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# Ternary intermetallic LaCoSi as a catalyst for N2 activation

## Abstract

Activating high-energy multiple bonds using earth-abundant metals is one of the most significant challenges in catalysis. Here, we show that LaCoSi—a ternary intermetallic compound—is an efficient and stable catalyst for N2 activation to produce NH3. The ammonia synthesis is significantly promoted by shifting the reaction bottleneck from the sluggish N2 dissociation to NH x formation, which few catalysts have achieved. Theoretical calculations reveal that the negatively charged cobalt mediates electron transfer from lanthanum to the adsorbed N2, which further reduces the activation barrier of N2 dissociation. Most importantly, the specific LaCoSi geometric configuration stabilizes the N2 adsorption with a strong exothermic effect, which dramatically decreases the apparent energy barrier of N2 activation. Consequently, LaCoSi shows a superior activity (1,250 μmol g−1 h−1), with a 60-fold increase over the activity of supported cobalt catalysts under mild reaction conditions (400 °C, 0.1 MPa).

## Main

Catalysts are at the core of the chemical industry and act by reducing the energy barrier for the activation of chemically inert reactants1. Transition metals often perform as good catalysts due to their ability to temporarily exchange electrons with reacting species2,3. The use of intermetallics shows great promise for regulating the activity of transition metals because the peculiar mixed bonding of the constituent elements can result in attractive combinations of crystallographic and electronic structures4, which provides perfect platforms for constructing new heterogeneous transition metal catalysts5,6.

Ammonia synthesis, which sustains the global food supply chain, is one of the most well-known reactions catalysed by transition metals7. The industrial iron-based Harber–Bosch catalyst has to be used under harsh reaction conditions (400–600 °C, 20–40 MPa) with large energy input. The primary challenge of ammonia synthesis lies in the activation of the N≡N triple bond, which has an extremely large bonding energy of 945 kJ mol−1; thus, N2 activation is widely regarded as the rate-determining step (RDS)8,9. The role of transition metal catalysts is to lower the energy barrier of N2 dissociation. Therefore, catalysts that could overcome the limitation of the slow N2 dissociation would exhibit extraordinary catalytic performance under mild reaction conditions (<400 °C, <2 MPa). However, the classic method of modifying transition metals (iron, ruthenium and cobalt) using alkaline earth metal oxides or even pure alkaline metals with low work function is unable to alter the RDS10,11,12,13,14,15,16. In fact, only very few recently reported catalysts have been shown to promote N2 dissociation with enough efficiency to shift the RDS of ammonia synthesis, even after numerous studies for over a century17,18,19,20. Ruthenium-based catalysts supported by electrides—compounds in which electrons serve as anions—dominate these cases17,20,21,22,23. The effective N2 dissociation has been ascribed to the strong electron-donating capability of electrides to ruthenium, which promotes the back-donation of electrons to N2 (ref. 21). However, the complicated synthesis of electrides and use of expensive metals are still issues that hinder the large-scale application of ruthenium-loaded electride catalysts. Moreover, it is difficult to construct a realistic model for theoretical calculations to study supported catalysts because too many factors have to be considered, including the transition metal particle size, the exact location of the particles on the support and how to simulate the inhomogeneous support structure. Oversimplification of these factors may lead to erroneous results. Recently, transition metal nitrides, especially Co3Mo3N, have drawn extensive attention for ammonia synthesis due to their specific structures and outstanding catalytic performance under mild conditions. The nitrides turned out to act as nitrogen transfer reagents and activated N2 by the Mars–van Krevelen mechanism24,25, which was further proved using A–Mn–N (A = Li, K, Fe or Co) materials26.

Intermetallic compounds are advantageous for the development of new ammonia synthesis catalysts due to: (1) the strong modification of the charge states of transition metals for N2 activation; (2) the robust stability obtained by implanting active sites into the lattice framework, which prevents active site aggregation; and (3) the relatively simple structures, which allow investigation of the mechanism by theoretical studies. In a recent study, we proposed that LaScSi (ref. 27)—one member of the so-called RTX intermetallics (R = rare earth, T = transition metal, X = p-block element) with more than 1,000 analogues—can act as a catalyst promoter for ammonia synthesis due to its unique electron-donating properties and the ability to dissociate H2. Although no catalytic activity was observed without loading expensive ruthenium, it provided a way of implanting transition metal sites into intermetallics for catalysis.

Here, via a combination of experiment and first-principles calculations, we successfully reveal that LaCoSi is able to shift the RDS of ammonia synthesis from N2 breakage to NH x formation and is, therefore, a highly effective catalyst for ammonia synthesis under mild conditions without the need to load expensive ruthenium. This occurs via an efficient electron transfer from lanthanum to cobalt. This electronic property, together with the special geometric arrangement of atoms in the catalyst, enhances N2 adsorption and greatly reduces the activation energy of N2 dissociation. LaCoSi is chemically stable under ammonia synthesis conditions, which enhances its prospects for long-term durability. These findings not only afford new insight into catalyst design from both electronic and structural standpoints, but open a perspective for RTX intermetallics in heterogeneous catalysis beyond the interest in their physical properties28.

