It depends, if you talk about oxide or sulfide or what kind or system. Then what is environment during annealing, and if you are starting with bulk material of precursor or nanoparticles! Effectively difficult to generalize.
As correctly mentioned , it suits more to film , possibly. If you are dealing with free standing nanopartilce powder, you can expect the growth of nanoparticle and increase and crystallinity, both will favour the material to attain bulk band gap.