Computational screening of perovskite redox

Catalysis Today 286 (2017) 124–130

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Computational screening of perovskite redox materials for solar thermochemical ammonia synthesis from N2 and H2 O Ronald Michalsky ∗ , Aldo Steinfeld Department of Mechanical and Process Engineering, ETH Zürich, Sonneggstrasse 3, 8092, Zürich, Switzerland

a r t i c l e

i n f o

Article history: Received 14 April 2016 Received in revised form 30 August 2016 Accepted 15 September 2016 Available online 22 February 2017 Keywords: Ammonia Thermochemical Redox Concentrated solar energy Perovskite Density functional theory

a b s t r a c t To circumvent the scaling relations of activation energies and adsorption energies at catalytic surfaces limiting their catalytic activity, perovskites are investigated for a solar-driven production of ammonia (NH3 ) from N2 and H2 O via a two-step redox cycle. The cycle consists of an endothermal reduction of N2 at 1400 ◦ C using solar process heat, followed by an exothermal hydrolysis forming NH3 at 400 ◦ C. Both steps are carried out at ambient pressure. Electronic structure computations are employed to assess the stability and surface activity of oxygen vacancies and lattice nitrogen at the (001) facet of nitrogendoped perovskites. The results are compared to the activities of Mo2 N(100), Mo2 N(111), and Mn2 N(0001) reference models. We find producing oxygen vacancies at high temperature that are active in N2 reduction is the energetically limiting reaction step of the redox cycle. The redox energetics can be tuned by the perovskite composition and are most sensitive to the type of transition metal at the B site terminating the surface. Promising perovskites contain Co or Mn at the surface and Co doped with Mo or W in the bulk, such as CaCoO3 -terminated La0.5 Ca0.5 Mo0.5 Co0.5 O3 , SrCoO3 -terminated Sr0.5 La0.5 Co0.5 W0.5 O3 , and CaMnO3 -terminated Sr0.5 Ca0.5 MnO3 . Trade-offs in the redox energetics are quantified to guide future experimental work. © 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

1. Introduction Thermochemical redox cycles facilitate the production of renewable chemical fuels using the entire spectrum of concentrated sunlight as the source of high-temperature process heat [1,2]. A promising example is splitting of CO2 and H2 O with a two-step metal oxide redox cycle into separate streams of CO, H2 (syngas) and O2 . Syngas can be further processed into liquid hydrocarbon fuels, e.g. kerosene [3] or methanol [4], via commercial catalytic technology. Concentrated solar process heat can also be used for the sustainable production of energy-intensive chemical commodities that are currently derived using finite and polluting fossil resources. One such example is the synthesis of ammonia from N2 and H2 via the catalytic Haber-Bosch process at up to 300 bar and 400–500 ◦ C [5,6]. The industrial implementation of this reaction consumes 28–166 GJ ton−1 NH3 [5,7], mainly supplied by natural gas, coal, or naphtha [7], at a global scale equivalent to 1–2% of the world’s annual energy production [8]. A major fraction of it is consumed for the production of the two elemental precursors, i.e. H2 – typically by

∗ Corresponding author. E-mail address: [email protected] (R. Michalsky).

steam-reforming of natural gas – and N2 – typically by cryogenic separation from air [7]. While renewable H2 and electricity may be employed for the Haber-Bosch process [9], an economic NH3 production from renewable resources remains challenging as about 15% of the net energy requirements of the industrially implemented Haber-Bosch process are consumed for cyclic heating/cooling and recompression to form NH3 and separate it from unconverted N2 and H2 [7]. Furthermore, the limited activity of the catalysts [7,10,11], calls for high-pressure high-temperature machinery that limit economical production to large-scale centralized plants with a capacity exceeding 1000 t NH3 day−1 [7,12]. Current research focuses on alternative routes to produce renewable NH3 , such as electrochemical [13–15], and low-pressure catalytic synthesis [16–18]. For example, certain metal nitrides are currently investigated for a catalytic NH3 synthesis at moderate process conditions [16], while other metal nitrides are studied for a two-step NH3 synthesis via separate N2 reduction and hydrogenation with H2 [17,19]. Density functional theory (DFT) suggests that materials such as Co3 Mo3 N may yield NH3 via a Mars-van Krevelen mechanism, where the lattice nitrogen partakes in the reaction [18]. The severe process conditions of the Haber-Bosch process are rationalized with the scaling of the activation energy for the N2 dissociation and the adsorption energy of nitrogen at catalytic surfaces

http://dx.doi.org/10.1016/j.cattod.2016.09.023 0920-5861/© 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4. 0/).