## Results

### Characterizations of LaCoSi

LaCoSi was fabricated by an arc-melting method using stoichiometric lanthanum, cobalt and silicon ingots, and ground into particles before use (Supplementary Fig. 1a,b). LaCoSi crystalized in a tetragonal structure with the space group P4/nmm (Fig. 1a). A single phase with high quality was confirmed by the Rietveld refinement of powder X-ray diffraction (Fig. 1b). The electronic and local structure of the prepared LaCoSi was investigated using X-ray absorption fine-structure measurements. Figure 1c displays the Fourier-transformed k2-weighted extended X-ray absorption fine-structure spectrum of the cobalt K-edge. The peaks were fitted using the LaCoSi structure model (Supplementary Table 1). The experimental data and fitted data were in good agreement, as suggested by the small R-factor (0.0071). The average bond distances for La–Co, Co–Co and Co–Si were estimated to be 3.06 Å, 2.85 Å and 2.33 Å, respectively, consistent with the parameters of previously reported LaCoSi (ref. 29) and the computationally relaxed structure (Supplementary Table 2). Scanning electron microscopy with energy dispersive X-ray spectroscopy maps showed that lanthanum, cobalt and silicon were homogeneously dispersed throughout the LaCoSi particles and the atomic ratio of La:Co:Si was 1.09:1:1.03, which tallies with the perfect LaCoSi composition (Supplementary Fig. 1c–f). The coordination number of the Co–Co bond in LaCoSi decreased from 12 in the cobalt foil30 to 1.75 and the coordination numbers of Co–La and Co–Si were 3.59 and 1.75, respectively. The results indicate that cobalt atoms were highly dispersed among the lanthanum and silicon atoms31. The total coordination number of cobalt was 7.09, which is significantly lower than that of monometallic cobalt (12). This may give the cobalt surface more unsaturated catalytic sites32. LaCoSi exhibits a metallic behaviour (Supplementary Fig. 2). The work function of LaCoSi was measured to be only 2.7 eV (Fig. 1d), reflecting the loosely bound nature of surface electrons in LaCoSi. The low work function would favour the surface electron donation from LaCoSi to the lowest unoccupied molecular orbits of the N2 molecule, which is expected to lower the activation energy of N2 dissociation21.

We then focused on the electronic structure of cobalt, which is the active site for N2 activation. The X-ray absorption near-edge structure spectrum of LaCoSi is compared with the spectra of cobalt foil, CoO and Co3O4 in Fig. 2a. The cobalt absorption edge for LaCoSi resides at an even lower energy relative to cobalt foil, indicating that cobalt is negatively charged in LaCoSi (ref. 33). In contrast, the lanthanum L3-edge of LaCoSi shifts to a higher energy compared with that of lanthanum metal (Fig. 2b). This finding indicates that lanthanum donates while cobalt accepts electrons in the LaCoSi system. The charge states of all the elements in LaCoSi were examined by quantitative Bader charge analysis34. Accordingly, 0.54 electrons (|e|) were transferred to cobalt and 0.55 |e| to silicon from lanthanum (Supplementary Fig. 3).

LaCoSi surfaces were characterized by X-ray photoelectron spectroscopy and Auger electron spectroscopy. As indicated by the results (Supplementary Figs. 4 and 5), cobalt and silicon are negatively charged while lanthanum is positively charged, consistent with the results in the bulk. In addition, lanthanum and silicon are more exposed than cobalt, which is shown by the fact that LaCoSi(001)–La and LaCoSi(001)–Si surfaces are more easily created than LaCoSi(001)–Co surfaces during grinding (Supplementary Fig. 6). The argon-etching experiments using Auger electron spectroscopy demonstrate that surface oxygen tends to bond with the lanthanum surfaces and has no influence on the exposed cobalt surfaces (Supplementary Fig. 7). Combined with the clue provided by the powder X-ray diffraction result (Supplementary Fig. 8) that (001) surfaces are distinctly preferred orientations in the synthesized catalyst, we built a series of (001) surface models terminated with lanthanum, cobalt and silicon atoms (Supplementary Fig. 9). The computed work functions for these surfaces are in the range 2.42–4.51 eV (Supplementary Fig. 9). The negatively charged cobalt- and silicon-terminated surfaces, respectively, possess work functions of 4.30 eV and 4.51 eV. The positively charged lanthanum-terminated surfaces have low work functions of 2.42–2.90 eV, which shows that the surface lanthanum atoms have a strong ability to donate electrons. This result is also consistent with the experimental measurement of ~2.7 eV. However, our experimental study of LaScSi revealed that the positively charged lanthanum- and scandium-terminated surfaces and negatively charged silicon-terminated surfaces do not show catalytic activity. Therefore, the catalytic difference between LaCoSi and LaScSi should originate from the differences of scandium- and cobalt-terminated surfaces. The calculated charge from redundant electrons over cobalt atoms at the LaCoSi(001)–Co surface is −0.37 |e|, 68.5% of that in the bulk material (Fig. 2c), while for metallic cobalt, the cobalt atoms at the Co(001) surface are only slightly negatively charged (−0.03 |e|; Supplementary Fig. 10). Also, the calculated work function of the LaCoSi(001)–Co (4.30 eV) is much smaller than that of Co(001) (5.04 eV) (Supplementary Fig. 9).

