Yuri A.
Mastrikov
ac,
Rotraut
Merkle
*b,
Eugene A.
Kotomin
ab,
Maija M.
Kuklja
c and
Joachim
Maier
b
aInstitute of Solid State Physics, University of Latvia, Riga, Latvia
bMax Planck Institute for Solid State Research, Stuttgart, Germany. E-mail: r.merkle@fkf.mpg.de
cMaterials Science and Engineering Department, University of Maryland, College Park, Maryland, USA
First published on 18th May 2018
The results of first principles calculations of oxygen vacancy and oxygen adsorbate concentrations are analyzed and compared for the polar (La,Sr)O and MnO2 (001) terminations of (La,Sr)MnO3 fuel cell cathode materials. Both quantities strongly depend on the average Mn oxidation state (La/Sr ratio). In thin symmetrical slabs, the cation nonstoichiometry also plays an important role by modifying the average Mn oxidation state. The surface oxygen vacancy concentration for the (La,Sr)O termination is more than 5 orders of magnitude smaller when compared to the MnO2 termination. The vacancy and adsorbed oxygen migration energies as well as the dissociation barriers of adsorbed molecular oxygen species are determined. The encounter of adsorbed atomic oxygen and surface oxygen vacancy is identified as the rate determining step of the oxygen incorporation reaction. Since the increase of atomic and molecular oxygen adsorbate concentration is limited by the typical saturation level in the range of 20% for charged adsorbates, the overall oxygen incorporation rate is predicted to be significantly smaller for the (La,Sr)O termination.
For undoped LaMnO3−δ (LM), the MnO2 (001) termination was calculated to be the most stable termination;5 however, with increasing Sr doping the (La,Sr)O termination is predicted to become energetically more favorable.6 Also, for a given average cation composition, it is frequently found that the surface exhibits a higher Sr content and/or an increased ratio of A-site to B-site cations either already introduced during film preparation by pulsed laser deposition7 or upon annealing.8–10 Segregation effects are also supported by theoretical calculations.6 Similar trends of A-cations and, in particular, Sr surface segregation were also found for perovskite La1−xSrxCo1−yFeyO3−δ (LSCF, see e.g.ref. 11–13) solid solutions, emphasizing the importance of better understanding of defect formation and oxygen reduction kinetics on the AO-type termination.
When comparing the different (001) terminations of LSM, the fact that these terminations represent polar surfaces has to be properly taken into account. The formation of polar terminations is rather frequent for oxides. The physics and chemistry of a broad class of oxide polar surfaces are summarized, for instance, in review articles.14,15 The pure polar terminations of a macroscopic sample are electrostatically unstable and must reconstruct to avoid the “polar catastrophe” due to a huge dipole moment. This could be achieved in several ways. In this paper, we assume that the LSM (001) surface polarity is negated by surface rumpling and the electron density redistribution near the surface. There are also other options to compensate for surface dipole moments, such as surface oxygen vacancy formation,16 structural changes through the formation of extended structural defects such as steps and trenches,17 or structural reconstruction through a complete rearrangement of the terminating planes into an ordered pattern of AO and BO2 stripes.18 However, a comprehensive study of these options, which strongly depend on particular experimental conditions, extends far beyond the goals of this article.
In the present paper, we analyze the oxygen vacancy formation, oxygen (both atomic and molecular) adsorption and dissociation on LSM (001) (La,Sr)O- and (001) MnO2-terminated surfaces (also comparing with previous results for (001) MnO2 (ref. 5,19,20)). To some extent, the nominal polarity of (LaO)+ and (MnO2)− layers may be decreased by surface rumpling and also by the electron density redistribution near the surface (see the discussion in Section 3.1). Nevertheless, the remaining polarity strongly modifies the defect formation and adsorption energies, and thus strongly influences the oxygen exchange surface reaction kinetics. It might also act as a driving force for surface reconstruction at elevated temperatures. Despite the importance of this phenomenon – also for related (Ba,Sr,La)(Fe,Co,Mn)O3 perovskites – it has rarely been systematically investigated. Also, the commonly neglected effect of different Mn oxidation states in slabs with different cation stoichiometry has to be taken into account. Based on our results, a semi-quantitative comparison of the oxygen reduction kinetics on LSM (001) MnO2 and on (La,Sr)O termination layers is given. The focus of the present investigation is on the relative differences between the (001) (La,Sr)O and (001) MnO2 terminations, rather than on absolute reaction rates or absolute values of defect energetics.
