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.[1][2] It is used in the determination of size of crystals in the form of powder.
The Scherrer equation can be written as:
where:
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;
is the X-ray wavelength;
is the line broadening at half the maximum intensity (FWHM), after subtracting the instrumental line broadening, in radians. This quantity is also sometimes denoted as ;
is the Bragg angle.
^P. Scherrer, Göttinger Nachrichten Gesell., Vol. 2, 1918, p 98.
^Patterson, A. (1939). "The Scherrer Formula for X-Ray Particle Size Determination". Phys. Rev. 56 (10): 978–982. Bibcode:1939PhRv...56..978P. doi:10.1103/PhysRev.56.978.
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