R. Michalsky, A. Steinfeld / Catalysis Today 286 (2017) 124–130

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Fig. 1. Optimized surface geometries for a representative perovskite (panels A to J), Mo2 N(100), Mo2 N(111) and Mn2 N(0001) (panels K to M). Perovskite surface conditions are shown representatively for Sr0.5 Ca0.5 Mo0.5 W0.5 O3-␦ N␧ (001) terminated by a CaWO3 layer and with AO- (panels A to E) and BO2 -surface geometry (panels F to J). The second and fourth image (counting starting from the left) of panels A and F show the periodicity of the models parallel to the surface. Introduction of oxygen vacancies (␦ > 0) and lattice nitrogen (␧ > 0) is shown with panels B to E and panels G to J for both surface terminations. As guide to the eye, solid lines around two atomic geometries in panel A show the boundaries of the periodic unit cell.

[20]. To circumvent these scaling relations, this paper investigates redox materials for production of NH3 from N2 , H2 O, and sunlight at ambient pressure via a two-step thermochemical redox cycle [21]. Separating the catalytic ammonia synthesis by use of a redox material into two reaction steps generally increases the degree of freedom when designing catalysts with desirable activation and adsorption energies [19]. Ammonia synthesis with redox materials has been demonstrated successfully by AlN hydrolysis at 900–1200 ◦ C to produce NH3 , followed by carbothermic reduction of the formed Al2 O3 with N2 using a biogenic reducing agent such as wood charcoal at 1500–1700 ◦ C [22–24]. Due to a trade-off in the redox energetics [25,26], materials that can be recycled more easily yield less NH3 , such as Cr2 O3 which can be recycled with gasified biomass below 1500 ◦ C into chromium nitrides [27]. The economic prospect of producing NH3 overall from air, water, and sunlight, with on-site solar-driven H2 O splitting to produce H2 as reducing agent, have been assessed previously and indicate that a major fraction of the required capital investment is due to the need for the H2 reducing agent [21]. Here, we explore the possibility of entirely eliminating the need for a reducing agent to facilitate the conversion of N2 and H2 O into NH3 and O2 using perovskites with ABO3 stoichiometry, where A and B are metal cations in twelve- and six-coordinated interstices of the metal oxide. Due to their stable crystal phase, tuneable oxygen vacancy concentrations, and high oxygen vacancy conductivities, perovskites are attractive materials for fuel cells and high-temperature oxygen separation [28–30], as well as for solardriven thermochemical splitting of CO2 and H2 O and solar-driven reforming of CH4 [31–33]. Conceptually, using concentrated solar

energy at high temperature and low O2 partial pressure a perovskite is reduced endothermically to form oxygen vacancies for N2 reduction: ABO3 +␧/2N2(g) → ABO3-␦ N␧ +␦/2O2(g)

(1)

where ␦ is the oxygen non-stoichiometry and ␧ ≤ ␦ is the amount of nitrogen incorporated into the crystal lattice. Assuming for simplicity that two thirds of the oxygen vacancies are active in N2 reduction, NH3 is formed exothermically in a second hydrolysis step at ambient pressure and lower temperature: ABO3-␦ N2␦/3 + ␦H2 O(g) → ABO3 + 2␦/3NH3(g)

(2)

In general, if ␧ > 2␦/3 some of the lattice nitrogen will yield N2 , while excess H2 will be formed if ␧ < 2␦/3. The thermodynamic activity of perovskites in these reactions is assessed here with electronic structure calculations. Section 3.1 computes the energy required for the O2 evolution reaction (OER) and the activity of oxygen vacancies in the N2 reduction reaction (NRR), described with Eq. (1). Section 3.2 quantifies the stability of oxygen vacancies and lattice nitrogen at the surface. Section 3.3 assess the energetics of the H2 O splitting reaction (WSR) and NH3 evolution reaction (AER), described with Eq. (2). 2. Computational methods 2.1. Electronic structure computations The thermochemical activity of 60 cubic A0.5 A’0.5 B0.5 B’0.5 O3-␦ N␧ (A, A’ = Ca, Sr, La; and B, B’ = Mn, Co, Mo, W) perovskites and of

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Fig. 2. The free energy change of reducing N2 into lattice nitrogen filling oxygen vacancies, Gf [N], versus that of forming oxygen vacancies via O2 evolution, Gf [vO ], both at 1400 ◦ C, 0.01 bar O2 , and 0.99 bar N2 , except for A ) OER at 1400 ◦ C and NNR at 400 ◦ C. A0.5 A’0.5 B0.5 B’0.5 O3-␦ N␧ (001) (A, A’ = Ca, Sr, La; B, B’ = Mn, Co, Mo, W; ␦ = 0, 0.5; and ␧ = 0, 0.5) models are marked with the composition and AO- or BO2 -type geometry of their surface termination (ter.). The computation of the reference metal oxide/nitride redox pairs is described in the text. A gray rectangle marks the exergonic reaction space and a gray circle marks 1 eV distance between a point in reaction space and the origin. The desirable quadrant of the reaction space is marked with A. The raw data is given in the Supporting information, such that this and the following graphs can be reproduced at any desired level of detail.