Moreover, it was shown that for the experimental orthorhombic geometry, such an approach correctly reproduces the A-type anti-ferromagnetic (AAF) structure of LM experimentally observed at low temperatures26,32 and the basic defect properties of many ABO3 perovskites and their solid solutions.3,5,33–37 The kinetic energy cut-off is set to 520 eV. Brillouin zone sampling is performed by the Monkhorst–Pack scheme38 with 30 and 20 k-points Å−1 for the bulk and the surface calculations, respectively.
Depending on the temperature and degree of (non)stoichiometry, three types of structural distortions have been observed in La1−tMnO3−δ, one rhombohedral Rc and two orthorhombic Pnma.39,40 These distortions could be a combination of the octahedral tilting, rotation and Jahn–Teller octahedral deformation.41 Energetically, the difference between rhombohedral and orthorhombic phases in the LM bulk does not exceed 0.05 eV per ABO3 formula unit. Experimentally, the orthorhombic phase of LM can easily be converted into the rhombohedral one by annealing in N2 at 600 °C,42 indicating that both structures are very close in energy, whereas the ideal cubic perovskite is considerably (by ∼0.3 eV) less favorable. Therefore, it is essential to introduce a lattice distortion into the modeling. The spin-polarization of B cations also strongly affects the energy of the structure. Diamagnetic solutions are considerably (by ≈1 eV) less favorable than magnetic solutions whereas the energies of FM and all high-symmetry A-, C-, GAF states lie close together, within 0.1 eV per formula unit. The choice of the exact magnetic structure is not expected to significantly affect the results, as long as it is consistent for all calculations (at cathode operating temperatures, LSM anyway loses its magnetic order and becomes paramagnetic).
In our slab calculations, we employed the ferromagnetic state (Mn in a high spin state) with a rhombohedral structure, which is lowest in energy. In this structure, the oxygen octahedra rotate alternately in all three main directions, whereas in the orthorhombic structure along the direction normal to the basal plane all octahedra rotate in the same direction (Fig. 1a and b). For defect calculations in the bulk, an 8 ABO3-unit pseudo-cubic 2 × 2 × 2 supercell was used. High-symmetry structures were constructed in such a supercell for 0, 25 and 50% relative Sr concentrations, creating bcc and simple cubic Sr-sublattices, respectively. Two concentrations of oxygen vacancies (δ = 0.125 and 0.25) were simulated by removing neutral oxygen atoms. This leads to an increased electron density of the nearest Mn ions (thus, decreasing their oxidation state). The electron density inside the oxygen vacancy is negligible (≤0.1 e), and the vacancy can thus be denoted as a doubly positively charged defect, , in the standard Kröger–Vink nomenclature. The oxygen vacancy formation energies are calculated according to for stepwise removal of O atoms from the AxByOz supercells.
In the (001) surface calculations, seven-layer 2D symmetric slabs were used (i.e. sequence AO–BO2–AO–BO2–AO–BO2–AO or BO2–AO–BO2–AO–BO2–AO–BO2; total thickness about 3.5a0 which corresponds to ≈14 Å), separated along the z axis by a 5a0 vacuum gap. The surface cell is made of eight AO or BO2 units (2a0√2 × 2a0√2, Fig. 1c). There are two, eight and four nonequivalent surface oxygen lattice sites for 0, 25 and 50% Sr concentrations, respectively. The removal/adsorption of a surface oxygen atom from these terminations (symmetrically on both sides) leads to a surface defect concentration of 12.5% (1/8 defect per AO or BO2 surface formula unit). The lattice constants were optimised in the bulk defect calculations (leading to a small energy reduction, ≤0.05 eV per formula unit). For the slab calculations only the atomic coordinates were optimized, with the lattice constants kept fixed at the respective bulk values.
