The best way of determining of instrumental broadening is to take the same sample after you  have performed all the measurements you needed for the grain size and strain measurements,  to give an isothermal annealing treatment in the temperature range where the grain growth process could take place. This way you can eliminate not only the stored strain energy as well as the broadening associated with the small grain size. Then use the standard W-H formula to get the corrected Betha hkl values knowing Betha -hkl obtained from the large grained strain free sample as prepared above. 

If it is possible to follow the procedure described by Tarik, then do it, it is the best way. But if is not possible dependig on your samples, there are two methods, the expensive and the cheap:

The expensive way is to get a NIST LaB6 standard powder (SRM 660-b), measure it in the powder diffractometer with exactly the same optical configuration that you used in your samples. Then you must to fit the Caglioti equation to the measured full width at half maximum (fwhm) of the LaB6 standard. By this way the Caglioti equation gives the instrumental fwhm at any 2theta position, then you can extract these values to the measurements.

The cheap way is to fabricate a powder from a singlecrystalline silicon wafer and follow the same procedure described for the Caglioti equation. It is possible to introduce defects to the Si powder by a mechanical milling of the wafer, so you should cold it with liquid nitrogen before the milling.

Totally agree with Dr. Oğurtani and Dr. Fernández.

A cheaper way is to measure accurately a (111) Si wafer.

You can refine this pattern using a Rietveld software.

Before you run your analysis, try to calibrate your diffractometer on zero point. You must see a perfectly Gaussian peak on 1º 2theta.

Closed inspection of the spectral pattern presented by  Sutripo, and comparing with XRPD diffraction obtained from various amorphous substances in the literature gave me the impression  we are dealing with  amorphous vanadium thin layer exhibiting two distinct types of   short orders.

The most accepted modeling of amorphous solids is Para-crystalline modeling which treats the X-ray    amorphous sample as being a sum of up to  3 non interacting linear stacks.  The 'd' value of the para-crystalline model is often related to the height, width or length of the molecule. 

The very broad hump mostly appears  in connection with the sharp low 2theta lying peak if the sample exposed to fast quenching during the formation for the nano-size thin layers..

As Dr. Gomez mentioned this type of pattern  is analyzed by Rietveld method. But for me this method contains too many adjustable  parameters without having any plausible justifications.  Appearance of the high theta angle broad hump is some how correlated with thickness of the nano layer. It becomes more pronounce in the range 10 nm of less depending upon the substance itself. 

Thanks to all of u sir, for suggesting me to think form different perspectives.

In case you expect large grains (above 100nm)  then you have to use a standard like SRM660 or LaB6. The instrumental broadening plays a very important role whenyou expect large size grains. The FWHM of the peak from a used staandard, which is calculated from the Scherrer Equation would be the instrumental error of your system.

I suggest to use Whole Powder Patter Modeling (WPPM), it can directly extract the instrumental parameters (Cagloiti and Lorentz).

It also can calculate the broadening contribution from crysallite size, dislocations, faulting, APB, grain surface relaxation, stoichiometry fluctuation etc.

One thing with with SF and WH Plot is “average domain size” is NOT the average size of the (nano) particles and “microstrain” is a quite general term and does not identify the defect types.

I would recomend NOT to use a single crystalline wafer since you will find only  hhh reflections (and I don't know, how many). The best way from my opinion is to use LaB6 standard which gives reflections in nearly equidistant 2theta.

Another way is BGMN, a Rietveld code which calculates mathematically the peak shape without any assumption of profile functions or asymmetry etc. The input data are the dimensions of your diffractometer, and of course one needs some measurements which show that the   assumed dimensions of slits, soller, distances, wavelength distribution, tube focus dimension etc are correct. Even then wave length artifacts of the tube (like tube tails) can be considered. For critical phases also the absorption effect can be simulated. As far as i know no other software is doing this. The simulation for the expected diffraction profiles as function of 2theta takes a few (ten) minutes but then for the given conditions a non-affected profile description without any questionable assumptions (Pearson7, Pseudo-Voigt etc.) is ready to go. All other effects which ar not describable by the profiles at the respective 2theta are coming automatically from your sample. A straightforward and reliable solution. Without any really good standard it is not clear how big is the amount of still existing residual effects.

Sutripto Majumder Broadening of the XRD peak can be due to the instrument as well as due to the sample. Do calculate broadening caused by the sample (from which we calculate different parameters associated with the XRD of the sample, the instrumental broadening is to be subtracted first.

In this video, I have explained an instrumental broadening caused due to the X-ray source (i.e. due to the overlap of Kα1 and Kα2 peaks). In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks

https://youtu.be/238yM0OgaH8

Sutripto Majumder How to subtract instrumental broadening (βi) from XRD data using origin. I have used NIST LaB6 as a standard sample. In the case you want to further ask about it, please do comment on the specific video, I'll respond to it shortly. I have provided the practice as well as calculations files here. Thanks

https://youtu.be/tO_frVLxmsg