Fig. 3. The stability of lattice nitrogen (negative values mark lattice nitrogen preferring sites below the surface) versus the stability of oxygen vacancies (negative values mark oxygen vacancies preferring sites at the surface) at perovskite surfaces. The perovskites labels are explained with Fig. 2. The discussion of the gray quadrants marked with A, B, C, and D in the text shows that the ideal redox material is located at the origin, tracked with a star. The Coloured lines mark the stability of nitrogen vacancies at the indicated metal nitride surfaces (negative values mark nitrogen vacancies preferring sites below the surface).

cubic ␥-Mo2 N and hexagonal ␨-Mn2 N, as reference, was quantified via DFT employing the Grid-based projector-augmented wave (GPAW) code [34,35], in the Atomic simulation environment (ASE) [36,37], with exchange-correlation interactions treated by the revised Perdew-Burke-Ernzerhof (RPBE) functional [38]. Similar to previous DFT studies of perovskites [39], the calculations reported here use the generalized gradient approximation (GGA) without a Hubbard U correction. We have reported previously that this addition does not improve surface activity calculations with the employed models [30,40]. Systems containing Mn or Co were modeled with spin-polarized calculations. Atomic geometries were optimized using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm until the maximum force was less than 0.05 eV Å−1 . Convergence was achieved with a Fermi-Dirac smearing of 0.1 eV and structure optimization results were extrapolated to 0 K.

stress in the reported calculations, the lattice constants were computed via DFT and are given along with the DFT-optimized magnetic moments in the Appendix A. The perovskite surfaces were modelled using the (001) facet that is geometrically symmetric to the (100) and the (010) facets (dependent on composition, of which all were tested in this work) and thermodynamically most stable [30,40]. The A2 B2 O6 (001) models contained one ABO3 surface layer that was allowed to relax and stacked in z-direction atop one ABO3 layer that was constrained to the bulk geometry. Varying the composition of the bulk and of the surface termination and between AO- and BO2 -geometry of the surface (Fig. 1) yielded 288 unique surfaces. To quantify thermodynamic stability, the energy required to form these surfaces is given with Supporting information. The metal nitride surfaces were modelled using the Mo2 N-terminated Mo2 N(100), Mo-terminated close-packed Mo2 N(111), and Mnterminated close-packed Mn2 N(0001) facets since these were observed experimentally or were used previously as surface models [41,42]. All surface models contained 10 Å of vacuum perpendicular to the surface and were repeated periodically in the directions parallel to the surface. A k-point sampling of 4 × 4 × 1 was used to sample the Brillouin zone in the x, y and z directions, with the z direction orthogonal to the surface.

2.2. Surface models

2.3. Free energy calculations

The perovskite and nitride surface models employed in this work are shown with Fig. 1. The bulk perovskites were modelled with two metals at the A-site, two metals at the B-site, and six oxygen atoms, i.e., with A2 B2 O6 stoichiometry. Bulk Mo2 N and Mn2 N were modelled with four and eight metal atoms, respectively, and nitrogen occupying half of the octahedral interstitial sites. All bulk models had periodic boundary conditions in all directions and used a k-point sampling of 4 × 4 × 4. All atoms in the bulk structures were allowed to optimize their positions (relax). To avoid reminiscent

The free energy of a chemical species i (Gi ) was calculated with [43]: Gi (T, P) = N i i (T, P) = E i + U ZPE,i − TS i (T, P)

(3)

where T is the absolute temperature, P is the absolute pressure, Ni is the number of atoms, i is the chemical potential, Ei is the DFT-computed total electronic energy, UZPE,i is the zero-point vibrational energy, and Si is the entropy. Thermodynamic properties of gases, assumed to be ideal gases, were calculated from


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and the reference energy of the lattice nitrogen formed from 1/2N2 gas. The thermodynamic stability of oxygen vacancies at the surface, Gsurf-subsurf [vO ], was assessed with: Gsurf -subsurf [vO ] = Gvo − Gsvo

(6)

where Gsvo is the free energy of the metal oxide with oxygen vacancies below the surface (Fig. 1, panels C and H). Negative values of Gsurf-subsurf [vO ] indicate oxygen vacancies preferring sites at the surface. Analogously, the stability of lattice nitrogen at the surface, Gsubsurf-surf [N], was assessed with: Gsubsurf -surf [N] = Gsn − Gn