The calculated binding energy for a gas-phase O2 molecule is −5.9 eV (the combination of pseudopotentials and exchange–correlation functionals used in the plane wave VASP code is known to overestimate the experimental value of 5.12 eV and thus the vacancy formation energy; however, this does not affect the differences of the defect and adsorbate formation energies that are the main focus of the present study. The calculated bond length of 1.23 Å is close to the experimental value of 1.21 Å). The lattice constants and angles in rhombohedral LM, LS25M and LS50M are a0 = 7.88 Å, α = 90.85; a0 = 7.81 Å, α = 90.54; and a0 = 7.77 Å, α = 90.50, respectively.
The oxygen adsorption was modeled on a 7-layer LaO-terminated symmetric non-stoichiometric La4Mn3O10 (001) slab. Such 7-layer slabs have been found to suffice for a good convergence of the main properties such as formation energy with a slab thickness5,26,27 and are used here for consistency with a previous study. The electron charge redistribution in the terminating planes of this slab is similar to that for stoichiometric slabs with an even number of layers.27 The total dipole moment normal to the (001) surface is naturally cancelled by the slab's symmetry, but two local dipole moments remain at the surfaces (charged surface and subsurface layer; also the adsorbate layer, if present, is charged) which are oriented in opposite directions. Transition states were calculated by the NEB method43 with eight intermediate images. The effective atomic charges were calculated with the Bader method.44 The atomic structures are visualized using VESTA software.45
x Sr | Bulk Mn | Bulk ionic charges/e | (La,Sr)O terminated slab | MnO2 terminated slab | |||||
---|---|---|---|---|---|---|---|---|---|
Ox. state | La | Sr | Mn | O | Ox. state | Composition | Ox. state | Composition | |
0 | +3.00 | 2.08 | 1.71 | −1.27 | +2.67 | La4Mn3O10 | +3.25 | La3Mn4O11 | |
0.25 | +3.25 | 2.09 | 1.59 | 1.78 | −1.25 | +3.00 | La3SrMn3O10 | +3.44 | La2.25Sr0.75Mn4O11 |
0.50 | +3.50 | 2.10 | 1.58 | 1.83 | −1.22 | +3.33 | La2Sr2Mn3O10 | +3.63 | La1.5Sr1.5Mn4O11 |
For all LM and LSM compositions discussed here, the AO and BO2 layers of the perovskite structure are charged (Table A2 in the ESI†). The layer charges for the bulk materials decrease from 0.96 e per formula unit for LM, down to 0.69 e per formula unit for LS50M (gray circles in Fig. 2), as expected for a partial substitution in the AO layers with and increasing Mn oxidation state in the BO2 layers. While for the same average Mn oxidation state, the BO2 layer charges for the bulk, central and surface layers of the slabs are quite similar, and the AO surface layer charges are systematically, by 0.2–0.25 e per formula unit, lower than those for AO layer deeper inside the slab. Also, the splitting into sub-planes is different for AO and BO2 surface layers (Fig. A1 in the ESI†). The surface rumpling can partially compensate for the surface dipole; for the BO2 termination, the subsurface AO layer also shows a pronounced distortion with La/Sr outward displacement.