The enrichment of electrons over the surface of cobalt demonstrates the potential of enhancing the back-donation of electrons to the antibonding π-orbitals of adsorbed N2 (ref. 22). According to hydrogen–deuterium exchange experiments, LaCoSi is capable of activating H2 dissociation at a temperature as low as 60 °C, and the activation energy barrier is estimated to be only 28 kJ mol−1 (Supplementary Fig. 11), which is much lower than that for the reported RDS of ammonia synthesis17. LaCoSi has been studied as a hydrogen storage material that can accommodate hydrogen atoms in the La4 tetrahedra (green tetrahedra in Fig. 1a), forming LaCoSiH. According to the powder X-ray diffraction result, the basic crystal structure of LaCoSi remains unchanged after hydrogenation, although there is anisotropic expansion of the lattice, as revealed by the shifts in the Bragg peak positions (Supplementary Fig. 12). The valence state of cobalt is also not altered after hydrogenation, as suggested by the unchanged adsorption edge of the cobalt K-edge X-ray absorption near-edge structure (Supplementary Fig. 13). The results of thermal desorption spectroscopy in Fig. 2d show that the saturated hydrogen intercalation stoichiometry is 1.0 atom per formula unit (f.u.), consistent with previous work35. Desorption of hydrogen starts at 110 °C and reaches its maximum speed at around 400 °C. The equilibrium adsorption capacities for hydrogen at 400 °C are 0.90 and 0.77 f.u.−1 in pure H2 gas and ammonia synthesis gas, respectively (Supplementary Fig. 14). These capacities demonstrate that the incorporated hydrogen atoms—at least those in the surface layers—can participate in ammonia formation. These features of LaCoSi allowed us to undertake ammonia synthesis with a noble-metal-free, unsupported (self-promoted) catalyst.

### Catalytic performances of LaCoSi for ammonia synthesis

Figure 3a reveals the ammonia synthesis activity of various cobalt-containing catalysts. Although it has a surface area of only 1.8 m2 g−1, LaCoSi shows a catalytic activity of 1,250 μmol g−1 h−1, which is the highest among the tested catalysts. The reaction rate is more than 60 times greater than that for 10 wt% Co/MgO (20 μmol g−1 h−1) and 10 wt% Co/activated carbon (12 μmol g−1 h−1), which is even better than that of Co3Mo3N (796 μmol g−1 h−1), which in turn is reportedly better than commercial graphite-supported ruthenium and Fe–K2O–Al2O3 under mild reaction conditions (Supplementary Fig. 15)25,36,37. The ammonia synthesis yield over LaCoSi (0.355%) is twice that over commercial Fe–K2O–Al2O3 (0.164%) (Supplementary Table 3). Evaluated by the specific activity, LaCoSi is two to five orders of magnitude more active than the supported cobalt catalysts. Under the previously reported conditions, LaCoSi gives a specific activity of 397 μmol m−2 h−1, which is more than 10 times that of Co3Mo3N (31 μmol m−2 h−1) and Fe–K2O–Al2O3 (24 μmol m−2 h−1) (Supplementary Table 3)38. Cobalt powder, with an average particle size of 1–2 μm, shows trace catalytic activity for ammonia synthesis under the tested conditions. The catalytic activities of La–Co–Si intermetallics (LaCoSi, LaCo2Si2 and LaCo10.5Si2.5) decrease dramatically with the reduction of lanthanum in the formula, demonstrating the advantages of LaCoSi. Although sharing the similar property of storing and releasing hydrogen atoms below 400 °C (Supplementary Fig. 16), LaCo10.5Si2.5 exhibits negligible activity, illustrating that the incorporated hydrogen is not the only driving force for efficient ammonia synthesis. As expected, no ammonia was observed for cobalt-free LaSi, La5Si3 or LaScSi compounds (Supplementary Table 3), substantiating that N2 dissociation occurs on the cobalt centres. Excellent durability of LaCoSi is shown by the constant activity over 100 h (Fig. 3b). Dispersion of these contiguous cobalt single-atom sites in the lattice framework may prevent cobalt aggregation. LaCoSi showed robust stability and no phase transition or morphology changes were observed in the used catalyst (Supplementary Figs. 17 and 18), in sharp contrast with the quick decomposition of binary intermetallics (without silicon) to corresponding rare earth nitrides and transition metals39.