(7)

where Gsn is the free energy of the metal oxide with lattice nitrogen below the surface (Fig. 1, panels E and J). Negative values of Gsubsurf-surf [N] indicate lattice nitrogen preferring sites below the surface. The free energy of forming NH3 and oxygen vacancies from the lattice nitrogen and the hydrogen obtained from the WSR, Gf [NH3 ], was described with: Gf [NH3 ] = Gvo − Gn + Gr,AER [N]

Fig. 4. The free energy of NH3 evolution via hydrogenation of the lattice nitrogen, Gf [NH3 ], versus the free energy of forming lattice oxygen with H2 O as oxidant, Gf [O], at perovskite surfaces. All data is given at 400 ◦ C, 0.1 bar NH3 , 0.9 bar H2 O, and 0.01 bar H2 , except data at 1000 ◦ C marked with dark gray circles. The perovskite labels are explained with Fig. 2. A gray rectangle marks the exergonic reaction space and a gray circle marks 1 eV distance between a point in reaction space and the origin. The desirable quadrant of the reaction space is marked with A. Coloured lines mark the free energy of NH3 formation from the lattice nitrogen of the indicated metal nitride surfaces.

vibrational frequencies and standard statistical mechanical equations, evaluated through ASE. Analogous to previous work, free energy corrections of the solids were neglected [44]. Due to the difficulty to correctly describe the complicated electronic structure of O2 via DFT [45], the free energy of O2 was correct by the addition of 0.717 eV to fix the free energy change of splitting 2H2 O into 2H2 + O2 at 1400 ◦ C and 0.01 bar O2 to 2.54 eV (i.e., at the OER conditions selected in this work) [46].

The following develops the descriptors of surface activity that are employed in Section 3.1 to Section 3.3 for the screening of perovskites for thermochemical NH3 production. The reduction of N2 starts with the formation of O2 and oxygen vacancies at a metal oxide surface. The free energy required for this reaction, Gf [vO ], was computed with: (4)

where Gvo , Gs and Gr,OER [O] are the free energies of the metal oxide with oxygen vacancies (i.e., A2 B2 O5 (001) where ␦ = 0.5, as shown with Fig. 1, panels B and G), of the stoichiometric metal oxide without oxygen vacancies (i.e., A2 B2 O6 (001) where ␦ = 0, as shown with Fig. 1, panels A and F), and the reference energy of the lattice oxygen yielding 1/2O2 gas [43]. We note, negative free energies of reaction indicate exergonic processes. The free energy of forming lattice nitrogen in the metal oxide crystal lattice, Gf [N], was calculated with: Gf [N] = Gn − Gvo − Gr,NRR [N]

where Gr,AER [N] is the reference energy of the lattice nitrogen and H2 yielding NH3 (i.e., Gr,AER [N] = GNH3 –3/2GH2 ). Finally, the free energy of forming H2 and of filling oxygen vacancies with oxygen obtained from the WSR, Gf [O], was calculated with: Gf [O] = Gs − Gvo − Gr,WSR [O]

(9)

where Gr,WSR [O] is the reference energy of the lattice oxygen and H2 formed from H2 O (i.e., Gr,WSR [O] = GH2O − GH2 ). For metal nitride surfaces, Gf [NH3 ] was calculated by replacing Gvo and Gn in Eq. (8) with the free energies of the metal nitride with nitrogen vacancies (12.5% relative to the lattice nitrogen of the stoichiometric metal nitride surfaces shown with Fig. 1, panels K, L, and M) and of the stoichiometric metal nitride without nitrogen vacancies, respectively. Analogous to Eq. (7), the stability of nitrogen vacancies at metal nitride surfaces, Gsubsurf-surf [vN ], was calculated with: Gsubsurf -surf [vN ] = Gsvn − Gvn

(10)

where Gsvn and Gvn are the free energies of the metal nitride with nitrogen vacancies below the surface and of the metal nitride with nitrogen vacancies at the surface.

