The weight fraction of each phase present in the X-ray diffraction pattern can be calculated if the calibration constant is known or, as mentioned in the post below, the phase fraction can be estimated using the internal standard method.

https://www.researchgate.net/post/How-to-determine-phase-fraction-from-XRD-pattern

Obviously, the intensity and shape of a peak depends on several factors: the types and relative concentrations of the atoms that occupy the plane that generates the peak for example, but it is more complicated to determine the weight fraction of an element by analyzing the peak.

Dear Osama Ibrahim, XRD pattern is not simple as peak fitting. The information of the structure or atom inside the crystal is in the intensity, not the broadening, though the data were fitted with the profile function (i.e. Voigt, pseudo-Voigt, Pearson-VII etc). Not yet taking into account the systematic error (instrument and or sample).

The structure factor quantifies the amplitude of X-rays scattered by a crystal, where the amplitude is determined by the position of the atom on the hkl planes (atomic coordinates), what atoms are on that plane (atomic scattering factor), an atomic vibration about its equilibrium (temperature factor) and occupancy.

The correct way to get the accurate quantitative result is using Rietveld refinement software such as GSAS, MAUD, Profex-BGMN, Rietan-FP, Fullprof, Powder Cell, JANA2006, Rietica, Z-Rietveld, etc. Or if you have access to commercial software such as TOPAS, High Score Plus, PDXL, XRDanalysis, Siroquant, etc

Thanks for your answers.

As I am working on solid solution alloy, both of Bragg's law and Vegard's law are likely significant to estimate the potential phase compositions for those fitted XRD peaks. However, we should be careful to avoid any deviation in lattice constant measurements. This could be due to either systematic errors or errors in the process of deconvolution by Gaussian.

Many thanks all for your interesting ideas.