Welcome to the world of X-ray diffraction or more generally diffraction and scattering, be it X-ray, neutron or electron. Of course X-ray diffraction is the most common tool. To understand X-ray diffraction it is necessary to have some idea of the structure of matter in general or crystallography for crystalline matter. For that just take a simple book on X-ray crystallography, e.g. D.E. Sands, Introduction to Crystallography, Dover (1993).

1. If you wish to do X-ray diffraction as a function of the sample position you need to have fine focussed X-ray beam. X-ray beam in the laboratory is of the order of aboui a mm in size. That is not great for your purpose. I shall advise you to contact an instrument scientist of a synchrotron laboratory. There are plenty of such laboratories in the world, e.g. ESRF in Grenoble. With synchrotron X-rays you can do diffraction on your sample easily with micron size resolution or even better. It is difficult to do this at the home laboratory.

2. If you have a cubic sample then you know what are the reflections you expect. For example for fcc structure you only expect either all even hkl or all odd hkl. Now you know that you will have reflections like 111, 200 etc. but not 100 or 110. You should gradually increase the integers in hkl but keeping them either odd or even. Now calculate their d values by the formula you already know and arrange them in decreasing order of d. In angle dispersive X-ray diffraction you will observe them as a function of increasing Bragg angle following Bragg's equation.

3. You can use Scherrer formula at the begining to calculate the crystallite size but you have to bother about instrumental resolution and also sample broadening due to strain and other defects. For that there is a huge literature (read B.E. Warren, X-ray diffraction for example) and you should also consult the discussions already existing in RG.

Now if you do not understand anything I have written above then please come back to me. It would be my pleasure to explain you further. But read you must first text books.

@Tapan Chatterji

thank for your answer,

for the question 2, how can we know the structure of sample ( say, fcc or bcc...) ?. Is it indicated from the diffraction graph ?

for the question 3, If I do want to know the effect of strain and instrumental, How can I estimate these effect?

X-ray diffraction can give information about the crystal structure. If you do powder X-ray diffraction then you will observe diffraction peaks at different Bragg angles. You must first index their hkl values by comparing the calculated and observed d values. For cubic samples this is very straight forward. After you have indexed the observed peaks you should check the extinction rules that can be derived from the structure factor equations. It can be shown that the fcc structure must have only all odd or all even Miller indices. For bcc structure the extinction rule is h+k+l = 2n (even). And if the structure is primitive then there is no extinction. This means all hkl indices are possible. Now do some home work. Get a copy of the book by Warren (X-ray diffraction, B.E. Warren, Addison-Wesley (1969)) and read carefully the section 5.3: Analysis of a cubic powder pattern by diffractometer recording, p. 57. Any other book on X-ray diffraction will also do. You can for example consult "Elements of X-ray diffraction", B.D. Cullity, Eddison-Wesley (1978).

A very good place to get a decent knowledge on the fundamentals of diffraction analysis is the course material of the Advanced Certificate in Powder Diffraction of the Birkbeck College, University of London. In your case the indexing and peak shape sections should contain answers to all your questions. I include a link to the site, though I do not know if ResearchGate will strip it from this post:

http://pd.chem.ucl.ac.uk/pdnn/pdindex.htm