calculate crystal size using XRD ( x-Ray Diffration) data
calculate crystal size using XRD ( x-Ray Diffraction) data
The average crystallite size usually calculated from the full width at half maximum (FWHM) of the diffraction peak using Debye- Scherrer’s equation:
where
τ is the mean size of the ordered (crystalline) domains, which may be smaller or equal to the grain size
K is a dimensionless shape factor, with a value(k = 0.89 ~0.94). The shape factor has a typical value of about 0.9, but varies with the actual shape of the crystallite
λ is the X-ray wavelength
β is the line broadening at half the maximum intensity (FWHM), after subtracting the instrumental line broadening, in radians
(θ is the Bragg angle (in degrees
Example:
Calculate the
crystal size at peak of ( 2θ=23.3) and (FWHM) = 0.5°
was measured by X- ray wavelength λ= 1.54060 Å
Answer:
1- convert (FWHM) from degree to radians
Degrees to Radians conversion
radians = degrees * 180/
π = 0.5*180/π = 28.65
2- find cosθ
2θ=23.3
θ=23.3/2= 1165
cos θ = cos (11.65) = 0.979
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