2.4. Descriptors of surface activity

Gf [vO ] = Gvo − Gs + Gr,OER [O]

(8)

(5)

where Gn and Gr,NRR [N] are the free energies of the metal oxide with lattice nitrogen (i.e., ␧ = 0.5, as shown with Fig. 1, panels D and I)

2.5. Thermochemical equilibrium calculations As a reference [21,25,47], the free energy changes of (1) reduction of MoO3 and MoO2 into Mo and O2 , (2) further reaction of Mo with N2 into Mo2 N, (3) reduction of MnO into Mn and O2 , and (4) further reaction of Mn with N2 into either Mn4 N or (6) Mn5 N2 were calculated from tabulated thermochemical data [46]. Data was extrapolated for MoO3 from 1127 ◦ C to 1400 ◦ C and for Mn4 N from 327 ◦ C to 400 ◦ C using third-order polynominal regressions with R2 > 0.999. 3. Results and discussion The following three sections screen perovskites for their potential as redox materials for solar-driven NH3 synthesis using the surface activity descriptors described in Section 2.4. 3.1. Reducing N2 at the ABO3 (001) surface To assess the possibility to produce O2 and oxygen vacancies that are active in N2 reduction into lattice nitrogen with

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perovskites, Fig. 2 plots the free energy of the N2 reduction, Gf [N], versus the free energy of the oxygen vacancy formation, Gf [vO ], for various perovskite surfaces at 1400 ◦ C, 0.01 bar O2 , and 0.99 bar N2 . Generally, we find that the redox energetics are more sensitive to the type of the B cation terminating the surface, than to that of the A cation. This can be seen by a partitioning of the Gf [vO ] values, which are within the relatively narrow ranges of −1.33 to 2.05, −0.49 to 2.58, 2.00 to 2.76, or 2.00 to 3.02 eV for ABO3 terminated surfaces with B = Co, Mn, Mo, or W, respectively, compared to −1.33 to 2.87, −1.30 to 3.02, or −0.40 to 2.83 eV for ABO3 terminated surfaces with A = Ca, Sr, and La, respectively. Furthermore, the plot shows a linear correlation of both reaction energetics at AMnO3 or ACoO3 terminated surfaces, i.e., Gf [N] = −0.958 × Gf [vO ] + 3.58 eV (R2 = 0.944), which reflects the redox trade-off between the OER and NRR. The slope is nearly −1, indicating an in principle identical underpinning process with inverse direction, that is the electron transfer from the oxygen anion to the solid when producing oxygen vacancies versus that from the solid to the nitrogen when consuming oxygen vacancies. The positive intercept of this correlation reflects the relative large amount of energy needed to break N2 triple bonds, compared to weaker O2 double bonds formed. That is, a surface that binds lattice oxygen weakly, allowing for a facile liberation of O2 , will bind lattice nitrogen weakly as well, limiting the N2 reduction yield [25]. The redox energetics at AMoO3 and AWO3 terminated surfaces favourably depart from this correlation (i.e., a steeper negative slope balancing the unfavourable positive intercept of the linear correlation). Oxygen vacancies formed by perovskites containing Mo or W at the surface have a stronger activity in reducing N2 into lattice nitrogen, relative to those containing Mn or Co at the surface. This can be understood due to the stable highly positive oxidation states of these transition metals. In that sense, an ideal perovskite redox material for N2 reduction would depart from this linear correlation in the same direction but without binding the lattice oxygen as strong, as AMoO3 and AWO3 terminated surfaces. For an energetically efficient N2 reduction into NH3 , the redox energetics are ideally exergonic and near-zero, as marked with quadrant A in Fig. 2. At the selected process conditions, we find that none of the studied surfaces is located within the desirable quadrant A in Fig. 2. At least one of the two reactions will show a low equilibrium yield at these conditions. This may be improved in various ways. On one hand, the extent of the endothermic OER may be increased by increasing temperature or by decreasing the partial pressure of O2 , comparable to the energetics of the metal oxide reduction step in solar-driven CO2 and H2 O splitting with redox cycles [1,3]. On the other hand, the extent of the exothermic NRR may be increased by decreasing the temperature. This is shown in Fig. 2 by more negative Gf [N] values for NRR at 400 ◦ C, which may be established during cooling, after producing oxygen vacancies at higher temperatures. As a reference for designing perovskite redox materials, Fig. 2 shows the free energy changes of the stoichiometric reduction of N2 with Mo and Mn into Mo2 N, Mn4 N, and Mn5 N2 , plotted versus those of the stoichiometric reduction of MoO3 , MoO2 , and MnO into Mo, Mn, and O2 , respectively. In principle, these metal nitride redox materials facilitate thermochemical reduction of N2 into NH3 . However, the equilibrium yield of at least one reaction is below half conversion, as indicated in Fig. 2 for example by the strongly endergonic character of the MnO reduction, and handling Mo2 N redox materials can be challenging due to the high volatility of MoO3 formed during the NH3 production [21,25,26,47]. Compared to these stoichiometric redox materials, non-stoichiometric perovskites offer the potential to tune the redox energetics at the surface, as shown with Fig. 2. From all converged perovskite surface calculations with OER at 1400 ◦ C and NNR at 400 ◦ C,