### Kinetic analysis

Apparent activation energies were calculated from the Arrhenius plots for the N2 activation, which is widely considered to be the RDS (Fig. 3c)40,41. The apparent activation energy of LaCoSi is 42 kJ mol−1 (Supplementary Fig. 19), which is around half that for the well-studied catalysts (Supplementary Table 4), providing evidence that N2 dissociation over LaCoSi is highly promoted. This value is close to that of ruthenium-loaded C12A7:e and Co–LiH, implying similarity in the reaction mechanism, in which formation of NH x species controls the overall reaction17. N2 reaction orders for the conventional heterogeneous catalysts are close to unity (0.8–1.0) because the overall reaction is limited by the rate of N2 cleavage (Supplementary Table 4). In contrast, the N2 reaction order was measured to be 0.45 over LaCoSi (Fig. 3d), indicating that N2 dissociation is sufficiently fast that the surface is continuously populated with activated nitrogen. This is in good agreement with the dissociation for the best-performing ruthenium-loaded electrides and Co–LiH, which have succeeded in changing the RDS of ammonia synthesis from the N2 activation step17,18. The reaction order of H2 over LaCoSi is 0.80, indicating that the problem of hydrogen poisoning with cobalt/activated carbon, which arises from the strong adsorption of hydrogen on the cobalt metal surface, is well solved by the reversible hydrogen storage capability of LaCoSi (Supplementary Table 4)20,40. The reaction rate over LaCoSi shows an approximately linear response to the pressure increase. It underwent a fourfold rise to 5,000 μmol g−1 h−1 when the reaction pressure increased from 0.1 MPa to 0.9 MPa (Supplementary Fig. 20).

The RDS was further examined by comparing the experimental reaction rates and calculated rates. The rate equations were established based on the Langmuir–Hinshelwood mechanism (Supplementary Fig. 21). The RDS is one of the four steps evaluated in Fig. 4 due to its high energy barrier42. Equations could be deduced by assuming the dissociation of N2 or formation of NH, NH2 or NH3 as the RDS (equations (1)–(4)). To identify the RDS of ammonia synthesis over LaCoSi, the derived equations were then fitted by a least squares method to the set of experimental rates acquired with various reaction gas compositions. Coefficients of determination (R2) were used to describe the fitting degree of modelled rates to the experimental rates. As shown in Fig. 4a, the fitting result is not so good with an R2 value of 0.583 when the activation of N2 is supposed to be the RDS. In contrast, R2 is 0.93 for the combination of N and H (Fig. 4b), which is much higher than that for N2 activation. Moreover, NH2 and NH3 formation reveal the highest R2 values of 0.982 and 0.987 (Fig. 4c,d), respectively. These fittings indicate that it is rational to consider that the RDS for ammonia synthesis over LaCoSi could be any formation steps of NH x species rather than the N2 dissociation step, which resembles the case for ruthenium-loaded C12A7:e (ref. 17). Together, the results reported here show that the RDS of ammonia synthesis can be altered by a single-phase intermetallic compound.

## Discussion

The structural simplicity of LaCoSi offers convenience for theoretical modelling by first-principles simulations to understand how N2 dissociation is promoted. For clarity, the behaviours of N2 dissociation on metallic Co(001) surfaces were also investigated for comparison. Based on the calculation results obtained using the Perdew–Burke–Ernzerhof functional (Supplementary Figs. 22–26), plausible reaction pathways of N2 activation on the surfaces of Co(001) and LaCoSi(001)–Co are proposed (Fig. 5). Important information can be extracted from these reaction energy profiles to understand the mechanism of N2 dissociation on LaCoSi(001)–Co. First, the electron injection from surface cobalt atoms of LaCoSi is not as strong as we expected. Charge density difference and Bader charge calculations (Fig. 5) both show that the electron gain of N2 from the LaCoSi(001)–Co surface (−0.48 |e|) is just slightly stronger than that from the Co(001) surface (−0.45 |e|). Indeed, the more negative charges on the nitrogen only reduce the calculated energy gap between adsorbed N2 and the transition state from 1.56 eV to 1.47 eV. One can see that the first step, N2 adsorption, is significantly enhanced on LaCoSi(001)–Co with respect to that over the Co(001) surface, which is triggered by the negatively charged cobalt and stabilized by the strong Coulomb attraction between the adsorbed N2 and the positively charged lanthanum atom, which is beneath the surface cobalt layer and centred within the square formed by cobalt atoms (Supplementary Figs. 24 and 26). This significantly exothermic process overcomes the weakness of low absorbability for N2, which is the main factor that limits the N2 activation under low reaction pressures43. Compared with the calculated adsorption energies of most stable N2 configurations on the LaScSi(001)–Sc (−3.98 eV) and Co(001) (−0.13 eV) surfaces, the appropriate N2 adsorption energy of −1.46 eV on the LaCoSi(001)–Co surface can be one crucial reason for the excellent catalytic performance of LaCoSi. Due to the exothermic effect of N2 adsorption, the overall N2 activation energy barrier on the LaCoSi(001)–Co surface is reduced to 0.01 eV, which is significantly lower than on the Co(001) surface (1.43 eV). This suggests that the so-called ‘hot atom’ mechanism44, in which the energy released in the adsorption process is used to elevate the molecule’s vibrational energy level, may work to promote the dissociation of N2 at the LaCoSi(001)–Co surface. The results calculated using revPBE—a functional reported to give a better description of the N2 dissociation on Co3Mo3N (ref. 25)—show the same adsorption behaviours and energy change trends as the calculations using the Perdew–Burke–Ernzerhof functional (Supplementary Table 5 and Supplementary Fig. 27).

