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The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre crystallites in a solid to the broadening of a peak in a diffraction pattern. It is often referred to, incorrectly, as a formula for particle size measurement or analysis. It is named after Paul Scherrer.
Bragg diffraction (also referred to as the Bragg formulation of X-ray diffraction) was first proposed by Lawrence Bragg and his father, William Henry Bragg, in 1913 [1] after their discovery that crystalline solids produced surprising patterns of reflected X-rays (in contrast to those produced with, for instance, a liquid).
Small-angle X-ray scattering (SAXS) is a small-angle scattering technique by which nanoscale density differences in a sample can be quantified. This means that it can determine nanoparticle size distributions, resolve the size and shape of (monodisperse) macromolecules, determine pore sizes and characteristic distances of partially ordered materials. [1]
The use of computational methods for the powder X-ray diffraction data analysis is now generalized. It typically compares the experimental data to the simulated diffractogram of a model structure, taking into account the instrumental parameters, and refines the structural or microstructural parameters of the model using least squares based ...
Particle-size analysis also helps the effectiveness of SAG Mills when crushing material. In the building industry, the particle size can directly affect the strength of the final material, as it observed for cement. [18] Two of the most used techniques used for the particle size characterization of minerals are sieving and laser diffraction.
Free-electron lasers have been developed for use in X-ray diffraction and crystallography. [27] These are the brightest X-ray sources currently available; with the X-rays coming in femtosecond bursts. The intensity of the source is such that atomic resolution diffraction patterns can be resolved for crystals otherwise too small for collection.
Crystallite size, the size of the crystal unit cell, can be calculated through the Scherrer equation. Generally, crystal structure is determined using powder X-ray diffraction, or selected area electron diffraction using a transmission electron microscope, though others such as Raman spectroscopy exist. X-ray diffraction requires on the order ...
A particle incident on a crystalline surface with momentum will undergo scattering through a momentum change of . If x {\displaystyle x} and y {\displaystyle y} represent directions in the plane of the surface and z {\displaystyle z} is perpendicular to the surface, then the scattered intensity as a function of all possible values of Q ...
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