if the only effect observed is a shift of ALL the Bragg peaks to higher values of the diffraction angle, this means that the lattice parameter is decreasing. Several reason are possible: elimination of defects, structural relaxation , enhanced crystallization, etc., but the net result on the part of lattice constant is a definite decrease. also the reason of shifting of peak to higher value  is : due to compressive residual stress developed in the material.

also As you can read in any textbook on XRD (for example, D.B. Cullity), among the most frequent cases, peak shift can be caused by strain or by changes in chemical composition. In case of strain resulting from a planar stress - very likely in a thin layer - peaks in a typical theta-2theta scansion will be shifted to lower angle for compressive stress and to higher angle for tensile stress. Change in stoichometry can produce similar effects .

also in supported catalysts the support is impregnated by active phase and then the catalyst will be calcined in order to remove impurities. It is desired that active phase cover the surface of the support.

I found a peak shifting in XRD when the active phase penetrated into pore of the support.

among the most frequent cases, peak shift can be caused by strain or by changes in chemical composition...larger angle could suggest tensile stress...is worth to check the composition,as any change in stoichometry could produce similar effects...sometimes error occurs due to sample preparations or zero error-sample is not in the calibrated position...

Dear Collegue,

A shift of 3 degree is to large to be atributed to stress or strain. Also, 500 C for two hours is too high and too long. I suggests an examination of your sample to check stoichiometry.

For curiosity, can you load the diffraction pattern before and after the thermal anneal?

Best regards,

Pedro

Thank you Dr Ewa and Dr.Pedro for the suggestions.