Dear Ismail I. Marhoon ,

I invite you to check these papers and RG discussion:

Article Determination of nanocrystal sizes: A comparison of TEM, SAX...

https://www.researchgate.net/post/what_is_the_approx_minimum_nanocrystal_size_at_which_XRD_fails_to_give_sharp_2-theta_peaks

Hope this helps.

You can check this paper

https://www.researchgate.net/publication/303880669_DEVELOPMENT_OF_ULTRA_FINE_GRAIN_STRUCTURE_IN_ALUMINIUM_ALLOY_BY_ROLLING

There is no such animal as the 'Debye‐Scherrer equation'.

Welcome back Dr. Rawle, long time no see.

First, you need to separate the XRD peak’s broadening caused by small zones of cohernt scattering from that caused by non-uniform stresses. At the next stage you can apply the Scherrer formula to calculate the first one. Assuming that the zones of coherent scattering are restricted by grain boundaries, the calculated value is an grain size in the examined volume. But be careful: the low-angle boundaries may also contribute to a peak broadening, so I recommend to recheck your measurement by additional technique, for example TEM.

Yes it is possible to calculate particle size using debye scherrer equation but it is not conclusive, to support it go for TEM also. Thank you

By applying Scherrer equation on the XRD pattern, the particle size can be calculated:

  (D=Kλ/(β cos θ)

     Where D is the mean size of crystallites (nm), K is crystallite shape factor a good approximation is 0.9, λ is the X-ray wavelength, B is the     full width at half the maximum (FWHM) in radians of the X-ray diffraction peak and θ is the Braggs' angle (deg.)

Scherrer’s equation:

Particle Size = (0.9 x λ)/ (d cosθ)

λ = 1.54060 Å (in the case of CuKa1) so, 0.9 x λ = 1.38654

Θ = 2θ/2 (in the example = 20/2)

d = the full width at half maximum intensity of the peak (in Rad) – you can calculate it using Origin software.

To convert from angle to rad

Rad = (22 x angle) / (7 x 180) = angle x 0.01746

Example: if d = 0.5 angle (θ)

= (22 x 0.5)/ (7x 180) = 0.00873 rad

Please this paper

Article Structural and physical characteristics of Au2O3 doped sodiu...

Yes, by applying Scherrer equation on the XRD peak