Moulay Jingkun Li

Tahar Sougrati

Andrea Zitolo

James M Ablett

Ismail Can Oğuz

Tzonka Mineva

Ivana Matanovic

Plamen Atanassov

Ying Huang

Iryna Zenyuk

Moulay Tahar Sougrati

Andrea Di Cicco

Kavita Kumar

Laetitia Dubau

Frédéric Maillard

Goran Dražić

Frédéric Jaouen
email: frederic.jaouen@umontpellier.fr

Identification of Durable and Non-Durable FeNx Sites in Fe-N-C Materials for Proton Exchange Membrane Fuel Cells

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Abstract

While Fe-N-C materials are a promising alternative to platinum for catalysing the oxygen reduction reaction (ORR) in acidic polymer fuel cells, limited understanding of their operando degradation restricts rational approaches towards improved durability. Here we show that Fe-N-C catalysts initially comprising two distinct FeN x sites (S1 and S2) degrade via the transformation of S1 into iron oxides while the structure and number of S2 were unmodified. Structure-activity correlations drawn from end-of-test [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy reveal that both sites initially contribute to the ORR activity but only S2 significantly contributes after 50 h of operation. From in situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy in inert gas coupled to calculations of the Mössbauer signature of FeN x moieties in different electronic states, we identify S1 to be a high-spin FeN 4 C 12 moiety and S2 a low-or intermediate-spin FeN 4 C 10 moiety. These insights lay the ground for rational approaches towards Fe-N-C cathodes with improved durability in acidic fuel cells.

Catalysis of the ORR is a cornerstone of industrially-relevant electrochemical devices [START_REF] Katsounaros | Oxygen electrochemistry as a cornerstone for sustainable energy conversion[END_REF] that convert chemical energy into electric power (metal-air batteries, [START_REF] Chen | Enhanced oxygen reduction with single-atomic-site iron catalysts for a zinc-air battery and hydrogen-air fuel cell[END_REF][START_REF] Jung | An improved highperformance lithium-air battery[END_REF] fuel cells (FCs), [START_REF] Chen | Enhanced oxygen reduction with single-atomic-site iron catalysts for a zinc-air battery and hydrogen-air fuel cell[END_REF][START_REF] Sharma | Support materials for PEMFC and DMFC electrocatalysts-a review[END_REF][START_REF] Rahimnejad | Microbial fuel cell as new technology for bioelectricity generation: a review[END_REF] or electric power into high-added value products (H 2 O 2 , [START_REF] Yin | 2, 2'-Dipyridylamine as Heterogeneous organic molecular electrocatalyst for two-electron oxygen reduction reaction in acid media[END_REF][START_REF] Sun | Activityselectivity trends in the electrochemical production of hydrogen peroxide over single-site metal-nitrogen-carbon catalysts[END_REF][START_REF] Yang | Toward the decentralized electrochemical production of H 2 O 2 : a focus on the catalysis[END_REF] Cl 2 with oxygendepolarized cathodes [START_REF] Moussallem | Development of high-performance silver-based gas-diffusion electrodes for chlor-alkali electrolysis with oxygen depolarized cathodes[END_REF][START_REF] Ziegelbauer | Chalcogenide electrocatalysts for oxygen-depolarized aqueous hydrochloric acid electrolysis[END_REF][START_REF] Li | Highly active and stable Fe-N-C catalyst for oxygen depolarized cathode applications[END_REF] ). The pH in those devices establishes the ground for selecting materials with promising ORR activity and durability. While proton exchange membrane FCs (PEMFCs) are appealing, [START_REF] Wang | Achievements, challenges and perspectives on cathode catalysts in proton exchange membrane fuel cells for transportation[END_REF] their acidic environment is challenging. Platinum-based catalysts now reach high activity and durability, [START_REF] Ott | Ionomer distribution control in porous carbon-supported catalyst layers for high-power and low Pt-loaded proton exchange membrane fuel cells[END_REF][START_REF] Huang | High-performance transition metal-doped Pt 3 Ni octahedra for oxygen reduction reaction[END_REF] but catalysts free of Pt-group-metals remain topical for cost and sustainability reasons. Although metal-nitrogen-carbon (M-N-C) catalysts (M=Fe, Co) have demonstrated high ORR activity, [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF][START_REF] Proietti | Iron-based cathode catalyst with enhanced power density in polymer electrolyte membrane fuel cells[END_REF][START_REF] Chung | Direct atomic-level insight into the active sites of a high-performance PGM-free ORR catalyst[END_REF] their durability in PEMFC is poor.

Their most active sites are atomically-dispersed MN x moieties, [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF][START_REF] Chung | Direct atomic-level insight into the active sites of a high-performance PGM-free ORR catalyst[END_REF] and main degradation mechanisms in acidic medium are demetallation, [START_REF] Choi | Minimizing operando demetallation of Fe-NC electrocatalysts in acidic medium[END_REF][START_REF] Choi | Unraveling the nature of sites active toward hydrogen peroxide reduction in Fe N C catalysts[END_REF][START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF][START_REF] Chenitz | A specific demetalation of Fe-N 4 catalytic sites in the micropores of NC_Ar + NH 3 is at the origin of the initial activity loss of the highly active Fe/N/C catalyst used for the reduction of oxygen in PEM fuel cells[END_REF][START_REF] Ferrandon | Stability of iron species in heat-treated polyaniline-iron-carbon polymer electrolyte fuel cell cathode catalysts[END_REF] surface carbon oxidation via Fenton reactions, [START_REF] Lefèvre | Fe-based catalysts for the reduction of oxygen in polymer electrolyte membrane fuel cell conditions: determination of the amount of peroxide released during electroreduction and its influence on the stability of the catalysts[END_REF][START_REF] Choi | The achilles' heel of iron-based catalysts during oxygen reduction in an acidic medium[END_REF] bulk carbon corrosion, [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF][START_REF] Choi | Stability of Fe-N-C catalysts in acidic medium studied by operando spectroscopy[END_REF][START_REF] Goellner | Degradation of Fe/N/C catalysts upon high polarization in acid medium[END_REF] and protonation of nitrogen groups followed by anion adsorption -a phenomenon particularly important for Fe-N-C catalysts comprising highly basic N-groups. [START_REF] Herranz | Unveiling Nprotonation and anion-binding effects on Fe/N/C catalysts for O 2 reduction in protonexchange-membrane fuel cells[END_REF] Exacerbated demetallation was recently reported in oxygenated acid medium for highly-active NH 3 -pyrolyzed Fe-N-C catalysts, explaining their poor durability in PEMFC. [START_REF] Chenitz | A specific demetalation of Fe-N 4 catalytic sites in the micropores of NC_Ar + NH 3 is at the origin of the initial activity loss of the highly active Fe/N/C catalyst used for the reduction of oxygen in PEM fuel cells[END_REF][START_REF] Santori | Effect of Pyrolysis Atmosphere and electrolyte pH on the oxygen reduction activity, stability and spectroscopic signature of FeN x moieties in Fe-N-C catalysts[END_REF] The demetallation rate was measured online in acidic aqueous condition, [START_REF] Santori | Effect of Pyrolysis Atmosphere and electrolyte pH on the oxygen reduction activity, stability and spectroscopic signature of FeN x moieties in Fe-N-C catalysts[END_REF] or indirectly assessed by [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy. [START_REF] Chenitz | A specific demetalation of Fe-N 4 catalytic sites in the micropores of NC_Ar + NH 3 is at the origin of the initial activity loss of the highly active Fe/N/C catalyst used for the reduction of oxygen in PEM fuel cells[END_REF] In contrast, high stability in acidic medium was reported by us for two catalysts exclusively comprising FeN x moieties, with only 25 % activity decrease after 30,000 load-cycles in Ar-saturated 0.1 M H 2 SO 4 at 80°C. [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF] However, after 10,000 load-cycles in the same conditions but in O 2 -saturated electrolyte, the decrease in activity and number of FeN x moieties was 65 and 83 %, respectively, forming iron oxide particles during cycling. [START_REF] Kumar | On the influence of oxygen on the degradation of Fe-N-C catalysts[END_REF] Carbon corrosion was observed from Raman spectroscopy after load cycles in O 2 -saturated electrolyte, [START_REF] Kumar | On the influence of oxygen on the degradation of Fe-N-C catalysts[END_REF] while restricted changes in cyclic voltammetry (restricted carbon corrosion) was observed by Dodelet et al. for an NH 3pyrolyzed Fe-N-C after a voltage hold of 6 h at 0.6 V in H 2 /air PEMFC at 80°C. [START_REF] Chenitz | A specific demetalation of Fe-N 4 catalytic sites in the micropores of NC_Ar + NH 3 is at the origin of the initial activity loss of the highly active Fe/N/C catalyst used for the reduction of oxygen in PEM fuel cells[END_REF] Therefore, Fe-N-C catalysts comprising more of the durable FeN x sites and less of the nondurable ones should be targeted. Before the community can engage in this challenge, the identification of which FeN x sites are durable and which are not is required. It was revealed with ex situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy that Fe-N-C catalysts comprise two types of FeN x sites, labelled D1 (doublet with quadrupole splitting (QS) values of 0.9-1.2 mm•s -1 ) and D2 (QS=1.8-2.8 mm•s -1 ), both having a similar isomer shift (IS). [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Kramm | Structure of the catalytic sites in Fe/N/C-catalysts for O 2 -reduction in PEM fuel cells[END_REF][START_REF] Kramm | Correlations between mass activity and physicochemical properties of Fe/N/C catalysts for the ORR in PEM fuel cell via 57 Fe Mossbauer spectroscopy and other techniques[END_REF] By bridging density functional theory calculations on QS-values with ex situ Mössbauer spectroscopy, we identified D1 to be a high-spin Fe(III)N x site (iron site S1) and D2 a low/medium-spin Fe(II)N x site (iron site S2), [START_REF] Mineva | Understanding active sites in pyrolyzed Fe-N-C catalysts for fuel cell cathodes by bridging density functional theory calculations and 57 Fe Mössbauer Spectroscopy[END_REF] in general agreement with two recent studies. [START_REF] Wagner | Elucidating the structural composition of a Fe-N-C catalyst by nuclear and electron resonance techniques[END_REF][START_REF] Zelenay | Hydrogen and Fuel Cells Program-2019 Annual Merit Review and Peer Evaluation Meeting-ElectroCat (Electrocatalysis Consortium[END_REF] While these sites are ubiquitous in Fe-N-C catalysts, their respective activity and durability are unknown.