36.1% show a favorably short distance to the origin, compared to the minimum value for stable manganese nitrides (i.e., 2.41 eV). We find minimum values for CaCoO3 -ter. La0.5 Ca0.5 Mo0.5 Co0.5 O3 (1.54 eV), SrCoO3 -ter. Sr0.5 La0.5 Mo0.5 Co0.5 O3 (1.61 eV), and SrCoO3 ter. Sr0.5 La0.5 Co0.5 W0.5 O3 (1.62 eV), all with AO-type ter. Comparing the termination of all surfaces with a distance to the origin less than 2.41 eV shows that 72.6% are AO-type terminated, 16.7%, 15.5%, and 14.3% are terminated by CaCoO3 , CaMnO3 , and SrMnO3 , respectively, and 47.6%, 41.7%, and 40.5% contain Co, Mn, and Ca, respectively. This suggests a favorable redox trade-off may be achieved with perovskites containing Co or Mn at the surface and Co combined with Mo or W in the bulk. The ability to fix nitrogen with a stable non-stoichiometric perovskite is an attractive materials property when developing materials for a sustainable production of synthetic ammonia from air, water, and sunlight. Perovskites may accomplish this without the need of a chemical reducing agent [24,27], at the expense of a larger amount of redox material required for a certain yield of fixed nitrogen. The chemical stability of perovskites is discussed in detail in the literature [28,48]. We note, however, while stable perovskite crystal phases have been reported for compositions containing the metals that are investigated here at the A- or B-site, studies of perovskites containing W at the B-site are limited [28]. Some of the more promising perovskite compositions for N2 reduction, such as those based on SrCoO3 or SrMnO3 , have been investigated previously as stable redox materials for H2 O splitting or O2 separation [32,30].

3.2. Stability of oxygen vacancies and lattice nitrogen For an efficient utilization of the redox material, the formed oxygen vacancies should be stable, on one hand, at the surface to reduce N2 into lattice nitrogen at OER conditions. On the other hand, oxygen vacancies should also be stable below the surface to facilitate forming O2 from the lattice oxygen of the bulk and to realize the NNR at temperatures below those of the OER. That is, Gsurf-subsurf [vO ] = 0. The lattice nitrogen should be stable at sites below the surface at NRR conditions to provide active sites for continuous NRR, and at the surface at AER conditions to facilitate hydrogenation into NH3 . That is, Gsubsurf-surf [N] = 0. We note, these criteria may change if entropic contributions of the solids are included in Eqs. (6) and (7). Fig. 3 shows a plot of these two quantities. Generally, the major fraction of the perovskite compositions studied in this work is located in quadrant B, indicating materials with oxygen vacancies and lattice nitrogen that are both more stable below the surface, than at the surface. Particularly perovskite surfaces with BO2 -type geometry containing Mo or W exhibit this set of materials properties, as shown by the location of the empty light and dark green symbols in Fig. 3. Some surfaces that contain Co or Mn at the B-site of the surface termination are located in the other three quadrants, with AO-type surfaces typically closer to the ideal location, the origin. The shortest distance to the origin we find for CaMnO3 -ter. Sr0.5 Ca0.5 MnO3 (0.04 eV), LaCoO3 -ter. Sr0.5 La0.5 Co0.5 W0.5 O3 (0.07 eV), and CaCoO3 ter. La0.5 Ca0.5 Mo0.5 Co0.5 O3 (0.16 eV), all with AO-type ter. These perovskite compositions exhibiting the most promising oxygen vacancy and lattice nitrogen stabilities are identical or similar to those compositions exhibiting the most promising activities of their oxygen vacancies in O2 evolution and N2 reduction, as discussed in Section 3.1. However, we note an ultimate assessment of the availability of oxygen vacancies and lattice nitrogen for NH3 formation with perovskites requires also an assessment of the oxygen vacancy and lattice nitrogen conduction kinetics.


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3.3. Hydrogenating lattice nitrogen with H2 O into NH3

