Dear Bhaskar sir,

please refer the following paper

http://www.ias.ac.in/article/fulltext/boms/039/06/1381-1387

It is well reported that, with decrease in size of crystal, the value of bandgap increases as an effect of quantum confine-ment. In case of CeO2, the presence of significant  fraction of Ce atoms (in either 3+ or 4+state) on the external surface leads to oxygen vacancies and defects, whose influ-ence on the bandgap overcomes the expected influence of regular quantum size effect.

In the above paper we have given detailed answer.

Hope that it is helpful for your work.

With warm and Best Wishes

Suhail A A R Sayyed

Dear Suhail,

Thank you for your answer. But I think you misinterpreted the question. In the present system Gd has been doped till 20 wt%, which creates oxygen vacany in CeO2. As a result, Ce4+ is converted to Ce3+ to maintain the charge neutrality.

In this case when Ce3+ and oxygen vacancy is increased, there should be decrease in band gap with increase in dopant concentration, which is opposite to present observation. 

it is interesting.

Dear Bhasker 

Thank you so much to interested answer and explanation of Dear Suhail , just i have the observe about the crystal size which no more chang which that indicated may be the doped  of Ga not into the unit cell matrix of CeO2 or may be on surface of CeO2. Therefore  the band gap not interact with the Ce in matrix cell to transfer of oxygen.

plz mak sure that doping inside the CeO2 stricture by XRD or TEM.

i hope can help you  as we sharing our acknowledge 

with best regards