Here, we separately interrogate S1 and S2 with in situ, operando and end-of-test (EoT) spectroscopies (see self-consistent definitions in Supplementary Note 1). With in situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy in O 2 -free PEMFC, we demonstrate that a fraction of S1 is stable, reversibly changing from high-spin ferric to high-spin ferrous state between 0.8 and 0.2 V, while the electronic state of S2 is potential-independent, being ferrous low-or medium-spin.

Ex situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy at 5 K after PEMFC potentiostatic operation reveals that S2 is durable while S1 is not, with corresponding Fe cations forming ferric oxide nanoparticles. We also provide evidence that S2 is the main contributor to ORR activity in PEMFC after short operation time.

Results

Ex situ characterization of pristine Fe-N-C catalysts

This study was conducted on two Fe-N-C catalysts, previously demonstrated to be free of iron clusters and containing only single-metal-atom FeN x sites, synthesized as previously reported (see Methods) [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF] and labelled Fe 0.5 (pyrolysis in argon) and Fe 0.5 -950 (10) (pyrolysis of Fe 0.5 in NH 3 at 950 °C for 10 min). Their ex situ structure and morphology are reported in Extended Data Figure 1 and Supplementary Table 1, the main ex situ differences between them being the higher surface basicity and microporous area of Fe 0.5 -950 (10). No Fe particles were observed by transmission electron microscopy (TEM) in both pristine powder catalysts, and the atomic-dispersion of Fe in Fe 0.5 was further confirmed by STEM (Extended Data Figure 1g-i). Their initial ORR activities in PEMFC (Figure 1a) are similar to values reported in Ref. 15 and representative for state-of-art Fe-N-C catalysts. [START_REF] Chung | Direct atomic-level insight into the active sites of a high-performance PGM-free ORR catalyst[END_REF][START_REF] Chenitz | A specific demetalation of Fe-N 4 catalytic sites in the micropores of NC_Ar + NH 3 is at the origin of the initial activity loss of the highly active Fe/N/C catalyst used for the reduction of oxygen in PEM fuel cells[END_REF][START_REF] Banham | Critical advancements in achieving high power and stable nonprecious metal catalyst-based MEAs for real-world proton exchange membrane fuel cell applications[END_REF] NH 3 pyrolysis introduces highly-basic nitrogen groups, increasing the turnover frequency (TOF) of FeN x sites but leading to decreased durability in PEMFC. [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Proietti | Iron-based cathode catalyst with enhanced power density in polymer electrolyte membrane fuel cells[END_REF] This was recently explained by higher demetallation rates for NH 3 -vs. Ar-treated Fe-N-C catalysts in acid medium, [START_REF] Proietti | Iron-based cathode catalyst with enhanced power density in polymer electrolyte membrane fuel cells[END_REF][START_REF] Santori | Effect of Pyrolysis Atmosphere and electrolyte pH on the oxygen reduction activity, stability and spectroscopic signature of FeN x moieties in Fe-N-C catalysts[END_REF] while demetallation rates were equally low in alkaline medium. [START_REF] Santori | Effect of Pyrolysis Atmosphere and electrolyte pH on the oxygen reduction activity, stability and spectroscopic signature of FeN x moieties in Fe-N-C catalysts[END_REF] These results support the involvement of highly basic nitrogen-groups in a significant fraction of FeN x sites in Fe 0.5 -950 (10), leading to higher TOF but also fast protonation of N-groups in acid medium, leading to demetallation of the most active sites. Due to its high stability in acid, [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF] Fe 0.5 was selected for in situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy in PEMFC. The ex situ Mössbauer spectra at 300 K of Fe 0.5 (powder) and Fe 0.5 -cathode are identical, identifying only D1 and D2 (Extended Data Figure 2a-b). However, one cannot exclude the formation of superparamagnetic ferric oxide nanoparticles during cathode preparation, which would contribute with a doublet overlapping with D1 signal from S1 sites. [START_REF] Zboril | Iron(III) oxides from thermal processes -synthesis, structural and magnetic properties, Mössbauer spectroscopy characterization, and applications[END_REF] To unveil this degeneracy, the spectra were acquired at lower temperature (5 K), which increases the magnetization time constant of nano ferric-oxides, contributing then with a sextet component, [START_REF] Kamali-M | Characterization of iron oxide nanoparticles by Mössbauer spectroscopy[END_REF][START_REF] Lyubutin | Structural and magnetic properties of iron oxide nanoparticles in shells of hollow microcapsules designed for biomedical applications[END_REF] while the signal of S1 remains a doublet. [START_REF] Sougrati | Probing active sites in iron-based catalysts for oxygen electro-reduction: A temperature-dependent 57 Fe Mössbauer spectroscopy study[END_REF] At 5 K, no sextet was visible for Fe 0.5 while a broad sextet representing only 9 % of the absorption area, assigned to superparamagnetic ferric oxide, appeared for Fe 0.5 -cathode (Extended Data Figure 2c-d). Thus, the low-QS doublet (labelled D1) in the Fe 0.5 -cathode spectrum at 300 K can mainly be assigned to S1 sites.

