Oxygen vacancy concentration in nanoobjects of CeO2−δ: Effects of characteristic size, morphology, and temperature

Abstract

A theoretical model has been developed that adequately describes the formation of oxygen vacancies in ceria at the nanoscale. The intrinsic regime of vacancy formation under equilibrium conditions is considered. An analytical relation describing the dependence of the enthalpy of oxygen vacancy formation on the characteristic size and morphology of nanoobjects is derived. This made it possible to perform quantitative calculations of the concentration of oxygen vacancies in cerium oxide nanoobjects for a wide range of their characteristic sizes, morphology and temperature. It is shown that the size effect becomes noticeable for the concentration of surface and bulk oxygen vacancies, approximately, at the characteristic sizes of nanoobjects less than 20 nm and 30 nm, respectively. The effect of morphology on the concentration of oxygen vacancies increases with a decrease in the characteristic size of nanoobjects. This effect is more significant for the concentration of bulk oxygen vacancies than for the concentration of surface oxygen vacancies. In addition, the morphological effect and the size-effect decrease with increasing temperature. In thin films of ceria, the concentration of bulk oxygen vacancies at 300 K is 1011 and 103 times lower than that of spherical ceria nanoparticles, with their characteristic size of 4 nm and 40 nm, respectively. At 1000 K, this ratio is 3∙103 and 7, respectively. Thus, the oxygen storage capacity is higher for spherical nanoparticles and increases with a decrease in their characteristic size.