The shifting of XRD diffraction is because of the lattice parameters as well exchange in cell parameters. If your material is cubic, you only change a parameter, but if your sample is triclinic you need to adjust a, or, b parameters. Cell parameters can change because of the impurities, preparation method, doping, calcined temperature, etc. In your case, the factor is doping or impurities diffusing crystal growth and alignment of the predominant plane as well as the lattice parameters, and the diffraction might be shifted. For preferred orientation, it might be the rightward shift as well.
If the compositions and other synthesis process are the same, the possible reason for the shift in the XRD peaks are the solubility of the materials with the increase of sintering temperatures and the rate of ionic diffusion in the matrix of the material.
The shifting of XRD peaks with changes in sintering temperature is primarily due to alterations in the material's lattice parameters, which can occur due to thermal expansion, phase transitions, or changes in defect concentrations like vacancies and interstitials. Additionally, sintering can introduce or relieve residual stresses, affect grain growth, and cause compositional changes or diffusion of elements, all of which can modify the crystal structure and result in the observed peak shifts.
The XRD diffraction shift is due to changes in lattice parameters, which can be affected by factors like impurities, preparation method, doping, and temperature. Doping or impurities likely caused the shift, affecting crystal growth and alignment. This can result in a rightward shift in diffraction, especially if there's preferred orientation.