the wide range of band gap energy with value of 3.85 to 3.45 eV for NiO nanoparticle it seems to me already explained in the attached paper, which I had already read, for other reasons, on RG.
As the authors state, this effect was achieved by increasing the processing temperature from room temperature (RT) to 75 °C. In this way, the specific surface area of nanoproducts is decreased. It could be explained in term of increasing the growth rate of particles with processing temperature which leads to the increase of particle size and subsequently a decrease in specific surface area of particles.
The increasing trends of the band gap energy upon the decreasing particles size is likely due to the defects or vacancies present in the intergranular regions generating new energy level to reduce the band gap energy (Ref.23).
the wide range of band gap energy with value of 3.85 to 3.45 eV for NiO nanoparticle it seems to me already explained in the attached paper, which I had already read, for other reasons, on RG.
As the authors state, this effect was achieved by increasing the processing temperature from room temperature (RT) to 75 °C. In this way, the specific surface area of nanoproducts is decreased. It could be explained in term of increasing the growth rate of particles with processing temperature which leads to the increase of particle size and subsequently a decrease in specific surface area of particles.
The increasing trends of the band gap energy upon the decreasing particles size is likely due to the defects or vacancies present in the intergranular regions generating new energy level to reduce the band gap energy (Ref.23).
As the size of semiconductor nanoparticles, such NiOx but also other oxides, decreases, from tens of nm downword, the GAP usually increases due to "quantum confinement" mechanism. The extent of Gap increase can be estimated by UV-Vis spectroscopy and analysis of the low-L absorption edge (for example by Tauc metgod). What is frequently observed is that , parallel to a GAP decrease, the pre-edge background an the same edge slope increase (Urbach tail) due to an increased defect concentration as the particle size is reduced.
I suggest you to search for the quantum confinement in nanostructures also from a theoretical viewpoint to better understand how it occurs.