analysis are used to study, for example, metals, alloys, minerals, inorganic and organic compounds, polymers, amorphous materials, liquids, gases, and the molecules of proteins and nucleic acids. Radiation of wavelength ~ 1 angstrom (Å), that is, of the order of atomic dimensions, is used to investigate atomic structure. The diffraction pattern depends on the wavelength of the X rays employed and on the structure of the object. When X-radiation interacts with the electrons of a substance, the X rays are diffracted. Like neutron diffraction and electron diffraction analysis, X-ray diffraction analysis investigates structure through the use of diffraction. The investigation of the structure of a substance by methods that make use of the spatial distribution and intensities of X-radiation scattered by the object under study. ![]()
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