Catalytic activity of Co-nanocrystal-doped tungsten carbide arising from an internal magnetic field

Pt is an excellent and widely used hydrogen evolution reaction (HER) catalyst. However, it is a rare and expensive metal, and alternative catalysts are being sought to facilitate the hydrogen economy. As tungsten carbide (WC) has a Pt-like occupied density of states, it is expected to exhibit catalytic activity. However, unlike Pt, excellent catalytic activity has not yet been observed for mono WC. One of the intrinsic differences between WC and Pt is in their magnetic properties; WC is non-magnetic, whereas Pt exhibits high magnetic susceptibility. In this study, the WC lattice was doped with ferromagnetic Co nanocrystals to introduce an ordered-spin atomic configuration. The catalytic activity of the Co-doped WC was ∼30% higher than that of Pt nanoparticles for the HER during the hydrolysis of ammonia borane (NH3BH3), which is currently attracting attention as a hydrogen fuel source. Measurements of the magnetisation, enthalpy of adsorption, and activation energy indicated that the synergistic effect of the WC matrix promoting hydrolytic cleavage of NH3BH3 and the ferromagnetic Co crystals interacting with the nucleus spin of the protons was responsible for the enhanced catalytic activity. This study presents a new catalyst design strategy based on the concept of an internal magnetic field. The WC–Co material presented here is expected to have a wide range of applications as an HER catalyst.


Introduction
The development of catalysts for the hydrogen evolution reaction (HER) is critical for producing hydrogen fuel as a substitute to fossil fuels to reduce global CO 2 emissions. Tungsten carbide (WC) has 10 valence electrons, 5d 6 from W and 2p 4 from C, similar to Pt (5d 10 ). Since 1973, when Levy and Boudart 1 proposed that WC exhibited singular catalytic activity similar to Pt, this topic has been investigated by many researchers. Bennett et al. 2 measured the valence band spectrum of WC using Xray photoelectron spectroscopy (XPS) and compared it with the spectra of W and Pt. Near the Fermi level (E F ), the electronic density of states (DOS) of WC more closely resembled that of Pt 3 than W. 4 Houston 5 compared the DOS of W, WC, and Pt using so X-ray appearance potential spectroscopy (SXAPA). Contrary to the results of previous studies, 3,4 the width of the unoccupied portion of the 5d band of W in WC was larger than in pure W. 5 Another study 6 showed that the differences between the DOS measured by SXAPA 5 and predicted using a rigid band model 1,2 resulted in different crystal structures of body centred cubic (bcc) W, face centred cubic (fcc) Pt, and hexagonal WC. Mattheiss and Hamann 7 investigated the DOS of the bulk and (0001) surface of WC using a relativistic linear augmented-plane wave method. 8 The DOS near the E F of the (0001) surface associated with the catalytic properties was larger than in the bulk. Recently, the electronic states of Pt were updated 9 using the projector-augmented-plane wave method implemented in the VASP code 8 using the generalised gradient approximation (Perdew-Burke-Ernzerhof version) (GGA-PBE), 10 which claried that E F is located at the top of the 5d DOS, consistent with its highest catalytic activity of all elements.
Esposite et al. 11 showed that a monolayer lm of Pt deposited on a bulk WC substrate exhibited a similar electrochemical hydrogen overpotential, h H 2 , to that of Pt in an aqueous H 2 SO 4 solution, indicating that the surface electronic and chemical properties of monolayer Pt on a bulk WC substrate are signicantly similar to those of bulk Pt. Zhang et al. 12 synthesised a Fe 3 C/Co 3 C/WC/C carbide composite prepared by combining hydrothermal synthesis with resin impregnation and pyrolysis. Linear-sweep voltammetry of the Fe 3 C/Co 3 C/WC/C in an aqueous KOH solution exhibited similar behaviour to that of a Pt/C electrode, indicating that it is a candidate cathode material for polymer electrolyte membrane fuel cells (PEMFCs). 13 In addition, a 7.5 wt% Pt/W 2 C catalyst showed a current density 2-3 times higher than that of a commercial 20 wt% Pt/C for electrolysis in H 2 SO 4 aqueous solution due to the synergistic effect of Pt and WC. 13 Good catalytic activity for the hydrogen evolution reaction (HER) via electrolysis of the H 2 SO 4 aqueous solution was observed using a powder microelectrode composed of 16.20 wt% Pt/WC 14 or a bimetallic carbide composed of Mo 2 C and WC. 15 Zheng et al. demonstrated that PEMFCs using a Naon membrane containing WC nanoparticles exhibited enhanced power density and durability over 100 h of use. 16 The catalytic activities of WC and its composites have only been observed under conditions of an applied external voltage, [11][12][13][14][15][16] and the predicted intrinsic catalytic activity of mono WC under voltage-free operation has not yet been veried. Although Levy and Boudart observed that WC catalysed the reduction of WO 3 with hydrogen gas in the presence of water, and the isomerisation of 2,2-dimethylpropane to 2-methybutane, the rates were merely 0.37% and 0.01%, respectively, in comparison with the performance of Pt. 1 Bennett et al. 2 noted that one of the intrinsic differences between WC and Pt is their magnetic properties; WC is nonmagnetic, whereas Pt exhibits high magnetic susceptibility. Cerri et al. 17 studied the magnetic properties of polycrystalline Gd and found that hydrogen chemisorption induced a disordering of the electronic spin polarisation on the surface. An FTIR spectroscopy study conrmed that antiferromagnetic LaFeO 3 accelerated the nucleus spin conversion of ortho liquid hydrogen (composed of two antiparallel nucleus spins) to para liquid hydrogen (composed of two parallel nucleus spins) to reach equilibrium. 18 Furthermore, Galces-Pineda et al. 19 observed that an external magnetic eld accelerated oxygen evolution during the electrolysis of water.
An application of HER catalysts is the generation of hydrogen fuel from NH 3 BH 3. In its stable crystal form, NH 3 BH 3 contains 19.6 wt% hydrogen, 20 and is being investigated for efficient transportation of hydrogen-based fuel for portable fuelcell systems. Previous studies investigated the HER by hydrolysis over 10 wt% Co 21 or 2 wt% Pt 22 (both supported by Al 2 O 3 ) and found that the HER in the latter was signicantly faster than that in the former. A similar HER in NH 3 BH 3 (aq) catalysed by Ni nanoparticles (NPs) supported by a zeolite molecular sieve was observed. 23 In this study, the WC lattice was doped with ferromagnetic Co nanocrystals (WC-Co carbide ) 24 to introduce an ordered-spin conguration as an internal magnetic eld to avoid the need for an external applied voltage. The catalytic performance of WC-Co carbide for the HER in NH 3 BH 3 (aq) was compared with that of Pt nanoparticles (PT_NPs), commercial mono WC, and a bcc W-Co solid solution (W-Co alloy ) in the spin glass state. The present study aims to investigate the (1) effect of an internal magnetic eld instead of an external voltage on the catalytic activity; (2) kinetics of the HER; and (3) practical applications of the catalyst.

