First-principles description of oxygen self-diffusion in rutile TiO₂: assessment of uncertainties due to enthalpy and entropy contributions

Abstract

Properties related to transport such as self-diffusion coefficients are relevant to fuel cells, electrolysis cells, and chemical/gas sensors. Prediction of self-diffusion coefficients from first-principles involves precise determination of both enthalpy and entropy contributions for point defect formation and migration. We use first-principles density functional theory to estimate the self-diffusion coefficient for neutral O0i and doubly ionized Oi2- interstitial oxygen in rutile TiO2 and compare the results to prior isotope diffusion experiments. In addition to formation and migration energy, detailed estimates of formation and migration entropy incorporating both vibrational and ionization components are included. Distinct migration pathways, both based on an interstitialcy mechanism, are identified for O0i and Oi2-. These result in self-diffusion coefficients that differ by several orders of magnitude, sufficient to resolve the charge state of the diffusing species to be Oi2- in experiment. The main sources of error when comparing computed parameters to those obtained from experiment are considered, demonstrating that uncertainties due to computed defect formation and migration entropies are comparable in magnitude to those due to computed defect formation and migration energies. Even so, the composite uncertainty seems to limit the accuracy of first-principles calculations to within a factor of ±103, demonstrating that direct connections between computation and experiment are now increasingly possible.

Kinetic Control of Oxygen Interstitial Interaction with TiO2(110) via the Surface Fermi Energy

“…Such statistical effects do not occur for a vacancy mechanism, or for an interstitial mechanism wherein the mobile species does not pair with a lattice atom. A previous first-principles study of ours determined D hop to be a factor of 150 above the reported microkinetic value for 18 O; , accounting for this statistical effect brings the two values into excellent agreement with each other.…”

“…First-principles DFT simulations were employed as detailed previously to yield reaction pathways and activation energies for elementary kinetic steps . Although DFT is beginning to yield reliable values for pre-exponential factors for solid-state diffusion, such computations were not performed here. The degree of confidence with which DFT rate constants may be compared to those from microkinetic analysis has been detailed elsewhere …”

“…Although DFT is beginning to yield reliable values for pre-exponential factors for solid-state diffusion, such computations were not performed here. The degree of confidence with which DFT rate constants may be compared to those from microkinetic analysis has been detailed elsewhere …”

“…The well-known O 2 overbinding issue in DFT-GGA was corrected according to the methods of ref in the DFT-computed total energy of O 2 . Implementation details for TiO 2 appear elsewhere …”

“…Such explicit synergy between DFT and microkinetic modeling has been attempted only recently in the case of O i in rutile TiO 2 near chemical equilibrium. That work focused only upon mesoscale diffusion or thermodynamics of the intermediate states of O i at or near the surface …”