Factors controlling surface oxygen exchange in oxides

Reducing the working temperature of solid oxide fuel cells is critical to their increased commercialization but is inhibited by the slow oxygen exchange kinetics at the cathode, which limits the overall rate of the oxygen reduction reaction. We use ab initio methods to develop a quantitative elementary reaction model of oxygen exchange in a representative cathode material, La0.5Sr0.5CoO3−δ, and predict that under operating conditions the rate-limiting step for oxygen incorporation from O2 gas on the stable, (001)-SrO surface is lateral (surface) diffusion of O-adatoms and oxygen surface vacancies. We predict that a high vacancy concentration on the metastable CoO2 termination enables a vacancy-assisted O2 dissociation that is 102–103 times faster than the rate limiting step on the Sr-rich (La,Sr)O termination. This result implies that dramatically enhanced oxygen exchange performance could potentially be obtained by suppressing the (La,Sr)O termination and stabilizing highly active CoO2 termination.

example of a slow mechanism (A39) are listed in Supplementary Table 3 and their energy   48 landscape is depicted in Figure 4 in the main text.    Step 3 *O2(Srbr)+ sAO (near) Step 4 Step   is adsorbed, and type of site the adsorbed molecule dissociates. Symbols `-', (C,M) and (C,I) are defined in "Methods" section in the main text. All 12 mechanisms that are studied are indicated and also described in detail in Supplementary Table 6, Supplementary Table 7.

Adsorbs at
Dissociates on Step Step  Fig. 3 in main text § Vibrational energies of adsorbed species (*O2 or *O) and O2 gas molecule are included, translational modes of O2 gas are not included. Configurational entropy is not included. Site fractions are calculated by using the scheme given in "Methods" Section and by constructing equations similar to equation (11) in main text.

Supplementary
zero-temperature DFT+U energetics. Our approximation in the treatment of vibrational free energy is that we assume the vibrational free energy of the solid phase atoms that are not involved in the reaction do not change significantly during the reaction 9,10 . For an adsorption reaction, Agas + * → *A, the ΔG * for adsorption step (= ), is described as where , , are the 0K energy of DFT supercell with adsorbed species is calculated using cNEB methods embedded in VASP 11,12 . Appropriate DFT corrections were applied in "Methods" section in the main text.

Example of rate calculation
At SOFC conditions of 650°C, 0.2 atm pO2, rates (R0, #O2/Co-site/second) of individual steps of Mech.B3 in order-of-magnitude approximation are as follows, Step 1 This step is O2 adsorption on Co near a surface vacancy and then insertion into a nearby vacancy. This step is barrierless and requires a fixed O-O orientation for insertion. where O2 adsorbs on a Co that is distant from a vacancy, and then diffuses towards a vacancy. Since the concentration of such species (CoO2+2s(far)) is predicted to be small (see Figure 3 in the main text and Table 1 in the main text for details), this path is not likely to be fast enough.
Step 2 This step involves diffusion of *O (from sO2) towards a second surface vacancy  we also get surface diffusion path much faster than the path where the bulk oxygen vacancy diffuses to the surface *O.
Step 3: This step involves the incorporation of species *O (species CoO+s(near)) into the nearby surface vacancy, with a 0.4eV barrier. The expression for R0 is: .
Thus the R0 for bulk diffusion is faster than the rate-limiting step of oxygen adsorption (step 1 above).

Error estimation for DFT energetics
In this section we discuss the various sources of error and the extent to which they may affect the predicted results.
where dif in this work, including that of the AO rate limiting reaction, could readily have an error bar as large as ±1.4 log units. This error bar is perhaps somewhat larger than, but similar to, the uncertainty in the experimentally-measured exchange rate. Jacob's et. al. 16 summarized the spreads in experimental k* values and found 0.91 to 1.63 mean squared errors in log units. Furthermore, we see a spread of 1 to 1.5 log units in the measurements of k* for La0.5Sr0.5CoO3 (see Figure 8 in the main text). While these are large errors, one of our key results, which is that the R0 for the CoO2 surface is 2-3 orders of magnitude larger than for the SrO surface (refer to Figure 8 in the main text), is at least somewhat larger than these uncertainties. Furthermore, we expect that errors in different reaction rates are likely to be correlated, and therefore relative values, like rates on two different surfaces, will likely have significantly smaller errors than any given rate. Thus, even with the error bars on the DFT predicted reaction rates, we still expect the SrO surface termination to offer slower ORR compared to the CoO2 termination.