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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.
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]
Small-angle scattering from particles can be used to determine the particle shape or their size distribution. A small-angle scattering pattern can be fitted with intensities calculated from different model shapes when the size distribution is known. If the shape is known, a size distribution may be fitted to the intensity.
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).
X-ray diffraction is a generic term for phenomena associated with changes in the direction of X-ray beams due to interactions with the electrons around atoms. It occurs due to elastic scattering , when there is no change in the energy of the waves.
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.