The hot atom hypothesis was proven by first-principles molecular dynamics simulations (Supplementary Figs. 28 and 29). The adsorbed N2 molecule vibrated around the most stable hollow site and did not show any signs of N–N bond dissociation after 1,200 fs without the involvement of released adsorption energy (starting from configuration 2 in Fig. 5b), while the N2 dissociation quickly happened (after 546 fs), when this energy was involved (starting from configuration 1 in Fig. 5b). These calculation results readily explain why the ammonia synthesis over LaCoSi was not controlled by the N2 activation step and the reason for the much-improved catalytic performance of LaCoSi over that of metallic cobalt. In addition, cleavage of the N2 molecule proceeds with a calculated energy gain of −1.76 eV for metallic cobalt and −3.45 eV for LaCoSi, indicating that dissociation of N2 is thermodynamically favoured on LaCoSi. As with the energy scaling relations over transition metals, the adsorption energy of nitrogen (EN) on LaCoSi(001)–Co increases as the activation energy for N2 activation (Ea) dramatically decreases45. However, the readily activated hydrogen atoms in LaCoSi may provide the second active centre that could extract nitrogen from cobalt sites, which could free the occupied active centre for N2 activation and break the limiting scaling relation18. Therefore, we can conclude that the promotion of N2 activation is a joint effect of the electronic states of lanthanum and cobalt, the specific geometric structure and the reversible hydrogen storage capability of LaCoSi. We note that constructing a specific geometric structure can be an efficient solution for novel catalyst design.

In summary, a stable ternary intermetallic compound, LaCoSi, was found to be a very convenient single-phase catalyst that could shift the RDS of ammonia synthesis from the sluggish N2 dissociation to the formation of NH x under mild reaction conditions. LaCoSi is characterized by robust stability and high catalytic activity, above 60 times higher than those of supported cobalt catalysts. Rather than the conventional surface electron donation scenario, we have unveiled a hot atom mechanism behind the excellent catalytic activity of LaCoSi. Specifically, the negatively charged cobalt atoms at the LaCoSi surface promote the initial adsorption of N2, help to prevent desorption of the N2 before dissociation and then mediate electron transfer from lanthanum to N2, lowering the activation barrier. The Coulomb attraction from the neighbouring positively charged lanthanum atoms triggers the initiation of N2 adsorption with appropriate stability through a moderately exothermic process that provides energy for N2 activation. Therefore, the overall N2 activation barrier is dramatically reduced. Our initial success with LaCoSi paves the way for more studies based on RTX intermetallic catalysts which feature extraordinary performance but are free of noble metals.

## Methods

### Sample preparation

Intermetallic LaCoSi was synthesized by arc-melting lanthanum, cobalt and silicon ingots at a mole ratio of 1:1:1. The obtained silver-coloured ingot was collected and sealed in an evacuated quartz tube and annealed for 5 days at 1,000 °C and then 10 days at 800 °C to obtain a pure single phase. Finally, the prepared LaCoSi was ground into powder in a glovebox. The powder was directly applied as a catalyst without further treatment.

