Is the Brus Equation Correct?

Short Communication

Metal oxides were widely used in the domains of materials, physics, and chemistry and have been extensively used in catalysts, fuel cells, piezoelectric materials, sensor materials, and optical components. Among various metal oxides, CeO2 is one of the extensively applied and discussed. It has a face-centered cubic structure with a high melting point (2400-2700 ℃) and possesses remarkable properties such as the number of effective redox Ce3+/Ce4+ sites and their ability to exchange oxygen [1]. Therefore, it has good optical properties, thermal stability and electrical conductivity, and oxygen storage function [2,3]. For instance, the optical property of UV-vis spectroscopy for the CeO2 nanoparticles exhibits a blue shift with respect to the bulk material due to quantum confinement, which have two limiting case, depending on the ratio of the crystallite radius to the effective Bohr radius of the electron-hole pair [4].

Therefore, the crystal size and energy gap measurements were significant in applications. Thus, a discussion of crystal size with energy gap was required. The relationship between crystal size and energy gap can be described by the Brus Equation [5]. In addition, a modified Brus equation was proposed by Ferreira et al. [4], where the modified values were smaller than that obtained from the Brus equation. In order to conduct comparisons between the Brus equation, several reported data in the literature were collected.

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