# Shape factor (X-ray diffraction)

Shape factor (X-ray diffraction)

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

:

where τ is the mean crystallite dimension, "K" is the shape factor, λ is the x-ray wavelength, typically 1.542 Å, β is the line broadening at half the maximum intensity in radians, and θ is the Bragg angle. [R. Jenkins & R.L. Snyder, "Introduction to X-ray Powder Diffractometry", John Wiley & Sons Inc., 1996, p 89-91, ISBN 0-471-51339-3.] 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.

References

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