I have done powder XRD (not single crystal XRD) measurements for single crystal substrate of different samples. I can see the peak shift after irradiation process. How to calculate strain induced for single crystal ?
If you apply Bragg-Brentano geometry, i.e. PXRD on a single crystal, peak shifts can easily the result of a slight misorientation. in so far I wouldn't automatically conclude that the visible shift is related to the strain you can derive.
IF the shift is really from the strain, i.e. the normal of your diffracting surface is EXACTLY between primary and "diffracted beam" defined by your detector position (!) and not by an assumed reflection (what would be a very very accidental case!) you simply determine the peak shift as Delta d and your strain is defined by the misfit Delta d/d. But as i pointed out several times, i do not believe that you measure a reliable signal. You need to use a texture diffractometer to carefully adjust your diffracting lattice planes by rocking curves, and only then when you find the intensity maximum you can use 2theta rocking curves or even 2theta/theta standard coupling in order to determine the Bragg angle. I personally would prefer rocking curves.