### Catalytic reaction

The catalytic reactions were conducted in a fixed-bed flow system with a gas flow of H2:N2 (3:1) at a flow rate of 60 ml min−1. In a typical run, 0.1 g or 0.4 g of LaCoSi was loaded into the reactor in the glovebox and then pre-treated in a stream of N2/3H2 under 0.1 MPa using a temperature programme of heating to 400 °C for 1 h and then holding at 400 °C for 2 h. The ammonia that was produced was monitored under steady-state conditions of temperature (250–400 °C) with a flow rate of 60 ml min−1 under 0.1–1.0 MPa. The produced ammonia was trapped in 5 mmol sulphuric acid solution and the amount of NH4+ generated in the solution was determined using an ion chromatograph (LC-2000 Plus, JASCO) equipped with a conductivity detector. For the measurement of reaction orders for N2 and H2, argon gas was used as a diluent to ensure a total flow of 60 ml min−1 when changing the flow rate of N2 and H2. The performance of control catalysts was evaluated under the same conditions.

### Sample characterization

Nitrogen sorption measurements were applied to evaluate the Brunauer–Emmett–Teller surface areas of the catalysts using a BELSORP-mini II (BEL). The crystal structure was analysed using a D8 ADVANCE X-ray Powder Diffractometer (Bruker) with monochromated copper Kα radiation (λ = 0.15418 nm). Ultraviolet photoelectron spectroscopy spectra were obtained using a VGS Class 150 electron analyser and discharge lamp that emitted excitation lines of He I (21.2 eV). The surface morphologies of the catalyst samples were investigated using high-angle annular dark field scanning transmission electron microscopy (JEM-2010F; Jeol). X-ray photoelectron spectroscopy (ESCA-3200; Shimadzu) measurements were performed using magnesium Kα radiation at <10−6 Pa (8 kV bias voltage applied to the X-ray source). X-ray photoelectron spectroscopy data were corrected according to the C (carbon) 1s peak (binding energy = 284.6 eV). Auger electron spectra were acquired with 10 keV primary electrons using the Scanning Auger Nanoprobe System (PHI 710; ULVAC-PHI). Hydrogen quantities were measured by thermal desorption spectroscopy (ESCO, 1400TV) with a ramping rate of 10 °C min−1 to 1,000 °C. The saturated hydrogen intercalation stoichiometry was estimated using LaCoSi samples treated at 200 °C for 8 h in 0.1 MPa of H2 flow. X-ray absorption fine-structure measurements were performed on the AR-NW10A beamline of the Photon Factory Advanced Ring at the Institute of Materials Structure Science, High Energy Accelerator Research Organization, Tsukuba, Japan. A silicon(311) double-crystal monochromator was used to obtain the monochromatized X-ray beam, and spectra were obtained in transmission mode. LaCoSi and boron nitride (dried at 300 °C) were mixed in an argon-filled glovebox and the mixture was pressed with a hand press apparatus to obtain a pellet sample, which was sealed in a plastic bag for measurement. X-ray absorption fine-structure spectra were analysed using the Athena and Artemis software packages46. The FEFF6 code was used to calculate the theoretical spectra47. The hydrogen–deuterium exchange was carried out in a fixed-bed flow system with 0.05 g of catalyst and a gas mixture of H2/D2/Ar (1:1:3); the reaction rate was monitored using a quadrupole mass spectrometer. The activation energy of the hydrogen–deuterium exchange was evaluated in the range of 60–120 °C. The electronic transport properties, magnetic susceptibility and heat capacity measurements were conducted using a physical property measurement system and a SQUID vibrating sample magnetometer from Quantum Design.

### Kinetic calculations

The rate equations of elementary steps 4–7 for ammonia synthesis (Supplementary Fig. 21) were expressed by the Langmuir–Hinshelwood mechanism42. Three typical assumptions were applied to deduce the rate equation when steps 4, 5, 6 and 7 were considered as the RDS: (1) the ammonia synthesis reaction can be divided into eight elementary steps; (2) one step controls the overall rate of reaction; and (3) adsorption behaviour follows the Langmuir model. In addition to these assumptions, we omitted the partial pressure of NH3 (pNH3) when it was sufficiently small in comparison with pN2 and pH2 at the outlet48. Under our reaction conditions, the ammonia partial pressures (pNH3) of the obtained experimental rates were much smaller than pN2 and pH2 at the outlet and the equilibrium value, which reasonably satisfied the applicable condition of the calculated equations derived with an elimination of the pNH3 term. The final rate equations are as follows:

