Structural, magnetic, electronic, defect, and diffusion properties of Cr₂O₃: A DFT+ U study

The structural, electronic, and magnetic properties for nondefective and defective structures and the diffusion of both cations and anions in chromium oxide (α-Cr₂O₃) are investigated theoretically with the periodic quantum-chemical method. Three different point defects are studied, namely, Cr vacancy, Cr Frenkel defect (composed of an interstitial Cr atom and a Cr vacancy), and O vacancy. All these defects affect the electronic properties of Cr₂O₃ drastically and are involved in diffusion processes in passive film growth. The calculated defect formation energy shows that the stability of defects falls in the following order: Cr Frenkel defect (E_Fr(Cr) = 2.36 eV) > Cr vacancy (E_V(Cr) = 4.84 eV) > O vacancy (E_V(O) = 5.12 eV). Relaxation occurs only on the first and the second nearest neighbors in each case. Each defect adds an extra localized level inside the band gap. Cr Frenkel defects add donor levels composed of O states; Cr vacancy defects add acceptor levels composed of states from both Cr and O atoms; and O vacancies do not give any level in the gap. Defects influence the magnetic moments on surrounding atoms, especially on the first nearest neighbors. Various diffusion processes of both cations and anions are investigated by calculating the Cr³⁺ and O^2- diffusion among various sites using the climbing-image nudged-elastic-band (cNEB) approach. The activation energy E_D (2.57-3.21 eV) obtained for the diffusion of Cr³⁺ is in good agreement with the experimental E _D (2.46 eV). The calculated E_D for O^2- ranges from 2.21 to 3.65 eV, which is in agreement with experimental data. For each investigated diffusion pathway, frequencies calculated by finite difference methods are used to obtain jump frequencies using transition state theory (TST). Combining the pre-exponential factors with activation energies, the diffusion coefficients are calculated which are compared with experimental values.