Fig. 2 Layer charges of LSM (001) (La,Sr)O and (001) MnO2 terminated slabs. For a comparison the charges of the central slab layers and bulk LSM are also shown. |
The decrease of the Mn oxidation state due to the variation of the La/Sr ratio and/or the formation of affects the electronic structure of both the bulk and the slabs, so that the Fermi energy increases (it is plotted in Fig. 3a relative to the deep reference O 2s states, see ref. 36 for more details). Interestingly, different slopes are observed for the bulk and AO and BO2 terminations. A similar effect was found for the surface work functions of the symmetrical 9-layer ABO3 slabs, which increase more steeply for the BO2 termination when moving through the element row, from B = Ti to Ni.46
Fig. 3b shows the formation energy for the bulk and the central layer of the slabs (cf. also Table A3 in the ESI†). The data for the bulk and MnO2-terminated slabs agree very well. in the central layer of AO terminated slabs is slightly lower, which might be affected by the electron density redistribution towards the surface AO layer with an excessive positive charge that correspondingly decreases the Mn effective oxidation state in the inner layers and lowers (cf. the differences in layer charges in Fig. 2). Overall, the trend of these with the Mn oxidation state is very similar to the variation in the bulk Fermi level (Fig. 3a). The bulk formation energies for LM and LS50M as well as the decrease for LS50M are in good agreement with literature values in ref. 47 and 48 (with Ueff = 0) and experimental data on La0.9Sr0.1MnO3, discussed in ref. 49. The fact that the bulk is rather similar for LM and LS25M was also noticed in ref. 50, although the use of the GGA+U method resulted in different absolute energies.
Finally, Fig. 3c displays for the surface oxygen vacancies (cf. also Table A4 in the ESI†). The difference between the symbols (surface ) and dashed lines ( for bulk/central layers) can be assigned to the true surface termination effect. Note that despite some difference in the LSM absolute bulk values between the present GGA study and the hybrid HSE approach,51 the changes of with the Mn oxidation state are quite comparable (for the FM state). For the BO2 termination, decreases with increasing Mn oxidation state with the same slope as for the bulk vacancy formation energy. The absolute formation energies are lower by ∼0.5 eV (light blue arrows), which represents the true surface effect. For the AO termination, increases with decreasing Mn oxidation state, but with a larger slope than the bulk Consequently, the resulting true surface effect (green arrows) is most pronounced for the LM slab, for which is by ∼0.7 eV larger than the respective value for the central layer.
Fig. 4 shows the layer-resolved values for LM, LS25M and LS50M slabs. For the central slab layer the surface formation energies closely approach the bulk values, indicating that the slab is sufficiently thick. The arrows indicate the difference between the surface and bulk with the respective oxidation state of the slab (neglect of this issue could lead to errors exceeding 1 eV), from which the difference in surface concentration compared to the bulk value can be estimated. However, to determine the differences in and vacancy concentration for AO and BO2 terminations having the same average Mn oxidation state one has to refer to Fig. 3c. A similar energy difference in surface vacancy formation energies for the (001) LM LaO and MnO2 terminations was also observed for larger, 16-layer slabs calculated using the GGA+U functional (these slabs were cation-stoichiometric, but exhibited a nonzero surface dipole).28
Fig. 4 The vacancy formation energies in the different layers of the (001) terminated slabs of LM (left), LS25M (middle), and LS50M (right). The arrows indicate the energy difference relative to bulk with the same average Mn oxidation state (dashed line; the same for both terminations of LM, but different for the LS25M and LS50M terminations because of the steep slope in the right hand part of Fig. 3b). |
The true surface effect on has two contributions: (i) contributions originating from under-coordinated atoms in the surface layer. Qualitatively, one might expect that formation is facilitated in both termination layers, because the number of Mn–O surface chemical bonds broken upon oxygen removal is smaller compared to the bulk. This effect is well known in covalent semiconductors and the so-called E′ centers (dangling bonds) in amorphous silica52 as well as for perovskites with neutral surface AO and BO2 layers such as SrTiO3 (e.g. it was found that is reduced by 0.8 eV on the TiO2 termination but is almost unchanged on SrO,28 whereas Alexandrov et al.53 estimated even larger changes of 1.4 eV and 1 eV; for BaZrO3, and was reduced by 0.5 eV on the ZrO2 termination54). (ii) Contributions which are related to the fact that the AO and BO2 (001) terminations are polar. To some degree, this polarity is attenuated by small relaxations of the surface layer (outward displacement of Mn ions at the MnO2 termination,32 and oxide ions at the LaO termination, cf. Fig. A1 in the ESI†). Furthermore, in a perovskite, such as (La,Sr)MnO3 with cations easily changing their oxidation state, one could expect the polarity to be partially compensated by the increased Mn oxidation state in the MnO2 termination layer. However, the data in Table A2† indicate a less positive surface Mn charge, i.e. an opposite trend, which can rather be interpreted as an increased Mn–O bond covalency (but the MnO2 surface layer charge hardly deviates from that of bulk with the same Mn oxidation state, cf.Fig. 2). A charge transfer of ≈+0.1 e per formula unit for the MnO2 termination and ≈−0.15 e for the LaO surface was found in ref. 28. However, this electron density redistribution does not suffice to fully compensate for the surface dipoles, and the remaining polarity affects the defect formation and oxygen adsorption energies.