Operando X-ray absorption spectroscopy of Fe 0.5 in PEMFC Operando (extended) X-ray absorption near-edge and fine structure (XANES and EXAFS, respectively) was acquired at Fe K-edge with fast acquisition mode in PEMFC (Cell 2, [START_REF] Principi | Performance of a fuel cell optimized for in situ X-ray absorption experiments[END_REF] Supplementary Figure 1a, Supplementary Note 2). Reversible changes with electrochemical potential were revealed (Figure 1b, Extended Data Figure 3), confirming in PEMFC the in situ and/or operando XANES-EXAFS results previously measured in aqueous acidic electrolyte for Fe 0.5 and other catalysts comprising only/mostly FeN x sites. [START_REF] Chen | Enhanced oxygen reduction with single-atomic-site iron catalysts for a zinc-air battery and hydrogen-air fuel cell[END_REF][START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF][START_REF] Li | Structural and mechanistic basis for the high activity of Fe-N-C catalysts toward oxygen reduction[END_REF][START_REF] Osmieri | Elucidation of Fe-N-C electrocatalyst active site functionality via in-situ X-ray absorption and operando determination of oxygen reduction reaction kinetics in a PEFC[END_REF] Operando XANES spectra indicate a Fe(III)/Fe(II) redox transition and conformational changes of a significant fraction of FeN x sites in the region 0.2-0.8 V (Extended Data Figure 3a), while operando EXAFS spectra indicate a change from an average O-Fe(III)N 4 to Fe(II)N 4 coordination as the potential is decreased (Extended Data Figure 3b). [START_REF] Li | Structural and mechanistic basis for the high activity of Fe-N-C catalysts toward oxygen reduction[END_REF][START_REF] Osmieri | Elucidation of Fe-N-C electrocatalyst active site functionality via in-situ X-ray absorption and operando determination of oxygen reduction reaction kinetics in a PEFC[END_REF][START_REF] Li | Asymmetric volcano trend in oxygen reduction activity of Pt and non-Pt catalysts: in situ identification of the site-blocking effect[END_REF] The redox transition is also seen by cyclic voltammetry in acid electrolyte and in line with the decreased average oxidation state of Fe identified by the threshold energy of the XANES spectrum (Extended Data Figure 3c).

In situ Mössbauer spectroscopy of Fe 0.5 in PEMFC X-ray absorption spectroscopies (XAS) however fail to provide separate information on S1 and S2. To this end, we resorted to in situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy with an inhouse single-cell PEMFC (Cell 3, Supplementary Figure 1b, Supplementary Note 2), whose proper electrochemical response was verified (Supplementary Figure 2). The transmitted γray signal was continuously acquired for 36 h during each in situ potentiostatic experiments at room temperature, with humidified H 2 /argon at anode/cathode. Following the potentiostatic controls shown in Extended Data Figure 4, we identified irreversible changes in the Mössbauer spectra of Fe 0.5 -cathode (during the first two cycles, discussed later) and, thereafter, reversible changes triggered by the potential. Figure 1c-d shows reversible changes for in situ Mössbauer spectra measured at 0.8 and 0.2 V during cycle 4, labelled 0.8 V (4) and 0.2 V (4). The hyperfine parameters IS and QS of D1 (labelled D1H for in situ spectra, see later) and of D2 are similar at 0.8 V (4) to those measured ex situ for the pristine Fe 0.5 -cathode (Supplementary Table 2). In contrast, at 0.2 V (4), both the IS and QS values for D1 (labelled D1L, see later) significantly increased, while those for D2 were unmodified (Figure 1d, Supplementary Table 2, row "0.2 V (4)"). After all potential holds (Extended Data Figure 4), we verified with ex situ Mössbauer spectroscopy at 5 K that the low-QS doublet (labelled D1H and observed in situ at high potential in cycles 1-4) can still be assigned to S1 sites (Supplementary Figure 3). D1H and D1L therefore represent the in situ Mössbauer signal of S1 sites at high and low potential, respectively. Figure 1c-d also identifies a third doublet D3, independent of potential and related to irreversible changes occurring to the Fe 0.5 -cathode during cycle 1 (discussed later).

We now discuss trends for all in situ Mössbauer spectra acquired at various potentials.

The spectrum 0.8 V (1) shows the doublets D1-D2 (Supplementary Figure 4a), with same IS and QS values as those of the pristine Fe 0.5 -cathode at 300 K (Extended Data Figure 2b).

However, the ratio D1/D2 is lower in 0.8 V (1) (Supplementary Table 2), indicating that some unstable S1 sites were lost during the 36 h-long 0.8 V (1) experiment. From 0.8 V (1) to 0.2 V (1), the spectral parameters and intensity of D2 remained unchanged (Supplementary Figure 4a-b). This applies also to all subsequent potential holds (Supplementary Figures 5678). In contrast, the signal from S1 at high potential (D1H) in 0.8 V (1) resulted in a much less intense central doublet in 0.2 V (1) (grey doublet in Supplementary Figure 4b). This indicates demetallation of a significant fraction of sites S1 during the first hold at 0.2 V, in line with 15-40% activity loss after 10k load-cycles in inert gas reported by us for two Fe-N-C catalysts (almost) exclusively comprising FeN x sites. [START_REF] Kumar | Physical and chemical considerations for improving catalytic activity and stability of non-precious-metal oxygen reduction reaction catalysts[END_REF] Since the 0.2 V (1) spectrum was acquired for 36 h, it may be regarded as a time-averaged spectrum reflecting irreversible phenomena. A detailed analysis of the time-dependence of 0.2 V (1) spectrum clearly reveals this (Supplementary Figure 9, Supplementary Note 3). During cycles 2-4 however, the switch between D1H and D1L was triggered solely by the electrochemical potential, with distinct IS and QS values (Figure 2a-b, Supplementary Figure 5b). Regarding doublet D3 (IS~1.15•mm s -1 and QS~2.5 mm•s -1 ), it appeared first in 0.2 V (1) (Supplementary Figure 4b) and is unambiguously assigned to high-spin Fe 2+ species due to its high IS. [START_REF] Fultz | Mössbauer spectrometry[END_REF][START_REF] Bonomi | Properties and Applications[END_REF] The spectral parameters and intensity of D3 remained almost unchanged from 0.2 V ( 1) and during all subsequent potential holds (Figure 2e-f, Supplementary Figures 5678). From 0.8 V (2) and afterwards, all spectral changes only reflect the reversible potential dependence of the Mössbauer signature from S1 sites (Figure 2, Supplementary Figures 567). To gain understanding on D3, we performed EoT Mössbauer spectroscopy of the Fe 0.5 -cathode at various temperatures, after completing all in situ measurements (Supplementary Figures 3b, 10-11, Supplementary Table 3, Supplementary Note 4). In summary, the in situ D3 component is assigned to high-spin Fe 2+ cations (possibly complexed with Nafion® sulfonic acid groups), formed from the demetallation of a fraction of S1 sites during 0.2 V (1) (scheme in Extended Data Figure 5). When exposed to air, such cations form superparamagnetic ferric oxide nanoparticles, overlapping then with D1 at 300 K (Supplementary Figure 10a-b). At T ≤ 80 K, they however then contribute with a sextet component with IS and hyperfine magnetic field corresponding to ferric oxide (Supplementary Figure 10b-f). A summary of the inter-relation between the Mössbauer components ex situ, in situ, and EoT after in situ measurements is given in Supplementary Table 4.