Acknowledgements

To assess the possibility of hydrogenating lattice nitrogen at perovskite surfaces with H2 O into NH3 and to fill the formed oxygen vacancies with oxygen derived from H2 O splitting, Fig. 4 plots the free energy of NH3 evolution, Gf [NH3 ], versus the free energy of H2 O splitting, Gf [O]. Generally, analogous to the tradeoff between OER and NRR, Fig. 4 quantifies a correlation between AER and WSR. This is due to weak lattice nitrogen binding yielding favourable NH3 formation energetics but unfavourable H2 O splitting energetics due to weak lattice oxygen binding. We note, clustering of perovskites containing Mo and W in their surface termination at negative Gf [O] and positive Gf [NH3 ] values is similar to the trend for OER and NRR, discussed in Section 3.1. Ideally, both reactions have a negative free energy change, which is accomplished at the selected conditions (i.e., 400 ◦ C, 0.1 bar NH3 , 0.9 bar H2 O, and 0.01 bar H2 ) by many compositions, indicated by data points located within the gray shaded rectangle. Analogous to the discussion in Section 3.1, the desirable reaction space for an energetically efficient NH3 production is marked with A in Fig. 4. We find the set of surface compositions located within quadrant A include promising surfaces that had been identified in the previous two sections, such as AO-type CaCoO3 -ter. La0.5 Ca0.5 Mo0.5 Co0.5 O3 (with a distance to the origin of 0.93 eV at 400 ◦ C), or that are similar in composition to previously identified promising surfaces, such as AO-type SrCoO3 -ter. Sr0.5 Ca0.5 Co0.5 W0.5 O3 (0.93 eV at 1000 ◦ C). We note, the large set of perovskite compositions in the exergonic reaction space indicates relatively high ammonia yields, compared to the limited NH3 yields [26] and energetics (Fig. 4) with binary nitrides of Mo and Mn. For this reason, perovskites may allow increasing the temperature of the AER to decrease irreversible heat losses and materials stress arising from the temperature swing of the redox cycle. Fig. 4 shows that a major fraction of the perovskites lies in the desirable exergonic reaction space even when conducting the AER and WSR at 1000 ◦ C. We note this conclusion holds also when decreasing the unknown value of pH2 (formally assumed in Eqs. (8) and (9)) from 0.01 to 0.001 bar, as this has a relatively minor effect on the WSR (Gf [O] more negative by 0.13 eV) and AER (Gf [NH3 ] more positive by 0.20 eV). In practice, this would require quick cooling of the formed NH3 to minimize its decomposition into N2 and H2 .

This work was supported financially by the European Research Council under the European Union’s ERC Advanced Grant (SUNFUELS − No. 320541). Electronic structure calculations were conducted at the High-Performance Computation cluster of ETH Zürich.

4. Conclusions We have developed descriptors for the surface activity of perovskites for a solar-driven thermochemical conversion of N2 and H2 O into NH3 and O2 , at ambient pressure and without chemical reducing agents or electricity. Density functional theory was employed to quantify the redox trade-off between the O2 evolution and N2 reduction at high temperatures and between H2 O splitting and NH3 evolution at low temperatures. While perovskites are promising redox materials due to their large oxygen nonstoichiometries, forming oxygen vacancies at high temperatures that are active in N2 reduction is the energetically limiting step of the redox cycle. Based on the surface activities in these reactions and the stability of oxygen vacancies and lattice nitrogen at the surface, we conclude that the redox energetics of perovskites for ammonia production are tunable by their composition and most sensitive to the type of transition metal at the B site that terminates the surface. Promising perovskites contain Co or Mn at the surface and Co doped with Mo or W in the bulk, such as CaCoO3 ter. La0.5 Ca0.5 Mo0.5 Co0.5 O3 , SrCoO3 -ter. Sr0.5 La0.5 Co0.5 W0.5 O3 , and CaMnO3 -ter. Sr0.5 Ca0.5 MnO3 . Future work will experimentally determine yields and kinetics of nitrogen fixation and ammonia formation.

Appendix A. The following Tables 1–3 provide a summary of the DFTcomputed lattice parameters and magnetic moments for bulk perovskites and the Mo2 N and Mn2 N reference metal nitrides. Comparing, for example, the computed value for the lattice constant of Sr0.5 La0.5 MnO3 (a = 3.957 Å) to the experimental value (3.915 Å for La0.67 Sr0.33 MnO3 ) [49] gives a relative error of 1.06%, which is a good agreement between theory and experiment. The DFTcomputed lattice constants for Mo2 N and Mn2 N compare also well with experimental values (a = 4.163 Å for Mo2 N [41] and a = 2.844 Å and c = 4.509 Å or Mn2 N [50]), that is a relative error of 0.32-2.57% which is within the uncertainty of DFT [43]. Table 1 The calculated lattice constants (a) and magnetic moments (M) of Mn and Co at the B-sites of ABO3 - and A0.5 A’0.5 BO3 -type perovskites. Perovskite bulk: cubic A0.5 A’0.5 B0.5 B’0.5 O3

a/Å

M(B)/␮B

M(B’)/␮B

CaMnO3 CaCoO3 CaMoO3 CaWO3 SrMnO3 SrCoO3 SrMoO3 SrWO3 LaMnO3 LaCoO3 LaMoO3 LaWO3 Sr0.5 La0.5 MnO3 Sr0.5 Ca0.5 MnO3 La0.5 Ca0.5 MnO3 Sr0.5 La0.5 CoO3 Sr0.5 Ca0.5 CoO3 La0.5 Ca0.5 CoO3 Sr0.5 La0.5 MoO3 Sr0.5 Ca0.5 MoO3 La0.5 Ca0.5 MoO3 Sr0.5 La0.5 WO3 Sr0.5 Ca0.5 WO3 La0.5 Ca0.5 WO3

