The FWHM values can be obtained by the X’PERT HIGHSCOE PLUS software to analyze the XRD patterns.

A right peak shift with respect to the incident or diffraction angle means smaller crystal size. If there is a decrease in FWHM with right shift, it would show that the crystal structure is more ordered at the higher angles. Lesser peak broadening could be related to the diffraction from lesser number of crystal planes that could be tilted / strained with respect to the expected plane at the specific 2-theta angle. This could be due to some characteristic of your material that reduces the crystal size and still makes it more ordered or uniform. It would be interesting to see that what property of your material or processing is causing the right peak shift with decrease in FWHM. Typically it makes more sense that the FWHM increases with right peak shifts due to the effect of strain on smaller crystal structures, but there could be other prospects in your case. You can check the correlation lengths using Sherrer equation (W-H method) to understand the crystal size and strain.

From the mathematical point of view, FWHM is NOT related to the value of mean, the peak position, but it is related to the standard deviation.

Dear Mohammed,

First of all, Temperature is the most crucial parameter in this case. As you said that there is a decrease in FWHM, meaning that there is a grain growth. Furthermore, shifting toward higher or lower 2 theta may related to the ionic size difference between Ga dopant and Zn cation of the host lattice. It's known that if the radius of the dopant smaller than the Zn, peaks will shift to higher 2 theta and vice versa. As stated by Dr. Imad, FWHM is not related to shifting of the peak position. In this case you have to consider the lattice strain. More shifting indicating a successful incorporation of the dopant into the host lattice without phase segregation. You will find that the d space will decrease as the doping concentration increase indicating a release of the strain in the lattice (grain growth).Taking the Bragg equation, n*lamda = 2d sin(theta), as the d space decrease, 2 theta will increase (shifting to higher 2 theta values). since there is a peak shift, it is valuable to estimate the dislocation density and staking fault probability or energy. There are many parameters that may associate with this nice field of study as stated by Mr. Vishal Saravade, such lattice defects, cation or anion vacancies, cation distribution in the octa and tetrahedral sites... etc. Rietveld method is the most reliable technique that may give you a meaningful results. Please do not forget to correct the instrumental broadening before profile fitting.

Good luck

P.S. Please check our these two articles for more detail information

DOI 10.1002/sia.6176

DOI 10.1080/10584587.2012.741905

Thank you Vishal Saravade, Imad Disher and Mohammed M. Obeid for your answers. I believe observed phenomenon wasnt a general rule but rather specific to the material properties involved. Thank you all for your valuable input.