Reversibly-changing in situ coordination of S1 with potential

We now discuss the structures and electronic states of S1 and S2. The in situ (absence of O 2 ) Mössbauer signal of the fraction of S1 sites that survived 0.2 V (1) reversibly switches between D1L at 0.2 V and D1H at 0.8 V (Figure 2a-b). D1H is identical to D1 measured ex situ on pristine Fe 0.5 , that we recently identified to be mainly Fe(III)N 4 C 12 periodic or cluster structures in high-spin state, with axial oxygen adsorbates. [START_REF] Mineva | Understanding active sites in pyrolyzed Fe-N-C catalysts for fuel cell cathodes by bridging density functional theory calculations and 57 Fe Mössbauer Spectroscopy[END_REF][START_REF] Li | Structural and mechanistic basis for the high activity of Fe-N-C catalysts toward oxygen reduction[END_REF] Due to its high IS-value, the assignment of D1L to a high-spin Fe(II) species is straightforward. [START_REF] Fultz | Mössbauer spectrometry[END_REF][START_REF] Bonomi | Properties and Applications[END_REF] Consequently, only a restricted change in the average iron-spin is expected for Fe 0.5 -cathode between high and low potential. We used a three-electrode cell (Cell 4, [START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF] Supplementary Figure 1c, Supplementary Note 2) to verify this with in situ Fe K β X-ray emission spectroscopy (XES), a technique well-suited to investigate the spin-state of metal centers. [START_REF] Vankó | Probing the 3d spin momentum with X-ray emission spectroscopy: The case of molecularspin transitions[END_REF] The overlapping in situ XES spectra at 0.2 and 0.8 V support that the sites S1 are in high-spin at all potentials (Supplementary Figure 12). The switch from D1H to D1L signal for S1 is thus the outcome of the reduction from Fe(III)N 4 C 12 to Fe(II)N 4 C 12 , also triggering the removal of an axial OH-adsorbate. To further support this, we applied our recently reported DFT methods [START_REF] Mineva | Understanding active sites in pyrolyzed Fe-N-C catalysts for fuel cell cathodes by bridging density functional theory calculations and 57 Fe Mössbauer Spectroscopy[END_REF] 5). The QS-values of high-spin Fe(II)N 4 C 10 structures are >3.0 mm•s -1 , significantly higher than those of D1L (Supplementary Table 5). These results confirm our recent assignment of D1 to high-spin Fe(III)N 4 C 12 structures with axial oxygen ligand, [START_REF] Mineva | Understanding active sites in pyrolyzed Fe-N-C catalysts for fuel cell cathodes by bridging density functional theory calculations and 57 Fe Mössbauer Spectroscopy[END_REF] and reveal their switch to high-spin Fe(II)N 4 C 12 structures, without axial ligand, at low potential (D1L). Operando EXAFS spectra (Extended Data Figure 3b) also support that the Fe(III)-to-Fe(II) reduction is accompanied by desorption of oxygen adsorbates. [START_REF] Li | Structural and mechanistic basis for the high activity of Fe-N-C catalysts toward oxygen reduction[END_REF][START_REF] Jia | Experimental observation of redoxinduced Fe-N switching behavior as a determinant role for oxygen reduction activity[END_REF] This redox switch is in line with in situ/operando XAS on numerous Fe-N-C catalysts [START_REF] Chen | Enhanced oxygen reduction with single-atomic-site iron catalysts for a zinc-air battery and hydrogen-air fuel cell[END_REF][START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF][START_REF] Li | Structural and mechanistic basis for the high activity of Fe-N-C catalysts toward oxygen reduction[END_REF][START_REF] Osmieri | Elucidation of Fe-N-C electrocatalyst active site functionality via in-situ X-ray absorption and operando determination of oxygen reduction reaction kinetics in a PEFC[END_REF] and with the significant presence of S1 in Fe-N-C catalysts. [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF][START_REF] Kramm | Structure of the catalytic sites in Fe/N/C-catalysts for O 2 -reduction in PEM fuel cells[END_REF][START_REF] Kramm | Correlations between mass activity and physicochemical properties of Fe/N/C catalysts for the ORR in PEM fuel cell via 57 Fe Mossbauer spectroscopy and other techniques[END_REF][START_REF] Li | Structural and mechanistic basis for the high activity of Fe-N-C catalysts toward oxygen reduction[END_REF] Here, we show that S1 undergoes this redox transition, but not S2. We then analysed the potential-dependence of the S1 hyperfine parameters. Figure 3a-b shows that they can be divided into those below 0.5 V and those above (D1L and D1H, respectively). For comparison, Figure 3c reports the DFT-calculated QS for high-spin OH-Fe(III)-N 4 C 12 and high-spin Fe(II)-N 4 C 12 structures, demonstrating that our DFT method correctly reproduces the change in QS. Supplementary Table 4 summarises the main findings on D1H and D1L and how they inter-relate with the site S1.

Different fates of sites S1 and S2 in an operating PEMFC

We then attempted to investigate the electronic states and durability of S1 and S2 with operando (O 2 ) Mössbauer spectroscopy. However, this proved impossible for S1. After a single potential hold at 0.2 V in O 2 , no S1 sites were observed in the EoT Mössbauer spectrum at 5 K while two sextets appeared, assigned to ferric oxide particles (Extended Data Figure 6c). The relative amount of sextets is much higher than in the pristine Fe 0.5 -cathode (Extended Data Figure 6a), supporting that the major fraction of S1 sites survived the MEA preparation, but transformed to ferric oxides during fuel cell testing. The cathode was also characterized before and after the potential hold with TEM (Extended Data Figure 6b,d) and XRD (Extended Data Figure 6e). Only TEM after operation identified Fe particles of ca 5-15 nm size. The operando Mössbauer spectra were comparable at OCP and 0.2 V (not shown) which, combined with the EoT spectrum at 5 K, suggests that the D1-like signal identified at 0.2 V under operando conditions already originated from ferric oxides instead of S1 sites.

The presence of ferric oxides at 0.2 V in turn suggests those particles are not electronically connected to the cathode, but only in contact with Nafion phase. In contrast, the parameters and absolute intensity of D2 were unmodified before and after 0.2 V hold in O 2 (Supplementary Table 6). This indicates that the electronic state of S2 is potentialindependent in the range 0.2-0.9 V and independent of the presence/absence of O 2 . This in turn indicates that S2 is either not accessible to O 2 or binds O 2 weakly, in line with our ex situ analysis. [START_REF] Mineva | Understanding active sites in pyrolyzed Fe-N-C catalysts for fuel cell cathodes by bridging density functional theory calculations and 57 Fe Mössbauer Spectroscopy[END_REF] The activity of Fe 0.5 -cathode before and after operando measurements (Cell 3) was measured in Cell 1 at 80°C. A restricted ORR-activity decrease from 23 to 15 mA•cm -2 is observed at 0.8 V (Extended Data Figure 6f). The remaining activity is much higher than that of the Fe-free N-doped carbon matrix (N-C), [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF] implying that either S2 or ferric oxides are active. To evaluate the ORR activity of the latter, we precipitated Fe 2 O 3 nanoparticles on the same N-C support. The activity of Fe 2 O 3 /N-C above 0.7 V is within reproducibility equal to that of N-C, implying no or negligible ORR activity of Fe 2 O 3 (Supplementary Figure 14).

