Reconstruction and stability of Fe ₃O ₄ (001) surface: An investigation based on particle swarm optimization and machine learning

Magnetite nanoparticles show promising applications in drug delivery, catalysis, and spintronics. The surface of magnetite plays an important role in these applications. Therefore, it is critical to understand the surface structure of Fe ₃O ₄ at atomic scale. Here, using a combination of first-principles calculations, particle swarm optimization (PSO) method and machine learning, we investigate the possible reconstruction and stability of Fe ₃O ₄(001) surface. The results show that besides the subsurface cation vacancy (SCV) reconstruction, an A layer with Fe vacancy (A-layer-V _Fe) reconstruction of the (001) surface also shows very low surface energy especially at oxygen poor condition. Molecular dynamics simulation based on the iron–oxygen interaction potential function fitted by machine learning further confirms the thermodynamic stability of the A-layer-V _Fe reconstruction. Our results are also instructive for the study of surface reconstruction of other metal oxides.