In the LaO termination layer with a formal charge of +1 e, the surface polarity is expected to disfavor the surface formation. Obviously, the polarity effect dominates here over the reduced number of broken chemical bonds, leading to an overall increased In contrast, for the MnO2 termination, the negative excess surface charge is expected to favor formation. Despite the additional contribution from the reduced number of broken bonds at the surface, the overall decrease of at the MnO2 termination remains quite moderate. The total difference of 1–1.2 eV in the surface for the two terminations (for a given average Mn oxidation state) leads to a large difference in the surface concentrations at 1000 K by more than 5 orders of magnitude (cf. Table A7†). This strongly affects the ORR rates, as discussed in Section 3.4. The decreased on the AO termination will also make it more susceptible to effects from segregation processes or poisoning by impurities.
The O adsorbed on the AO termination carries a significant negative charge of −1.19 to −1.28 e (comparable to that for oxide ions) in the bulk (−1.22 to −1.27 e) and only slightly smaller than for O in the AO surface layer (−1.33 to −1.34 e), which allow us to consider it as Oad2− rather than Oad−. On the other hand, O adsorbates on another MnO2 termination (−0.49 to −0.69 e on the present rhombohedral slabs and −0.62 e on orthorhombic slabs5) are less charged and should rather be considered as Oad−. This difference could be related to the lower electronegativity of La cations compared to Mn. The slight outward displacement of the La cations neighboring Oad (Fig. 5a and 8c) further stabilizes the more negative Oad charge. For LS25M slabs, the atomic O adsorption energies Eads,O (as well as Eads,O2) are on average by ≈0.3 eV less negative, when one Sr ion is located close to the “hollow” adsorption site (on LSM50 there is always such a Sr neighbor).
Fig. 6 summarizes the O–O bond length and charges of molecular oxygen adsorbates. This overview indicates that the assignment to superoxide or peroxide should always be based on several descriptors; in the present case the O–O bond length is a stronger criterion than the charge of the adsorbate (comparing only the charge of the superoxide species of 1.03–1.20 e with that of bulk oxide ions, one might be tempted to assign it also to doubly charged peroxide O22−). The comparison between MnO2 and AO terminations also emphasizes the influence of the nature of adsorbate–slab interaction (partly covalent on MnO2 but largely ionic on AO) on the character of the adsorbed species.