To follow spectral changes as a function of operating time, a series of cathodes was prepared from a same Fe 0.5 batch and operated at 0.5 V in Cell 1 for either 5, 10, 25 or 50 h. Polarisation curves were recorded before and after each experiment. Each MEA was characterized with EoT [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy at 5 K (Figure 4a-c

, Supplementary

Figure 15, Supplementary Table 7). The fittings indicate unmodified spectral parameters and absolute intensity for D2 with operation time, continuously decreasing signal intensity for D1 and continuously increasing signal intensity for the two sextets, assigned to superparamagnetic ferric oxide (Figure 4a-c, Supplementary Figure 15). EoT XANES reveals only minor changes (Supplementary Figure 16a) while EXAFS spectra after 10-50 h reveal a small increase in the Fe-Fe signal at ~2.7 Å, matching the Fe-Fe distance in Fe 2 O 3 (Supplementary Figure 16b). X-ray computed tomography performed ex situ after 50 h of operation at 0.5 V shows the presence of Fe particles (Figure 4e, Supplementary Figure 17a).

Most particles are present on or near the outer surface of the N-C matrix. Size distribution analysis (Supplementary Figure 17b) reveals the presence of particles 5 to 60 nm in size, with the most frequent sizes being between 5 and 10 nm (47.5%). The initial and final polarisation curves indicate a sharp activity decrease after 5 h operation at 0.5 V followed by a slow but steady activity decrease (Figure 4d, Supplementary Figure 18a).

Evidence for ORR activity contributions from S1 and S2 sites

To identify structure-activity relationships, we plotted the absolute area of each spectral component and the current density at 0.8 V as a function of time (Figure 5a-d). The results indicate a trend of decreased activity with operation time, decreasing amount of sites S1, increasing amount of ferric oxides (sextets) and unchanged amount of sites S2. Based on this, we plotted in Figure 5e the current density at 0.8 V as a function of the absolute absorption area for either D1 or (D1+D2). Except for the initial activity measurements, the results reveal a linear correlation between the activity and either D1 or (D1+D2), demonstrating that S1 contributes to ORR activity. The data for the initial activity (star symbol) is an outlier and this can be explained by a higher TOF of Fe-based sites during the first polarisation curve. This hypothesis is in line with our recent work that demonstrated decreased TOF of Fe-based sites by chemical reaction of Fe 0.5 with H 2 O 2 . [START_REF] Choi | The achilles' heel of iron-based catalysts during oxygen reduction in an acidic medium[END_REF] The activity drop from 0 to 5 h of operation is thus assigned to both decreased TOF via mild surface oxidation of carbon (vertical arrows in Figure 5e), and decreased number of S1 sites (arrows along the dashed lines in Figure 5e). After 5 h operation, the TOF of the Fe sites seems stabilized, leading to linear correlations between the overall activity and either D1 or D1+D2. The extrapolation at x = 0 of the plot of activity vs. absolute area of D1 leads however to a positive y-intercept, indicating that the Fe 0.5 -cathode should have a significant ORR activity even in the absence of S1. This is supported by the results after operation at 0.2 V in O 2 (Extended Data Figure 6). In contrast, the extrapolation at x = 0 of the plot of activity vs. absolute area of D1H+D2 is near zero, supporting the fact that both S1 and S2 are ORRactive in acidic medium. A rigorous analysis shows that this near-zero y-intercept can be interpreted either as S2 sites being all located on the surface and having a similar TOF as S1, or only a fraction of S2 sites are on the surface and implying then a higher TOF than S1 (Supplementary Note 5). From EoT Raman spectroscopy, no carbon corrosion was identified (Supplementary Figure 18b). We verified that these trends also apply to the initially more active Fe 0.5 -950 (10) catalyst (Extended Data Figure 7, Supplementary Table 8, and Supplementary Note 6). The relative % area of D1 decreased from 32 to 6 % during 50 h at 0.5 V for Fe 0.5 -950 (10) and from 43 to 6% for Fe 0.5 . For D2, the relative % area decreased from 40 to 38 % in 50 h for Fe 0.5 -950 (10) but slightly increased from 49 to 51 % for Fe 0.5 .

The variation of ± 2 % in D2 is within the error, and D2 can be considered durable in both cathodes. Comparative STEM-EDX analysis of Fe 0.5 -950(10) fresh and aged (50 h at 0.5 V) cathodes identify few large Fe particles in the fresh cathode but numerous Fe nanoparticles after aging (Supplementary Figure 19). In addition, the correlation between Fe and F mapping in the aged cathode suggests that Fe clustering is linked to the presence of Nafion ionomer (Supplementary Figure 20).

Conclusions

In conclusion, we identify with Mössbauer spectroscopy the high-spin S1 site and the low-or intermediate-spin S2 site, both assigned to FeN 4 moieties but embedded in different ways in the carbon matrix. Iron in the site S1 switches oxidation state III/II in the region 0-1 V while S2 does not, remaining Fe(II). We also identify that both sites initially contribute to the ORR activity of Fe-N-C in acidic medium. However, S1 is not durable in operating PEMFC, quickly transforming to ferric oxides (Figure 6). In contrast, S2 is shown to be more durable, with no measurable decrease of the number of active sites after 50 h operation at 0.5 V. The lack of change of oxidation state for Fe in S2 in the region 0-1 V is not contradictory with catalysis. For example, we showed with in situ XAS that CoN x sites do not change oxidation state in acidic medium in the same region but catalyze ORR. [START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF][START_REF] Li | Asymmetric volcano trend in oxygen reduction activity of Pt and non-Pt catalysts: in situ identification of the site-blocking effect[END_REF] The degradation of S1 into ferric oxides may be a direct or indirect demetallation, the indirect pathway possibly triggered by localized carbon surface oxidation or protonation of highly basic nitrogens involved in S1. The stability of S2 may be due to a more graphitic local structure, lower amount of reactive oxygen species (ROS) produced during ORR in acid, or its sub-surface location activating the N-doped carbon top-surface. These results and/or methods are of high interest to the improved understanding of Fe-N-C materials for application in PEMFC but also in anion-exchange membrane fuel cells and for CO 2 electroreduction. [START_REF] Hossen | Synthesis and characterization of high performing Fe-N-C catalyst for oxygen reduction reaction (ORR) in alkaline exchange membrane fuel cells[END_REF][START_REF] Varela | pH Effects on the Selectivity of the Electrocatalytic CO 2 Reduction on Graphene-Embedded Fe-N-C Motifs: Bridging Concepts between Molecular Homogeneous and Solid-State Heterogeneous Catalysis[END_REF] For PEMFC application, further efforts should be devoted to increasing the site density of S2 sites and/or to stabilize S1 in acidic and oxygenated environment. The former goal might be achieved by depositing a thin overlayer of N-doped carbon on top of Fe-N-C (possibly transforming S1 into S2 sites) and the latter goal by adding co-catalysts (to scavenge H 2 O 2 or ROS formed during ORR in acid medium) or by integrating S1 sites in a more graphitic carbon support. In addition, the targeted removal of sites S1 before integrating Fe-N-C materials in PEMFC cathodes would avoid the formation of ferric oxides under operando conditions, in turn likely forming ROS in the presence of H 2 O 2 .

