Why is XRD Peaks Shift due to Doping

How is the XRD peak shift due to doping?
Doping - Introduction of impurities into a crystal lattice can cause to expand or contract the host lattice volume - changes lattice parameters or produce strain within the material - leads to a significant shift in the XRD peaks. Due to doping, changes in crystal structure, change the lattice parameters, or strain within the material. Here are the main ways doping can cause XRD peak shifts
1- Expansion & contraction of the unit cell due to substitutional doping: Expansion means increasing the lattice parameters (d-value increasing), causes XRD peaks to shift to lower 2θ, while contraction means decreasing the lattice parameters (d-value decreasing) cause peaks to shift to higher 2θ. This doping changes the lattice parameters but does NOT change the crystal structure.
2- Expansion & contraction of the unit cell due to substitutional doping: Whereas the interstitial doping causes the same expansion (large d-value) and contraction (small d-value), therefore causing the XRD peak to shift lower 2θ and higher 2θ, respectively. This doping not only changes the lattice parameters BUT also the CRYSTAL STRUCTURE!
3- Doping can cause strain effects i.e., tensile strain- expands the lattice (larger d-value), shifting peaks to lower 2θ while the compressive strain- contracts the lattice (smaller d-value), shifting peaks to higher 2θ.
4- Formation of secondary phases (maybe new peaks)- If the concentration of doping is too high, new peaks may appear in the XRD pattern. For example , Al doped ZnO can result in the formation of Al2O3.
The doping mechanism increases or decreases the lattice parameters (a, b, c, and d). This is mainly due to the size of the dopant ion/atom than the host. A bigger dopant ion/atom produces an increase in the unit cell volume, while the smaller one results in a decrease in the unit cell volume. This expansion or contraction of the unit cell volume (lattice parameters, a, b, c, and d) is reflected in the XRD using Bragg's formula. The expansion of the unit cell ( increasing in d value) keeps the Bragg’s angle lower because of a peak shift to the left in the XRD graph. Similarly, a contraction of the unit cell (decreasing the d-value) makes the Bragg’s angle increase as a result a peak shift to the right in the XRD graph.