I observed two high intensity diffraction peaks at 19.36º and 23.72º in pure PEO, but on addition of Li salt the peaks shifted to lower 2 theta values (18.8º and 23º). Can anybody tell me the exact reason?
Lower 2theta means larger lattice parameters. This probably means that Li salt was incorporated into the PEO structure and some kind of PEO/salt complex is formed in your system. There is a number of articles concerning this type of structures, try to search for your own composition.
This usually happens when d-spacing between two atomic layers is increased (Bragg's law) which results in larger unit cell volume. This is because when larger sized ion is replaced with the smaller one in the crystalline material to be investigated.
Usually the shift in 2-theta value towards towards lower angle in case of PEO/Li-salt complexes is related to the formation of salt-polymer complex with increased d-spacing. But, as suggested by Missyul, you should refer the relevant article to draw a conclusion. Because it may also occur due to presence of solvent/ plasticizers or some other additive as the case may be.