Williamson–Hall analysis- is applicable for powders with no preferred orientation.

Does your "thin film" conform to this requirement? Polycrystalline or epitaxial?

I suspect it to be oriented polycrystalline. Tough to resolve "crystal size and strain in thin films" considering the model used for the W-H method, in my opinion as of now. I remain open-minded :-)

Post some literature references for the work you are thinking of. Describing the materials system better may be a good start along with your objective for using XRD.

Try XRR first to characterize the film thickness and flatness 1st:

https://www.researchgate.net/post/Can_XRR_X-Ray_Reflectivity_be_implemented_in_the_Topographic_Mode_with_spatial_resolution_over_the_sample_surface_Is_there_value_for_such_analyses?_tpcectx=profile_questions

Well I have preferred orientation along (100)..It seems epitaxial. XRD results showed only one orientation of the deposited material similar w.r.t Substrate orientation. estimated thickness of films is around 20-25 nm. So can i apply W-H analysis on that? 

we have Pan analytic XRD with Monochoromater.. 

• What substrate?
• What film?

You'll probably need to simulate using LEPTOS or equivalent software in Panalytical package.

Mgo 100 is substrate and NiFe film..

Then, in all likelihood, your Nano structure includes polycrystalline film with varying "preferred orientation". This implies that the W-H will not apply directly.

However, if you used dental film or a 2D detector, you'll be able to quantify the "preferred orientation" (ODF, OREINTATION DISTRIBUTION FUNCTION) and any variations topographically. Depending on the size of crystallites and the spatial resolution of the 2D image recording devise, you may be able to estimate the crystallite size in the film.

Caution:

Dear Ali

Please, open the attach file that contains, How to calculate the Crystal size and Strain in thin films by Williamson–Hall analysis in details

I see clear evidence of "preferred orientation" or other components in the XRD profiles (hump at center) shown in Figure 3 in the above article with notable integrated intensity compared with the signal from the more "periodic crystalline Nano structure". Any conventional use of W-H technique would inherently neglect effects of "aperiodic" components that are non-random including amorphous, oriented, semi or para crystalline, which would invariably be present to some degree or the other in most hetro-epitaxial processes where the substrate and film lattice are not matched.

"It seems epitaxial. XRD results showed only one orientation of the deposited material similar w.r.t " - post your XRD data if possible. You'll get better feedback thus. Unless you have a 2D beam and a real time 2D detector, it would be tough to back up any claims of "complete epitaxy". As there are "degrees" of epitaxy which also change topographically (spatially) :-) See example below for the NIST 2000 standard reference material.

I suggest looking into Bruker LEPTOS for a potential solution. You may be able to assume a model and then tweak it by simulating the XRD pattern from such a structure to match with experimental data. Several such examples are noted in the attached including GaAs (004)s reflection and NIST2000 XRR:

https://www.researchgate.net/post/What_is_the_best_way_to_interpret_REAL_TIME_3D_X_Y_o-2TH_o_ph_ch_reciprocal_space_relative_intensity_data_from_HRXRD_rocking_curve_analyses?_tpcectx=profile_questions

Dr. Mr. Ali Hassan Kazmi,

I have done this kind samples before. Before you go farther for XRD-based analysis, it will be good that knowing the consideration about the instruments and the samples in depth.

We all exactly know that thin film sample particularly having preferred orientation, because their formation direction on specific (hkl) direction. So, it will be nice if we perform rietvield refinement method.  The first consideration is focusly observe the preferred orientation first, and then the crystallite size-strain could be attributed through gaussion-lorentzian peak shape refinement.

Through that, we can find specifically the preferred orientation,which represents the formed crystal shape, then also we can calculate the crystallite size-strain, then performs their crystallite size distribution.

The calculation of crystallite size-strain were described previously by the attachment from Dr./Mr. Essam R. Shaabban, so you can analyse the crystallite size and their lattice defects of your samples.

Dear Mr. Ali Hassan Kazmi,

Crystallite size represents their structural formation of unit cells growth in similar lattice parameters, to be a aingle crystallite.

From that, we can justify that higher crystallite size represents high structural crystal formation, and high homogeneity of the formed crystal.

It can be conducted higher piezoelectricity performance, and more fine optical activity performance, and so on.

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).

Syed Ali Hassan The Williamson-Hall Plot. W-H plot is used to calculate the crystallite size and microstrain from complex XRD data. That's when both the crystallite size and microstrain vary as a function of the Bragg's angle, we can only calculate these parameters from XRD data using W-H plot. I have provided the practice file (Origin file) as well as the calculation file (Excel file) in the video description. Thanks

https://youtu.be/ipX3iUJ5VcU