Density-functional theory calculations were performed to investigate the adsorption of oxygen on 3C-SiC(111) and $(\overline{1}\overline{1}\overline{1})$ surfaces, including single O atom, double O atoms, and variable oxygen coverage adsorptions. We find that the bridge (BR) and on-top (OT) sites are the most stable adsorption sites for the (111) and $(\overline{1}\overline{1}\overline{1})$ surfaces, respectively. According to the two-dimensional potential energy surface achieved, the lowest continuous oxygen diffusion path over the whole surface seems to be $\text{BR}\ensuremath{\rightarrow}\text{H}3\ensuremath{\rightarrow}\text{BR}\ensuremath{\rightarrow}\text{BR}(\text{neighbor})\ensuremath{\rightarrow}\text{etc}\text{.}$ By studying the double O atoms adsorption on 3C-SiC(111) surface, we find that 2-BR is the most favorable configuration. By comparing adsorption energies and O-O distances with reference values, we get that there is an electronic induction effect, which helps to get a more stable adsorption structure, between neighboring O adatoms with small amount of negative charge, which favors a medium O-O distance. Spin-unrestricted first-principles molecular-dynamics calculations have been carried out to achieve more dynamic information and comprehensive understanding of the molecular oxygen adsorption on a 3C-SiC(111) surface. The results confirm our determined diffusion path and one of the preferred double atoms configuration. By studying the adsorption of oxygen at 3C-SiC(111) and $(\overline{1}\overline{1}\overline{1})$ surfaces as a function of oxygen coverage, we find that the adsorption energy initially increases [1/9--3/9 monolayer (ML)] then significantly decreases (3/9--6/9 ML) with increasing oxygen coverage and finally reaches a stable value (7/9--1.0 ML) for 3C-SiC(111) surface. For $3\text{C-SiC}(\overline{1}\overline{1}\overline{1})$ surface, the trend is similar to the (111) surface case; however the variation is small when the oxygen coverage is above 3/9 ML and the adsorption energy at 1/9 ML coverage is lower. By combining the results of adsorption energy, structure evolution, and electronic-density difference calculations, we get that the total adsorption energy is determined by the interaction between adatoms and surface reconstructions: attractive (respectively, repulsive) interactions between adatoms make the adsorption structure more (respectively, less) stable, i.e., it gets a larger (respectively, smaller) adsorption energy; however, surface reconstructions can eliminate the stress caused by repulsive interactions between adatoms and make the adsorption structure to be stable.
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