PEMFC Tafel plots of Fe 0.5 and Fe 0.5 -950 (10); (b) Fe K-edge XANES spectra measured under operando conditions in PEMFC as a function of potential; in situ [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectra at 0.8 V (c) and 0.2 V (d) acquired during the fourth cycle. For (a), the cell temperature was 80 o C, the flow rates of O 2 and H 2 were 60 sccm with 100% relative humidity, the gauge pressure was 1 bar and the cathode loading was 4 mg•cm -2 . For (b), all the testing conditions were the same as (a), except that no backpressure was applied. For (cd), the cell was at room temperature, the humidifiers were at 50 o C, Ar and H 2 gases were fed at cathode and anode respectively, and no backpressure was applied. Each Mössbauer spectrum was collected for 36 hours. D1H is the Mössbauer signature of S1 sites at high potential while D1L is their signature at low potential.

Methods

Synthesis. The synthesis of Fe 0.5 and Fe 0.5 -950 (10) was reported previously. [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF] Catalyst precursors were prepared from a Zn(II) zeolitic imidazolate framework (Basolite Z1200 from BASF, labelled ZIF-8), Fe(II) acetate (Fe(II)Ac), and 1,10-phenanthroline (Phen). [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe(II)Ac was used as iron precursor for all Mössbauer studies. For operando XAS, natural Fe(II)Ac was used. The catalyst Fe 0.5 was synthesized via the dry ball-milling of ZIF-8 (800 mg), Phen (200 mg) and Fe(II)Ac (16 mg) in a zirconium oxide crucible filled with 100 zirconium oxide balls (5 mm diameter) at 400 rpm for 2 hours (Fritsch Pulverisette 7 Premium, Fritsch, Idar-Oberstein, Germany). The subscript in Fe 0.5 corresponds to the Fe content (wt %) in the entire catalyst precursor before pyrolysis. Then the mixed precursor was pyrolyzed in flash mode in Ar at 1050 o C for 1 hour. Owing to a mass loss of 65-70 wt % during pyrolysis in Ar, caused by volatile products formed from ZIF-8 and Phen, the iron content in Fe 0.5 is about three times the iron content in the catalyst precursor. Fe 0.5 was subjected to a second flash pyrolysis for 10 min at 950 o C in NH 3 , yielding Fe 0.5 -950 (10). The mass loss of carbon during NH 3 pyrolysis was 25-31%, further increasing the iron content.

To synthesize Fe 2 O 3 /N-C, the Fe-free N-C was firstly synthesized identically with Fe 0.5 -950 except for the first ball-milling step, where no Fe(II)Ac was added. Then 15 mg of XRF. The metal content in Fe 2 O 3 /N-C was measured via X-ray XRF spectroscopy (Axios Max from PANanalytical, Netherlands). Fe 2 O 3 /N-C powder was mixed with boric acid as a binder in a ratio of 1:3 by weight via ball-milling at 400 rpm for 30 min. Then 200 mg of the mixture was pelletized as a disk of 13 mm diameter for XRF measurements. The calibration curve was performed using 0.1, 0.2, 0.5, 1.0, 1.5 and 2.0 wt% Fe in a mixture of Fe(II)Ac and Vulcan XC72R. The Vulcan XC72R (mixed with Fe(II)Ac) were mixed with boric acid in a ratio of 1:3 by weight via ball-milling at 400 rpm for 30 min, and then 200 mg of the mixture was pelletized as a disk of 13 mm diameter.

XRD. X-ray diffraction patterns were recorded using a PANanalytical X'Pert Pro powder Xray diffractometer with Cu Kα radiation.

STEM.

Probe Cs-corrected scanning transmission electron microscope Jeol ARM 200 F, equipped with a cold field emission electron source, was used for imaging atomicallydispersed FeN x C y moieties in Fe 0.5 pristine powder. To minimize the beam damage, 80 keV and low beam current were used. High-angle annular dark-field (HAADF) images were obtained using 68-180 mrad collection half-angles at 24 mrad probe convergence semi-angle.

Images were filtered with non-linear filter which is a combination of low-pass and Wiener filters. The presence of iron and nitrogen was confirmed with Gatan Quantum ER dual Electron Energy-loss Spectroscopy system.

TEM and STEM-EDX. A JEOL 2010 Transmission Electron Microscopy operated at 200

kV was used to examine Fe-N-C cathodes before testing or at EoT. The resolution was 0.19 nm. Elemental mapping was performed on fresh/aged Fe0.5-950(10) cathode using a 200 kV JEOL 2100F microscope equipped with a retractable large angle Centurio Silicon Drift Detector (SDD) detector. The Fe K, C K and O K lines and the K-factors specified by the JEOL software were used for elemental quantification.

Raman spectroscopy. Raman spectra were collected using a LabRAM ARAMIS Raman microscope with a 473 nm laser. N 2 sorption isotherms acquisition and analysis. N 2 adsorption/desorption was performed at liquid nitrogen temperature (77 K) with a Micromeritics ASAP 2020 instrument. Prior to the measurements, all samples were degassed at 200 °C for 5 h in flowing nitrogen to remove guest molecules or moisture. The pore size distributions were calculated by fitting the full isotherm with the quench solid density functional theory model with slit pore geometry from NovaWin (Quantachrome Instruments).

Basicity measurement of pristine Fe-N-C powders. The basicity measurement of Fe 0.5 and Fe 0.5 -950 (10) has been reported elsewhere. [START_REF] Zitolo | Identification of catalytic sites for oxygen reduction in iron-and nitrogen-doped graphene materials[END_REF] A solution with pH 6.0 was first prepared by the titration of a 0. Ex situ and operando XAS. Fe K-edge X-ray absorption spectra were collected at room temperature at SAMBA beamline (Synchrotron SOLEIL). The beamline is equipped with a sagittally focusing Si 220 monochromator, and X-ray harmonics are removed by two Pdcoated mirrors. For ex situ measurements on pristine Fe-N-C catalysts, the powders were pelletized as disks of 10 mm diameter with 1 mm thickness, using Teflon powder (1 μm particle size) as a binder and XAS measured in transmission mode. For ex situ measurements on Fe-N-C cathodes (before testing or at EoT), XAS was acquired in fluorescence mode. For operando XAS experiments, MEAs were prepared identically as for measurements in the commercial PEMFC (Cell 1). The design of the PEMFC used for operando XAS study (Cell 2, see also Supplementary Note 2) was reported in Ref. 41. The cell temperature was 80 o C, 60 sccm O 2 and H 2 with 100% relative humidity were fed at cathode and anode respectively, and the cathode loading was 4 mg•cm -2 . No backpressure was applied.

Operando measurements were performed by recording the Kα X-ray fluorescence of Fe with a Canberra 35-elements monolithic planar Ge pixel array detector.

Ex situ and in situ Mössbauer spectroscopy. [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe-enriched Fe(II)Ac was used as iron precursor for all Mössbauer studies. The 57 Fe Mössbauer spectrometer (Wissel, Germany) was operated in transmission mode with a 57 Co: Rh source. The velocity driver was operated in constant acceleration mode with a triangular velocity waveform. The velocity scale was calibrated with the magnetically split sextet of a high-purity α-Fe foil at room temperature.