Fig. 6 Charge of molecular oxygen adsorbates on the (La,Sr)O termination and MnO2 termination versus O–O bond length; for comparison gaseous O2 is also included (bond length from DFT), and the experimental O–O bond lengths in HO2 and H2O2 are indicated.57 This plot allows for a distinction of superoxide vs. peroxide species. On the AO termination the superoxide not only has a shorter O–O bond than the peroxide, but also significantly larger average distances to the surface A cations (Table A5†). |
Fig. 7a shows Ead,O for the two different 7-layer terminations. The dotted lines indicate the expected effect of the different Mn oxidation states of the considered slabs on Eads,O, as estimated from the variation in the slab Fermi energy in Fig. 3a. Eads,O on the AO termination becomes more negative with decreasing Mn oxidation state, with a much steeper slope than the slab Fermi energy. This could be caused by two contributions: (i) transfer of more than one electron per adsorbed O atom and (ii) the electrostatic attraction of negatively charged Oad species with the positive charge of the AO surface layer, which is stronger for LM than LS25M and LS50M terminations. Since the Oad species on AO termination roughly correspond to Oad2−, this stronger electron transfer can largely explain the variation of Eads,O (indeed, doubling the slope of the green dotted line in Fig. 7a to account for the transfer of two electrons per O reproduces very well the trend in Eads,O). This explanation leaves only a minor role for the electrostatic contributions to Eads,O at the AO termination (cf. the smaller formal layer charges of the AO termination compared to MnO2 in Table A2†). Most probably, the very negative adsorption energies also contain a contribution from the stabilizing effect of the adsorbed oxygen species on the AO surface plane, which otherwise attempts to mitigate the structural disruption by pronounced surface rumpling as indicated in Fig. A1.†
Fig. 7 (a) Atomic oxygen and (b) molecular oxygen adsorption energy as a function of the average Mn oxidation state. Dispersion in energies for the same composition and oxidation state corresponds to different adsorbate configurations as indicated in Table A5.† The dotted lines indicate the slope of the Fermi level (Fig. 3a), but with an opposite sign since electrons are transferred to adsorbed species. |
Despite the expected effect of the slab Fermi energy variation (blue dotted line in Fig. 7a), Ead,O on the MnO2 termination is nearly independent of the Mn oxidation state. This results from the repulsion between negatively charged adsorbates Oad− (more negative for a lower Sr content, cf. Table A5†) and the negative surface layer charge (also more negative for a lower Sr content), which apparently cancels the more favorable electron transfer for Sr-poor slabs with a higher Fermi level. Thus, for the MnO2 termination we are left with a true termination effect on O adsorption caused by the surface dipole as indicated by the blue dashed arrows; however, since the position of the blue dashed line cannot be fixed on an absolute energy scale, the picture here is only qualitative.
Fig. 7a convincingly demonstrates the importance of considering the actual Mn oxidation states caused by the slab cation stoichiometry. Indeed, a direct comparison of the atomic O adsorption energies on the LaO and MnO2 terminations of symmetrical 7-layer slabs55,58 or 9-layer slabs19 yields a difference in Eads,O of 3–4 eV. However, Fig. 7 clearly indicates that most of this difference is due to the Mn oxidation state variation, and only less than 1 eV is the true termination effect when comparing the data for a fixed Mn oxidation state (e.g. Mn3.3+).
For both terminations, the Ead,O2 values for molecular adsorption are less negative than the sum of the two respective atomic O adsorption energies – i.e. O2 dissociation is energetically favored. The energies, charges and distances are given in Table A5, ESI†. Molecular adsorption on the AO termination occurs in a tilted configuration (Fig. 5b), but for LS25M and LS50M also in a horizontal configuration (Fig. 5c) which yields the most negative Ead,O2. Based on the O–O bond lengths and charges (cf. Fig. A2 in the ESI†), the adsorption on the AO termination occurs as peroxide species (O22−) on LM and LS25M, while on LS50M with a higher average Mn oxidation state superoxide (O2−) is also formed (however, O22− yields the most negative Eads,O2). Peroxide species in the horizontal configuration were also found to be the most stable ones on the LaO termination of La2NiO4 in ref. 56, with a tilted superoxide being by 0.14 eV less favorable. On the MnO2 termination only tilted superoxide is present (Fig. 5e). Fig. 7b shows the molecular adsorption energies; the trends and their interpretation are very similar to that of atomic adsorption.
The more negative Ead,O and Ead,O2 for the AO termination should lead to much larger adsorbate coverages compared to the MnO2 termination (for the same Mn oxidation state). However, the increase will be limited by saturation effects which arise for charged adsorbates and tend to limit the coverages to about 20%.5 This point will become important in the kinetics discussion in the last section.
