A shape factor is used in x-ray diffraction and crystallography to correlate the size of sub-micrometre s, or crystallites, in a solid to the broadening of a peak in a diffraction pattern.

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  • A shape factor is used in x-ray diffraction and crystallography to correlate the size of sub-micrometre s, or crystallites, in a solid to the broadening of a peak in a diffraction pattern. In the Scherrer equation, <math>\tau = \frac {K \lambda}{\beta \cos \theta}</math> where K is the shape factor, λ is the x-ray wavelength, typically 1.54 Å, β is the line broadening at half the maximum intensity in radians, and θ is the Bragg angle; τ is the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size. The dimensionless shape factor has a typical value of about 0.9, but varies with the actual shape of the crystallite. The Scherrer equation is limited to nano-scale particles. It is not applicable to grains larger than about 0.1 μm, which precludes those observed in most metallographic and ceramographic microstructures.
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  • A shape factor is used in x-ray diffraction and crystallography to correlate the size of sub-micrometre s, or crystallites, in a solid to the broadening of a peak in a diffraction pattern.
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  • Shape factor (X-ray diffraction)
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