Effect of dopant size on XRD peak shift If we add an impurity atom (doping) to the crystalline struture of another material and take the XRD of the doped material what kind of peak shift can we expect. For the better description of my question i have added an image below



In the image black bold line ($2\theta $) is the standard XRD peak of a material; blue ($2\theta ^{L}$) and green ($2\theta ^{R}$) dotted lines are the peak shift caused due to the doping of impurity atom. Can you tell me if there is any relationship between dopent size and peak shift (right/left dotted lines).
Doping, not to confuse with alloying, introduces a low amount of impurities or more generally point defects in a crystal. The overall periodicity of the system is thus not changed and no shift should be expected in XRD. However doping introduces some disorder that makes XRD peaks broader.