Fig. 8 Representative top and side views of oxygen dissociation on the (001) AO termination of LS25M (larger light green spheres = Sr). (a) The initial state (horizontal configuration), (b) transition state (energy higher by 0.60 eV than the initial state), and (c) one frame after the transition state (energy 0.14 eV lower than the initial state). The final state geometry is similar to that given in Fig. 9c. |
The trends in dissociation barriers for LM, LS25M and LS50M AO-terminated slabs are revealed in Fig. 10. The energies of the dissociation transition states ETS (relative to O2 in the gas phase) become systematically more negative with the decrease of the dissociation energy ΔEdiss (Fig. 10a, Table A6†). Note that the ΔEdiss depends mainly on the average Mn oxidation state, with some additional contributions stemming from different adsorption configurations. The scattered actual dissociation barriers (Fig. 10b) show a clear trend of decrease for more negative ΔEdiss, which corresponds to the Bell–Evans–Polanyi principle.59,60 Interestingly, the dissociation barrier calculated for adsorbed peroxide on the LaO termination of La2NiO4(ref. 56) (1.35 eV for ΔEdiss = 0.4 eV) also nicely fits into this plot.
Fig. 10 (a) Energies of the dissociation transition state ETS (relative to O2 in the gas phase) on the AO termination as a function of the dissociation energy ΔEdiss. (b) The dissociation barrier E≠diss (relative to adsorbed molecular oxygen species) as a function of ΔEdiss (ETS, E≠diss and ΔEdiss are also illustrated in Fig. 11). |
Let us now compare the O2 dissociation barrier on the AO termination of LS50M (Mn3.33+) with that on the LM MnO2 termination (Mn3.25+) since both refer to similar Mn oxidation states. On the AO termination, the barriers of 0.7–1.3 eV considerably exceed that of 0.6 eV found for the LM MnO2 termination in ref. 5. This may be related to the dissociation pathway on AO being more complicated than on MnO2 where it proceeds from a peroxide bridging between two surface Mn ions to two separate O atoms attached to exactly these two Mn ions. The variation of the energy barrier with Mn oxidation states is expected to be roughly similar for both terminations because a lower oxidation state (higher Fermi level) favors the electron transfer to antibonding π* orbitals of the oxygen molecule and thus facilities the dissociation. Owing to the low concentration in the AO surface layer, dissociation processes with assistance are not considered for the AO termination here. For the AO termination of La2NiO4, a strongly decreased dissociation barrier of 0.28 eV was obtained for molecular oxygen species vertically inserted into a 56 but such a reduced barrier cannot outweigh the effect of the extremely low vacancy concentration on the AO termination of the LSM slabs.
The formation energies for the AO termination are higher by 0.5–0.7 eV compared to bulk with a comparable Mn oxidation state (Fig. 3c). At 1000 K this corresponds to a decrease of the concentration by roughly 3 to 4 orders relative to the bulk (these numbers are compiled in Table A7†). Therefore, ORR mechanisms which proceed via direct O2 adsorption into a on the AO termination can be ruled out. In other words, the thermally activated dissociation rate of O2,ad2− adsorbed on the perfect AO termination is higher than the rate of O2 adsorption into a surface followed by subsequent fast dissociation.
Both the atomic and molecular oxygen adsorption energies on AO terminations are very negative (range of −4.5 to −2 eV per O Fig. 7a and −5 to −2.5 eV per O2Fig. 7b). This means that at SOFC operating temperatures in air the concentration of adsorbed oxygen species could become so high that it reaches the plateau of ∼20% coverage, limited by the mutual repulsion of charged adsorbates.5,63 The adsorbate coverages calculated with reasonably estimated ΔS0add values are also given in Table A7.† Because of the more negative ΔH0add for the formation of two atomic species compared to one molecular adsorbate (Fig. 7a and b), Oad2− on AO and Oad− on MnO2 are always in majority. Only for molecular oxygen species on the MnO2 termination, smaller coverages in the range of 10−4 to a few % are obtained. This means that the molecular adsorbate coverage on the AO termination is increased from these values to the saturation limit of ≈20%, i.e. varying by a factor of 4 to 2000. Since the chemisorption is assumed to proceed without a significant barrier, this is not the rate limiting step.
