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The Scherrer equation is limited to nano-scale crystallites, or more-strictly, the coherently scattering domain size, which can be smaller than the crystallite size (due to factors mentioned below). It is not applicable to grains larger than about 0.1 to 0.2 μm, which precludes those observed in most metallographic and ceramographic ...
Grain size (or particle size) is the diameter of individual grains of sediment, or the lithified particles in clastic rocks. The term may also be applied to other granular materials . This is different from the crystallite size, which refers to the size of a single crystal inside a particle or grain.
Abnormal grain growth, where a small number of crystallites are significantly larger than the mean crystallite size, is commonly observed in diverse polycrystalline materials, and results in mechanical and optical properties that diverge from similar materials having a monodisperse crystallite size distribution with a similar mean crystallite size.
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 ...
The WAXS technique is used to determine the degree of crystallinity of polymer samples. [3] It can also be used to determine the chemical composition or phase composition of a film, the texture of a film (preferred alignment of crystallites), the crystallite size and presence of film stress.
Grain boundaries disrupt the motion of dislocations through a material, so reducing crystallite size is a common way to improve strength, as described by the Hall–Petch relationship. Since grain boundaries are defects in the crystal structure they tend to decrease the electrical and thermal conductivity of the material.
Wavelength function accounts for the distribution of the wavelengths in the source, and varies with the nature of the source and monochromatizing technique. The specimen function depends on several things. First is dynamic scattering, and secondly the physical properties of the sample such as crystallite size, and microstrain.
The expression is a combination of the Scherrer equation for size broadening and the Stokes and Wilson expression for strain broadening. The value of η is the strain in the crystallites, the value of D represents the size of the crystallites. The constant k is typically close to unity and ranges from 0.8 to 1.39.