There are a number of causes of XRD line broadening - including instrumental, crystallite size, and strain broadening. All can be assessed in different way.  I suggest you read a text book such as Klug and Alexander (X-Ray Diffraction Procedures for Polycrystalline and Amorphous Materials Chapman and Hall 1954) or X-Ray diffraction by polycrystalline materials (H S Peiser, H P Rooksby, A J C Wilson: The Institute of Physics, (1955)

The general idea is that the size and microstrain contributions to broadening have different dependencies on angle, so from the W-H plot we obtain the strain component from the slope and the size component from the intercept.  I would urge anyone who will listen to never use the scherrer equation because, it assumes all broadening is due to size!  Of course you subtract the instrumental contribution, but, in general, there will also be microstrain contributions to broadening.  Maybe the microstrain is small, but you don't know that until you measure it by W-H.

See the link for a brief discussion

http://pd.chem.ucl.ac.uk/pdnn/peaks/sizedet.htm

so you are rating W-H plot over Scherrer??

emphatically

For Scherrer equation, crystallite size was calculated based on the measurement of a(hkl) peak using the following equation:

L =Kλ / Bsize cos θ

where L is crystallite size, K is a dimensionless shape factor (0.9), Bsize is line broadening at half of the maximum intensity (FWHM) in radian, λ is the X-ray wavelength for example for Cu Kα radiation (1.5406 Å) and θ is Bragg angle in degree.

Meanwhile, Williamson–Hall plot was used to estimate the crystallite size and lattice strain of the samples using the following formalism:

Btot = Bstrain + Bsize = 4Cε tanθ + Kλ/ L cosθ

where Cɛ is the lattice strain, Βsize is the particle size broadening, Βstrain is the strain broadening, L is the crystallite size, K is a dimensionless shape factor (0.9), λ is the X-ray wavelength for Cu Kα radiation (1.5406 Å) and θ is Bragg angle in degree.

Then Eq. 2 is multiplied by cosθ to yield:

Btot cosθ = 4Cε sinθ + Kλ/L

Hence, by plotting the graph of Βtot cosθ against 4 sinθ, the lattice strain, Cɛ of the sample can be obtained from the slope (gradient) while the crystallite size can be estimated from the intercept (Kλ/L).

Thank you yassine

Yassine Slimani Hi, I am studying graphite which has following diffraction peaks (002) (100) (101) (004) (103) (110) (112) and (006). I used Scherrer equation to measure the crystallite size (coherence lengths in Lc & La). To calculate Lc I used (002) (004) &(006) and for La (100) and (110). Is it possible to use W-H plot to separate size and micro strain in my material? If yes should I use peaks from the same crystallographic direction (e.g (002)(004) and (006) for Lc )?

but for La I just have (100) & (110) which are not from same crystallographic directions? and what is minimum peaks number use to apply this method? because my material after irradiation some peaks are disappeared such as (006)??.

Thanks