$$r=\frac{\left(\vec{{k}_{4}}{K}_{2}{p}_{{{\rm{N}}}_{2}}\right)}{{\left(1+{K}_{1}{p}_{{{\rm{H}}}_{2}}+{K}_{2}{p}_{{{\rm{N}}}_{2}}+\sqrt{{K}_{1}{K}_{3}{p}_{{{\rm{H}}}_{2}}}\right)}^{2}}$$
(1)
$$r=\frac{\vec{{k}_{5}}\sqrt{{K}_{1}{K}_{2}{K}_{3}}\sqrt{{K}_{4}{p}_{{{\rm{H}}}_{2}}{p}_{{{\rm{N}}}_{2}}}}{{\left(1+{K}_{1}{p}_{{{\rm{H}}}_{2}}+{K}_{2}{p}_{{{\rm{N}}}_{2}}+\sqrt{{K}_{1}{K}_{3}{p}_{{{\rm{H}}}_{2}}}+\sqrt{{K}_{2}{K}_{4}{p}_{{{\rm{N}}}_{2}}}\right)}^{2}}$$
(2)
$$r=\frac{\vec{{k}_{6}}{K}_{1}{K}_{3}\sqrt{{K}_{5}{K}_{2}{K}_{4}}\sqrt{{p}_{{{\rm{H}}}_{2}}}{p}_{{{\rm{N}}}_{2}}}{{\left(1+{K}_{1}{P}_{{{\rm{H}}}_{2}}+{K}_{2}{p}_{{{\rm{N}}}_{2}}+\sqrt{{K}_{1}{K}_{3}{p}_{{{\rm{H}}}_{2}}}+\sqrt{{K}_{2}{K}_{4}{p}_{{{\rm{N}}}_{2}}}+{K}_{5}\sqrt{{K}_{1}{K}_{2}{K}_{3}{K}_{4}{p}_{{{\rm{H}}}_{2}}{P}_{{{\rm{N}}}_{2}}}\right)}^{2}}$$
(3)
$$r=\frac{\vec{{k}_{7}}{K}_{1}{K}_{3}{K}_{5}{K}_{6}\sqrt{{K}_{1}{K}_{2}{K}_{3}{K}_{4}}\,{p}_{{{\rm{H}}}_{2}}\sqrt{\,{p}_{{{\rm{H}}}_{2}}{p}_{{{\rm{N}}}_{2}}}}{{\left(1+{K}_{1}{p}_{{{\rm{H}}}_{2}}+{K}_{2}{p}_{{{\rm{N}}}_{2}}+\sqrt{{K}_{1}{K}_{3}{p}_{{{\rm{H}}}_{2}}}+\sqrt{{K}_{2}{K}_{4}{p}_{{{\rm{N}}}_{2}}}+{K}_{5}\sqrt{{K}_{1}{K}_{2}{K}_{3}{K}_{4}{p}_{{{\rm{H}}}_{2}}{p}_{{{\rm{N}}}_{2}}}+{K}_{1}{K}_{3}{K}_{5}{K}_{6}\sqrt{{K}_{2}{K}_{4}{p}_{{{\rm{N}}}_{2}}}{p}_{{{\rm{H}}}_{2}}\right)}^{2}}$$
(4)

where $$\vec{{k}_{i}}$$ is the rate constant of the forward reaction and Ki is the equilibrium constant in step i. To examine the RDS for ammonia synthesis over LaCoSi, derived equations were separately fitted into the sets of experimental rates by a least squares method and evaluated to determine which equations best described the experimental rates.

### Theoretical calculations

All of the structure relaxation and electronic structure calculations were performed using the density functional theory as implemented in the Vienna Ab initio Simulation Package49,50. The generalized gradient Perdew–Burke–Ernzerhof51 functional was adopted in the density functional theory calculations and the core electrons were described using the projector augmented wave method. First, the lattice parameters of the bulk cobalt and LaCoSi were relaxed using Monkhorst–Pack grids of 22 × 22 × 12 and 10 × 10 × 6, respectively. An energy cutoff of 600 eV, with the total energy convergence set to 10−5 eV, was used to create the plane wave basis set. To reveal the electron distributions in different structures, Bader charge analysis was performed for the bulk cobalt and LaCoSi (ref. 34).

The adsorptions of nitrogen and N2 on the Co(001) and LaCoSi(001) surfaces were studied. The Co(001) and cobalt-terminated LaCoSi(001) (LaCoSi(001)–Co) surfaces were constructed based on the optimized bulk lattice parameters. A Co(001) surface was built with a periodic supercell containing a vacuum width of 40 Å and a slab consisting of 9 layers of cobalt atoms with a 3 × 3 lateral unit cell. A symmetrical LaCoSi(001)–Co surface was built with respect to the central cobalt atom layer containing a vacuum width of 40 Å and 11 layers of La(Co or Si) atoms with a 2 × 2 lateral unit cell. A cutoff energy of 500 eV and a Monkhorst–Pack K-mesh setting of 3 × 3 × 1 were employed in the calculation for the (001) surfaces of LaCoSi and cobalt. The central layers of atoms of two surface models were kept fixed to hold the characteristics of realistic surfaces, while the rest of the unit cell was allowed to be fully relaxed during the geometry optimizations. After surface relaxations, Bader charges were calculated to reveal the charge redistribution of the LaCoSi(001) and Co(001) surfaces. The work function for each surface was estimated using the relaxed slab models, in which the vacuum level was used as a reference. The vacuum level was confirmed as the energy level at which the electrostatic potential became constant.

