The stress-strain calculations, energy density GI index calculations are also being done.
Well... when I was doing this sort of thing, we used a diffractometer with a primary-beam monochromator, so that we got rid of the Kα2 before it caused any problems. The other way I would have tackled it would be to fit suitable profiles to the diffraction peaks and take it from there.
One needs the hardware, the other needs software (ours was home-grown, written by my predecessor)
hth
David
Peak overlapping is not the only cause of peak broadening. Please consider also other effects like, for instance, incomplete charge collection in your detector. The peak shape has been extensively studied and there are many articles in literature. The detail to study the peak shape depends much on your detector intrinsic resolution. I can suggest two articles of mine and the citations inside: "Understanding the X-ray emission spectrum after excitation with a source of X-rays: From theory to experiment. DOI: 10.1016/j.radphyschem.2024.111648" and "A modeling tool for detector resolution and incomplete charge collection: A modeling tool for detector resolution. DOI: 10.1002/xrs.2597".