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is the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size, which may be smaller or equal to the particle size; is a dimensionless shape factor, with a value close to unity. The shape factor has a typical value of about 0.9, but varies with the actual shape of the crystallite;
A powder X-ray diffractometer in motion. X-ray crystallography is the experimental science of determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract in specific directions.
The most common powder X-ray diffraction (XRD) refinement technique used today is based on the method proposed in the 1960s by Hugo Rietveld. [2] The Rietveld method fits a calculated profile (including all structural and instrumental parameters) to experimental data.
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.
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 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.
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).
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.