Non-monotonic lattice parameters variation with crystal size in nanocrystalline CeO₂

In the present paper we report proof of consistent non monotonic lattice variation (NMLV) as a function of grain size in nanocrystalline CeO2. By analyzing more than 30 powder samples of CeO2 with grain size ranging from 5 to 200 nm which were synthesized by three different methods, it was found that in the nanocrystalline powders the unit cell parameters are smoothly varying along the decreasing of grain size with moderate contraction between 100 to 30 nm and severe expansion when the grain size become smaller than 20 nm. As a result of these two opposite trends a minimum value of unit cell parameter was detected in grain size between 25 to 50 nm. The lattice parameter change can be modeled as two global effects acting simultaneously. The first one is a contraction due to surface tension and the second one is a lattice expansion caused by ionic bonds weakening as the grain size decreases. This model can be applied to most ionic nanocrystalline materials. Consequently, it is recommended to add a new category "ambient-nano"in the crystallographic and diffraction data bases for nanomaterials with structures controlled by grain size.