Vacancies and Vacancy-Mediated Self Diffusion in Cr₂O₃: A First-Principles Study

Abstract

Charged and neutral vacancies and vacancy-mediated self-diffusion in α-Cr 2 O 3 were investigated using firstprinciples density functional theory (DFT) and periodic supercell formalism. The vacancy formation energies of charged defects were calculated using the electrostatic finite-size corrections to account for electrostatic interactions between supercells and the corrections for the bandgap underestimation in DFT. Calculations predict that neutral oxygen (O) vacancies are predominant in chromium (Cr)-rich conditions and Cr vacancies with −2 charge state are the dominant defects in O-rich conditions. The charge-transition levels of both O and Cr vacancies are deep within the bandgap, indicating the stability of these defects. Transport calculations indicate that vacancy-mediated diffusion along the basal plane has lower energy barriers for both O and Cr ions. The most favorable vacancy-mediated self-diffusion processes corresponds to the diffusion of Cr ion in Cr 3+ charge state and O ion in O 2− state, respectively. Our calculations reveal that Cr triple defects composed of Cr in octahedral interstitial sites with two adjacent Cr vacancies along the c axis have a lower formation energy compared with that of charged Cr vacancies. The formation of such triple defects facilitates Cr self-diffusion along the c axis.

First-Principles Investigation of Native Interstitial Diffusion in Cr2O3

“…The computed bandgap in these figures is 2.8 eV [18]. The plots reveal that the energy states corresponding to both Cr and O interstitials are located in the bandgap, and are of hybrid O-p and Cr-d character, which is similar to the nature of the vacancy states [18]. The defect levels of the neutral Cr interstitial, which are located in both the lower and upper parts of the bandgap, are occupied with electrons and the Fermi level is closer to the conduction band.…”

“…Compared to Cr vacancies, which have the lowest diffusion barrier energies of 2.01 eV (V −3 Cr along basal plane) [18], Cr interstitials have even lower barrier energies of 1.86 eV (Cr 1 i along [221]). The 0.15 eV lower barrier implies that Cr interstitials are more mobile than Cr vacancies by two orders of magnitude at room temperature.…”

PyCDT: A Python toolkit for modeling point defects in semiconductors and insulators

“…The mixing scheme was shown to give formation energies that are consistent with experimental data with a mean absolute relative error of under 2%. The resulting correction term to the chemical potentials was found to be important in several defect studies [47,48].…”

Temperature Dependence of Self-Diffusion in Cr2O3 from First Principles

“…For bandgap fitting, we used a fixed cell size that was optimized with PBEsol+U approach in our previous studies. [23,28] The bandgaps obtained with different screening parameters are listed in Table 1. The results indicate that calculations with the screening parameter of 0.6 provide the best match between the computed and experimental bandgap.…”

“…The resulting phase diagram (given in SI Figure S1 Defect calculations were performed using a 2×2×1 supercell containing vacancies and interstitials and generated from the optimized primitive cell. In addition to vacancies and interstitials, Cr vacancy triple defect (or split-vacancy) identified in our earlier work [23] was also considered. The ionic positions in the defect supercells were optimized under fixed volume and shape conditions.…”