Three processes could be potentially considered as the rate determining step on the AO termination: (i) the O2 dissociation, with a barrier of 0.1–0.8 eV (Fig. 11), (ii) the encounter of Oad2− species with a and (iii) the final incorporation of an atomic Oad2− species into a neighboring For the MnO2 termination, step (iii) was found to occur with no barrier,5 and also on the AO termination it is reasonable to assume that it proceeds fast. For step (ii), migration exclusively in the LaO surface layer is not possible since in perovskites the O migration path/transition state configuration always contains in the transition state a B-site cation.37,64 Thus, jumps from/to the subsurface MnO2 layer must be involved, with a barrier that comprises the (bulk) migration barrier of 0.95 eV5,26 and additional contribution from the unfavorable configuration of being in the surface layer (about 0.5 eV, Fig. 4), resulting in an effective migration energy of 1.4 eV. On the other hand, the Oad2− migration barrier on the AO surface layer amounts to 1.3 eV. So the migration of to Oad2− and vice versa contribute equally to the encounter. An encounter of peroxide ions with surface followed by a dissociation (case (iii)) would yield a lower rate than the encounter because of the lower peroxide coverage compared to Oad. This mutual approach is also expected to be slower than the dissociation step (i) because it involves which exhibits extremely low concentrations (see above and Table A7†) while the coverage of adsorbed superoxide or peroxide ions as the precursor for the dissociation is high. Summing up, we conclude that the mutual approach of and Oad2− could be regarded as the rate determining step on the AO termination.
Notwithstanding the fact that the same step is rate determining for the AO and MnO2 terminations (at least, at comparably high pO2 (ref. 5) as relevant for a cathode material), the ORR is expected to be much slower for the former termination. On one hand, the adsorption energies for atomic as well as molecular oxygen species are much more negative on the AO termination compared to MnO2 (for the same Mn oxidation state), but since the coverage by charged adsorbates approaches a saturation at about 20%5 this more favorable adsorption energetics can only partially be translated into a higher concentration of O2,ad−/2− and Oad−/2− (the latter being the relevant concentration for the rate determining step). On the other hand, the surface concentration is lower by more than 5 orders of magnitude on the AO termination, and the migration barrier for the encounter is more than 0.6 eV higher (Table A7†) which corresponds to a 3 orders of magnitude decrease of the encounter rate at 1000 K. Although these numbers are only a rough estimate, it indicates that even if most of the surface on a real SOFC cathode has a (La,Sr)O termination, even small patches of the MnO2 termination (or any other terminations more active than (La,Sr)O) in the percent range might still make a significant contribution to the overall ORR kinetics. This is in line with the observation for thin film La0.6Sr0.4CoO3−δ cathodes that already the addition of a monolayer of only 4% Sr strongly decreases the exchange rate of a freshly deposited film.65 While we are not aware of direct experimental determinations of adsorbed oxygen coverage on exclusively AO- or BO2-terminated perovskites, a recent ambient-pressure XPS investigation demonstrated distinct differences in the water adsorption of LaO- and FeO2-terminated LaFeO3.66
The main trends found here for the (La,Sr)MnO3 system (decreased and increased adsorbate coverage on the AO termination) are expected to hold also for related (Ba,Sr,La)(Fe,Co,Mn)O3 perovskite cathode materials. However, the detailed dependence on the cation composition is far from trivial to predict since the decreased and increased adsorbate coverage exert a counteracting effect on the oxygen exchange rate. The contribution of the AO termination to the overall rate is expected to become larger in materials with a less negative oxidation energy which increases the bulk and typically makes the adsorption energies less negative (i.e. decreases adsorbate coverages). Then, a larger part of the more negative adsorption energy for the AO termination may actually translate into increased oxygen coverages before the saturation limit is met.
Footnote |
† Electronic supplementary information (ESI) available. See DOI: 10.1039/c8ta02058b |
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