3.846 3.842 4.008 4.021 3.920 3.918 4.055 4.065 3.997 3.907 4.073 4.081 3.957 3.884 3.924 3.911 3.879 3.877 4.065 4.032 4.045 4.076 4.044 4.057

2.844 2.306

2.845 2.307

2.891 2.355

2.892 2.356

3.833 1.771

3.834 1.776

3.368 2.866 3.358 2.120 2.323 2.082

3.370 2.867 3.360 2.122 2.324 2.083

Table 2 The calculated lattice constants (a) and magnetic moments (M) of Mn and Co at the B-sites of AB0.5 B’0.5 O3 - and A0.5 A’0.5 B0.5 B’0.5 O3 -type perovskites. Perovskite bulk: cubic A0.5 A’0.5 B0.5 B’0.5 O3

a/Å

M(B)/␮B

CaMn0.5 Mo0.5 O3 CaMn0.5 Co0.5 O3 CaMo0.5 Co0.5 O3 CaMn0.5 W0.5 O3 CaMo0.5 W0.5 O3 CaCo0.5 W0.5 O3 SrMn0.5 Mo0.5 O3 SrMn0.5 Co0.5 O3 SrMo0.5 Co0.5 O3 SrMn0.5 W0.5 O3 SrMo0.5 W0.5 O3 SrCo0.5 W0.5 O3 LaMn0.5 Mo0.5 O3

3.948 3.844 3.932 3.962 4.015 3.941 4.005 3.920 3.998 4.016 4.060 4.009 4.039

3.132 2.854

M(B’)/␮B 2.224 2.105

3.258 2.028 3.196 2.932 3.334 2.371 3.898

2.313 2.279

130


Table 2 (Continued) Perovskite bulk: cubic A0.5 A’0.5 B0.5 B’0.5 O3

a/Å

M(B)/␮B

M(B’)/␮B

LaMn0.5 Co0.5 O3 LaMo0.5 Co0.5 O3 LaMn0.5 W0.5 O3 LaMo0.5 W0.5 O3 LaCo0.5 W0.5 O3 Sr0.5 La0.5 Mn0.5 Mo0.5 O3 Sr0.5 La0.5 Mn0.5 Co0.5 O3 Sr0.5 La0.5 Mo0.5 Co0.5 O3 Sr0.5 La0.5 Mn0.5 W0.5 O3 Sr0.5 La0.5 Mo0.5 W0.5 O3 Sr0.5 La0.5 Co0.5 W0.5 O3 Sr0.5 Ca0.5 Mn0.5 Mo0.5 O3 Sr0.5 Ca0.5 Mn0.5 Co0.5 O3 Sr0.5 Ca0.5 Mo0.5 Co0.5 O3 Sr0.5 Ca0.5 Mn0.5 W0.5 O3 Sr0.5 Ca0.5 Mo0.5 W0.5 O3 Sr0.5 Ca0.5 Co0.5 W0.5 O3 La0.5 Ca0.5 Mn0.5 Mo0.5 O3 La0.5 Ca0.5 Mn0.5 Co0.5 O3 La0.5 Ca0.5 Mo0.5 Co0.5 O3 La0.5 Ca0.5 Mn0.5 W0.5 O3 La0.5 Ca0.5 Mo0.5 W0.5 O3 La0.5 Ca0.5 Co0.5 W0.5 O3

3.946 4.012 4.052 4.079 4.062 4.041 3.931 4.005 4.045 4.072 4.022 3.978 3.882 3.965 3.989 4.038 3.973 4.010 3.893 3.977 4.021 4.051 3.985

3.544

1.853 2.012

3.895 2.840 3.096 3.164

2.216 2.105

3.639 2.320 3.165 2.891

2.267 2.164

3.298 2.156 3.540 3.116

2.138 1.993

3.624 1.996

Table 3 The calculated lattice constants (a, c) and magnetic moment of Mn (M) for the indicated metal nitrides. Metal nitride bulk

a/Å

c/Å

M/␮B

cubic Mo2 N hexagonal Mn2 N

4.220 2.855

4.400

2.210

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