When we tried to take powder XRD for a reported material why we observe the peaks are either left or right shifted when compared to the PDF5+ database?
one of the reasons of small peak shifts (either left or right) is the incorrect height adjustment of the sample surface with respect to the center of the gonimeter circle.
You may have a look at the following link for estimations of such peak shifts:
Presentation XRD and XRR angular shifts due to sample height variations
I would suggest to check the whole mechanical alignment of your diffractometer and compare with measurements of the exact same samples (to exclude effects of contamination) at the same temperature (presumably room temperature?) on a well calibrated diffractometer.
The typical instrumental errors could be zero error (a constant shift is verified on all the peaks, at left or right) or displacement error (a shift with an angular dependence). Peaks could be also shifted due to differences in the lattice parameters with respect to the values reported in the database
The stress that was developed during preparation process is one reason for xrd peak shift. The change in lattice parameters when particle size reduces to nano causes stress/strain.