The adsorption energies of X (Ead(X)) (X stands for N, N2) species on the LaCoSi(001) and Co(001) surfaces were calculated using the following equation:

$${E}_{{\rm{ad}}}\left(X\right)={E}_{{\rm{tot}}}\left(X{\rm{/}}{\rm{surface}}\right)-{E}_{{\rm{tot}}}\left(X\right)-{E}_{{\rm{tot}}}\left({\rm{surface}}\right)$$
(5)

where Etot(X/surface) is the total energy of the optimized X molecule divided by the atom adsorption configuration at different surfaces, Etot(X) is the total energy of an X molecule or atom and Etot(surface) is the total energy of the surface model. It is worth mentioning that we used half of the total energy of an N2 molecule as the total energy of a nitrogen atom in this work.

The charge transfer between absorbed N2 and the LaCoSi(001)–Co surface was studied by employing charge density difference calculations. The charge transfer between absorbed N2 and the Co(001) surface was studied as well. The charge density difference of an adsorption configuration X/surface is defined as:

$$\Delta \rho =\rho \left(X/{\rm{surface}}\right)-\rho \left(X\right)-\rho \left({\rm{surface}}\right)$$
(6)

Three kinds of charge density calculation for the systems X/surface, X and surface were performed using the Vienna Ab initio Simulation Package. In the calculations for X and surface, the atomic positions were fixed as those in the X/surface system.

The energy barriers of the N2 dissociation were calculated using the nudged elastic band method implemented in the Vienna Ab initio Simulation Package with 11 replicas, which included initial and final structures and 9 nudged intermediate images.

First-principles molecular dynamics calculations were performed using the Vienna Ab initio Simulation Package code to simulate the process of N2 dissociation on the LaCoSi(001)–Co surface. The first-principles molecular dynamics simulations were performed with an NVT ensemble (where the number of atoms N, volume V and temperature T are kept constant) with a Nosé thermostat, the same slab model used for the adsorption calculations, a temperature of 773 K and a time step of 3.0 fs. The simulation starting from configuration 1 (Fig. 5b) was performed for a total of 618 fs; that is, after N2 had dissociated. For the simulation starting from configuration 2 (Fig. 5b), the atomic coordinates were collected for a total of 1,200 fs.

### Data availability

All data are available from the authors upon reasonable request.

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## Acknowledgements

This work was supported by the Accelerated Innovation Research Initiative Turning Top Science and Ideas into High-Impact Values (ACCEL) programme of the Japan Science and Technology Agency. H.H. was supported by the Japan Society for the Promotion of Science through a Grant-in-Aid for Scientific Research (S), No.17H06153. The authors thank S. Fujitsu (Tokyo Institute of Technology) for technical support with the Auger electron spectroscopy measurements.

## Author information

### Author notes

1. Yutong Gong and Jiazhen Wu contributed equally to this work.

### Affiliations

1. #### Materials Research Center for Element Strategy, Tokyo Institute of Technology, Yokohama, Japan

• Yutong Gong
• , Jiazhen Wu
• , Masaaki Kitano
• , Junjie Wang
• , Tian-Nan Ye
• , Jiang Li
• , Yasukazu Kobayashi
• , Kazuhisa Kishida
• , Hongsheng Yang
•  & Hideo Hosono
2. #### ACCEL, Japan Science and Technology Agency, Kawaguchi, Japan

• Yutong Gong
• , Jiazhen Wu
• , Tian-Nan Ye
• , Jiang Li
• , Yasukazu Kobayashi
• , Kazuhisa Kishida
• , Hitoshi Abe
•  & Hideo Hosono
3. #### High Energy Accelerator Research Organization, Tsukuba, Japan

• Hitoshi Abe
•  & Yasuhiro Niwa
4. #### Department of Materials Structure Science, School of High Energy Accelerator Science, Graduate University for Advanced Studies, Tsukuba, Japan

• Hitoshi Abe

### Contributions

H.H. proposed the idea behind the research and supervised the project. Y.G., J.Wu, M.K., T.-N.Y., J.L., K.K. and H.Y. performed the synthesis, characterization and catalytic measurements. J.Wang carried out the model construction and density functional theory calculations. H.A. and Y.N. helped with the X-ray absorption fine-structure measurements. Y.G. and Y.K. performed the kinetic calculations. Y.G., J.Wu, J.Wang and H.H. co-wrote the paper. All authors discussed the results and commented on the manuscript.

### Competing interests

The authors declare no competing financial interests.

### Corresponding authors

Correspondence to Junjie Wang or Hideo Hosono.

## Supplementary information

1. ### Supplementary Information

Supplementary Methods; Supplementary Figures 1–29; Supplementary Tables 1–5; Supplementary References

### DOI

https://doi.org/10.1038/s41929-017-0022-0