The spectra were fitted to appropriate combinations of Lorentzian profiles representing quadrupole doublets, sextets by least-squares methods. IS values are reported relative to α-Fe at room temperature. Unless otherwise mentioned in the Supplementary Tables 2, 3, 6-8, the fittings were performed with unconstrained parameters (relative area, IS, QS, LW, H) for each spectral component. For ex situ measurements on pristine Fe-N-C catalysts, powders (20-30 mg) were mounted in a 2 cm 2 holder. For ex situ measurements on Fe-N-C cathodes, before testing or at EoT, 5 cm 2 electrodes were cut into four pieces and stacked on each other. Mössbauer measurements below 100 K were performed in a helium flow cryostat (SHI-850 Series from Janis, USA). For in situ Mössbauer experiments, MEAs were prepared as described for testing in the commercial PEMFC (Cell 1), except that the anode was 0.1 mg Pt cm -2 to maximize γ-ray transmission through the cell. The design of the PEMFC for in situ Mössbauer spectroscopy (Cell 3, see also Supplementary Note 2) is shown in Supplementary Figure 1b. The cell was at room temperature, the humidifiers were at 50 o C, Ar and H 2 gases were fed at cathode and anode respectively, and no backpressure was applied. The Mössbauer signal was continuously acquired for 36 hours at each cathode potential.

In situ XES. Fe K β X-ray emission spectra were collected at room temperature using a 1m radius Germanium 620 analyzer crystal at GALAXY inelastic scattering end-station (Synchrotron SOLEIL). [START_REF] Ablett | The GALAXIES inelastic hard X-ray scattering end-station at Synchrotron SOLEIL[END_REF][START_REF] Rueff | The GALAXIES beamline at the SOLEIL synchrotron: inelastic X-ray scattering and photoelectron spectroscopy in the hard X-ray range[END_REF] The incident energy was 8500 eV (using a silicon double-crystal monochromator) and the focused beam size was 30 [ver.] x 90 [hor.] μm 2 . The sample, analyser crystal and silicon drift detector were all arranged in a vertical Rowland circle geometry and air absorption was reduced by using helium flight paths. The electrochemical cell (Goodfellow cat. C 000200/2) used for operando XES in liquid electrolyte with a three electrode system is the same as the one previously for in situ or operando XAS measurements (Cell 4, see also Supplementary Note 2). [START_REF] Zitolo | Identification of catalytic sites in cobalt-nitrogen-carbon materials for the oxygen reduction reaction[END_REF] Catalyst inks were prepared by mixing 10 mg catalyst with 50 µL de-ionized water and 100 µL of 5 wt% Nafion® solution with ultrasounds. A 50 µL aliquot was then pipetted on ~3 cm 2 circular area of a 100-µmthick graphite foil, resulting in a catalyst loading of ~1 mg•cm -2 . The graphite foil with deposited catalyst then served as a working electrode, Ag/AgCl and Pt were used as reference and counter electrodes, respectively. The cell was filled with 0.5 M H 2 SO 4 and saturated with N 2 by continuously bubbling gas in the electrolyte.

X-ray computed tomography (CT). X-ray CT imaging was performed at the Advanced

Photon Sources (APS) at Argonne National Laboratory (ANL) using Beamline 32-ID, with 8 keV energy and 0.4 s exposure time. Fresnel zone plates with grading of 44.6 nm were used to achieve resolution of 44.6 nm. Zernike phase contrast was used to detect soft elements, whereas absorption contrast was used for imaging hard materials. Image phase retrieval and reconstructions were performed using TomoPy. [START_REF] Gürsoy | Tomopy: a framework for the analysis of synchrotron tomographic data[END_REF] The volume-rendering structure and analysis were done in Dragonfly 4.1. [START_REF]Dragonfly 4.1 Computer software[END_REF] The calculated volume-to-surface area ratio was considered as the sizes of the particles. The surface area was calculated by pixel-wise method.

DFT computation. Density functional theory (DFT) spin-polarized calculations were carried out with the cluster and periodic approaches using respectively, deMon2k.6.0.2 developers version [START_REF] De La Lande | Molecular Simulations with in-deMon2k QM/MM, a Tutorial-Review[END_REF][START_REF] Koster | deMon2k, Version 6, The deMon developers[END_REF] and VASP [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF][START_REF] Kresse | Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set[END_REF] computer programs on graphene sheets (with defects) integrating various moieties from the ferrous and ferric FeN 4 C 10 and FeN 4 C 12 sub-groups. The considered cluster and periodic models are reported in Supplementary Figure 13. The dangling bonds in all structures were saturated with hydrogen atoms. In the cluster calculations, the electrons of the C, H and N atoms are described by triple-ξ basis set and of Fe by double-ξ plus polarization (DZVP2). [START_REF] Godbout | Optimization of Gaussian-type basis sets for local spin density functional calculations. Part I. Boron through neon, optimization technique and validation[END_REF] Electronic exchange and correlation effects were described within the generalized gradient approximation (GGA) in the Perdew-Burke-Ernzerhof (PBE) parametrization. [START_REF] Perdew | Generalized Gradient Approximation Made Simple[END_REF][START_REF] Zhang | Generalized Gradient Approximation Made Simple[END_REF] No symmetry constraints were imposed. In deMon2k code, for all atoms, automatically generated auxiliary functions up to orbital quantum number, l = 3 were used for fitting the density with the GGA functionals. [START_REF] Köster | Calculation of exchange-correlation potentials with auxiliary function densities[END_REF] The GGA functionals were also coupled to an empirical dispersion (D) term. [START_REF] Wu | Empirical correction to density functional theory for van der Waals interactions[END_REF] A quasi-Newton method in internal redundant coordinates with analytical energy gradients was used for structure optimization of ferrous and ferric models in high spin state. For the numerical integrations of the XC energy and potential, we used an adaptive grid with tighten threshold (10 -8 a.u.). [START_REF] Krack | An adaptive numerical integrator for molecular integrals[END_REF] The convergence was based on the Cartesian gradient and displacement vectors with thresholds of 10 -3 a.u. and the energy convergence was set to 10 -7 a.u. The DFT calculations with periodic boundary conditions, carried out with VASP code, used the models 2e and 2a to build the unit cells for periodic calculations. In the case of the cluster model 1e, the corresponding periodic structure 2e was modelled using a cell size 17.19 Å×20.89 Å. In the case of model 1a, the corresponding periodic structure 2a was constructed using cell size of 9.94 Å×12.64 Å. Vacuum region of 15 Å was introduced in the z-direction in order to eliminate interactions between the graphene sheet and its periodic images. All the DFT calculations with periodic boundary conditions (PBC) were performed using PBE exchangecorrelation functional and VASP 5.2 recommended projector augmented-wave pseudopotentials. [START_REF] Blöchl | Projector augmented-wave method[END_REF][START_REF] Kresse | From ultrasoft pseudopotentials to the projector augmentedwave method[END_REF] For the calculation of structural and electronic properties, standard PAW potentials supplied with VASP were used, with 4 valence electrons for C (2s2 2p2), with 5 electrons for O (2s 2p3), 8 valence electrons for Fe (4s2 3d6), and 6 valence electrons for O (2s 2p 4), respectively. Electric field gradients at the positions of the Fe nuclei were calculated using the method reported in reference [START_REF] Petrilli | Electric-field-gradient calculations using the projector augmented wave method[END_REF] as implemented in VASP. When calculating electric field gradient, we have used the corresponding GW potentials, which give a better description of high-energy unoccupied states. For GW Fe pseudopotential that treats 3s and 3p states as valence states was used. Cut-off energy for the plane wave basis set of 800 eV, break condition for electronic SC-loop of 10 -6 eV and 8×8×1 gamma centred mesh for the model 2a, and 4×4×1 mesh for the model 2e were found to lead to the converged electric field gradients. In all cases, the Fermi-Dirac smearing method with sigma set to 0.03 was used. In addition, all the calculations included support grid for the evaluation of the augmentation charges.

  to calculate the QS-value of different high-spin OH-Fe(III)N 4 C 12 , OH-Fe(III)N 4 C 10 , Fe(II)N 4 C 12 and Fe(II)N 4 C 10 models (Supplementary Figure 13, the atomic coordinates of the optimised models are provided in Supplementary Data 1). While high-spin OH-Fe(III)N 4 C 12 and OH-Fe(III)N 4 C 10 structures lead to QS-values of 0.6-1.0 mm•s -1 , matching those of D1H, only the high-spin Fe(II)N 4 C 12 structures lead to QS-values of 1.7-2.0 mm•s -1 , matching those of D1L (Supplementary Table

Figure 2 .

