Debye Scherrer equation for calculating the crystallite size is given by = / (1) where K is the Scherrer constant, λ is the wavelength of light used for the diffraction, β the “full width at half maximum” of the sharp peaks, and θ the angle measured. The Scherrer constant (K) in the above formula accounts for the shape of the particle and is generally taken to have the value 0.9. The results revealed that the crystallite size is less than 100 nm. , was developed in 1918, to calculate the nano crystallite size (L) by XRD radiation.cos Scherrer Equation, L K of wavelength λ (nm) from measuring the full width at half maximum of peaks (β) in radian located at any 2θ in the pattern. The shape factor of K can be 0.62 - 2.08 and is usually taken as about 0.89. But, if all of the peaks of a pattern are going to cosθ must be identical. Given a similar value of L, X-ray diffraction is a convenient method for determining the mean size of nanocrystallites in nanocrystalline materials.
There is no such thing as the "Debye-Scherrer equation". Note that 'Scherrer' is the last name of a person and should have an upper case (not 'scherrer'...).
The only formula for the determination of crystallite sizes is that of Scherrer, otherwise you can use a structural refinement that also provide the crystallite sizes values
Dear Isam Alkhalifawi ,
unfortunately the Scherrer equation often is erroneously named as the ' Debye-Scherrer' equation.
But there is a second equation, which considers the residual strain.
It is called the Williamson-Hall or Hall-Williamson relation.
Please see the section 'Size and strain broadening' for the fromula.
https://en.wikipedia.org/wiki/Powder_diffraction
A screenshot of that section is attached.
You see, that when neglecting the strain (eta) the Willianson-Hall expression reduces to the Scherrer equation.
From this perspective, one should use the Williamson-Hall approach, because in this relation the additional peak broadening via the residual strain is considered.
See for example also:
http://pd.chem.ucl.ac.uk/pdnn/peaks/sizedet.htm
Best regards
G.M.
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