 2 Figure 2. Effect of PEMFC potential on doublets from fitted in situ Mössbauer spectra.

Figure 3 .

 3 Figure 3. Experimental and calculated values of hyperfine parameters vs. potential.

Figure 4 .

 4 Figure 4. Characterisation of Fe 0.5 -cathode after operation at 0.5 V in PEMFC. (a) Ex situ[START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectrum at 5 K of the pristine Fe 0.5 -cathode. EoT Mössbauer spectra at

Figure 5 .

 5 Figure 5. Correlations between FeN x site amount in Fe 0.5 -cathode and activity over time.

Figure 6 .

 6 Figure 6. Coordination or structural changes of the sites S1 and S2 under in situ or

FeCl 2 •

 2 4H 2 O was dissolved in 7.5 mL H 2 O/ethanol solution (v:v=24:1). Then 300 mg N-C was added, and well-mixed via sonication for 1 hour. The obtained slurry was stirred continuously for another 48 hours, followed by filtration, washing with water, and dry in the oven at ~50 o C overnight. The Fe 2 O 3 /N-C sample was obtained by a final heat treatment at 200 o C for 2 hours in Ar with a ramping rate of 5 o C•min -1 . The Fe content in Fe 2 O 3 /N-C was found to be 1.3 wt.% by X-ray fluorescence (XRF) spectroscopy.

  1 M H 2 SO 4 solution by 0.1 M KOH. Then 40 mg catalyst was dispersed into 20 ml aqueous solution with an initial pH (pH i ) of 6.0. The solution was constantly saturated with N 2 to avoid acidification from air. The final pH (pH f ) after the dispersion of the catalyst was measured once the pH meter indicated a stable value. Electrochemical characterisation. The ORR activities of Fe 0.5 and Fe 0.5 -950 were investigated in a single-cell PEMFC (Cell 1, see also Supplementary Note 2). For the membrane electrode assembly (MEA), cathode inks were prepared by sonicating for 1 hour the mixture of 20 mg of catalyst, 652 μL of a 5 wt% Nafion solution containing 15-20% water, 326 μL of ethanol and 272 μL of de-ionized water. Then, three aliquots of 405 μl of the catalyst ink were successively deposited on the microporous layer of a 4.84 cm 2 gas diffusion layer (Sigracet S10-BC). The cathode was then placed at 60 o C to dry for 2 hours. The anode used for all PEMFC tests in Cell 1 was 0.5 mg Pt •cm -2 on Sigracet S24-BC. Nafion NRE-211 was used as membrane. No hot-pressing was applied in order to easily peel off the cathode for EoT characterisation. PEMFC tests were performed with a single-cell fuel cell with serpentine flow field (Fuel Cell Technologies) using an in-house test bench and a Biologic potentiostat with a 50 A load and EC-Lab software. The fuel cell temperature was 80 o C, the humidifiers were set at 85 o C and the inlet pressures were set to 1 bar gauge for both anode and cathode sides. The flow rate for humidified H 2 and O 2 gases was 60 sccm downstream. No break-in was applied before recording the first polarisation curve. Polarization curves were recorded by scanning the voltage at 1 mV•s -1 .

Acknowledgements

The research leading to these results has received partial funding from

French National Research Agency under the CAT2CAT contract (ANR-16-CE05-0007), the FCH Joint Undertaking (CRESCENDO Project, Grant Agreement n°779366) and the Centre of Excellence of Multifunctional Architectured Materials "CEMAM" (ANR-10-LABX-44-01) . We acknowledge Synchrotron SOLEIL (Gif-sur Yvette, France) for provision of synchrotron radiation facilities at beamline GALAXIES (proposal number 20170390) and at beamline SAMBA (proposal number 99190122). I.Z. acknowledges the resources of the Advanced Photon Source, a U.S. Department of Energy (DOE) Office of Science User Facility operated for the U.S. DOE Office of Science by Argonne National Laboratory under contract No. DE-AC02-06CH11357. I. M. thankfully acknowledges the computational resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility operated under Contract No. DE-AC02-05CH11231. This paper has been assigned LA-UR-19-31453. The computational work of T.M and I.C.O. was granted access to the HPC resources of IDRIS/TGCC under the allocation 2019 -A0050807369 made by GENCI and supported by the LabExCheMISyst ANR-10-LABX-05-01. G. D. acknowledges the financial support from Slovenian Research Agency (P2-0393).

Code availability

The source code used for DFT calculation with deMon2k is available at http://www.demonsoftware.com/public_html/download.html, upon request for academic purpose. The Vienna Ab Initio Simulation Package (VASP) is a proprietary software available for purchase at https://www.vasp.at/.

The Bader charge density analysis [START_REF] Bader | Atoms in Molecules: A Quantum Theory[END_REF] with the implementation of Henkelman and co-workers [START_REF] Tang | A grid-based Bader analysis algorithm without lattice bias[END_REF] in VASP code was used to obtain the spin charge density of the periodic structures. The charge-spin density of the cluster structures was obtained using Mulliken population scheme.

The atomic spin densities were computed for all cluster and periodic models in order to verify the spin density at the ferric or ferrous Fe site. The Fe spin density in its high and intermediate spins was found to amount to ~4e -and ~2e -, respectively. Note that in high-spin models, spin-polarisation of C and N sites occurs prior to the increase of spin density on Fe.

Therefore, the total spin of each cluster or unit cell model was increased until the spin density on Fe became ~4e -, for which the quadrupole splitting energies were obtained (see Supplementary Table 5). This approach differs from our previous study on high-spin ferric models, [START_REF] Mineva | Understanding active sites in pyrolyzed Fe-N-C catalysts for fuel cell cathodes by bridging density functional theory calculations and 57 Fe Mössbauer Spectroscopy[END_REF] where the spin-state referred to the total spin of the clusters.

The quadrupole splitting energy is computed as the coupling between the nuclear quadrupole moment (Q) the non-spherical nucleus and the principle components V ii (i=x,y,z) of the electric filed gradient (EDF) tensor at [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe nucleus using the following equation:

Where e is the charge of the electron and the asymmetry parameter is computed as =

Data availability

The raw data that support the findings of this study are available from the corresponding authors upon request. In particular: The X-ray absorption spectroscopy raw data associated with this work is permanently stored at synchrotron SOLEIL and available upon request; the raw data related to electron microscopy images are permanently stored at LEPMI and available upon request; the raw data related to X-ray radiographs are permanently stored at the APS synchrotron and available upon request;

the [START_REF] Kresse | Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set[END_REF] Fe Mössbauer spectroscopy data and the raw and reconstructed tomography data are available at Institut Charles Gerhardt Montpellier and available upon request. performed tomography and TEM analyses. J.L., M.T.S. and F.J. wrote and edited the manuscript with input from all authors. The project was supervised by F.J.

Author

Additional information

Supplementary information is available in the online version of the paper. Correspondence and requests for materials should be addressed to F.J.

Competing interests

The authors declare no competing interests.