Materials and methods
The W-Co alloy powder consisting of a solid solution of Cosupersaturated bcc W was prepared using a hydrothermal synthesis method that we have described previously. 24 The precursor materials were 99% ammonium tungstate pentahydrate (5(NH 4 ) 2 O$12WO 3 $5H 2 O; Kanto Chemical Co. Inc., Japan) and 99% cobalt acetate tetrahydrate (Co(C 2 H 3 O 2 ) 2 $4H 2 O; Kojundo Chemical Laboratory Co. Ltd, Japan), which were mixed to achieve a molar ratio of W : Co ¼ 80 : 20. Briey, W-Co alloy was carburised at 1173 K with a gas with a composition of 23 vol% CO 2 , 32 vol% H 2 , and 45 vol% Ar to form WC containing Co nanocrystals (WC-Co carbide ). In this study, CO 2 was used as the carburisation gas instead of CO to increase the safety of the process. Since CO 2 barely carburises the W-Co alloy based on the thermochemical equation, CO 2 was converted into CO in situ in the furnace using 50 : 50 mol% Fe-Al powder, where the Al thermally reduces CO 2 into CO. Although 10.8 ks was shown to be a sufficient processing time for carburisation using CO, 24 a total of 32.4 ks was required when CO 2 was used. During this carburisation procedure, the samples were ground at each 10.8 ks interval.
The chemical composition and structure of WC-Co carbide were conrmed by X-ray diffraction (XRD; Rigaku, Ultima IV) and electron probe microanalysis (EPMA; JOEL, JXA-8900) operated at a 15 kV accelerating voltage. The nanostructure of the Co crystal was observed by high-resolution transmission microscopy (HRTEM; JOEL, JEM-2100) operated at an accelerating voltage of 200 kV. The metallic state of the surface of the Co crystal was conrmed via XPS (ULVAC-PHI Inc., PHI5000) using monochromatic X-rays (Al Ka, 1486.6 eV). The specic surface area (SSA) of all samples was measured using the Brunauer-Emmett-Teller method (Shimadzu, TriStar II 3020) with the Kr physisorption isotherm obtained at 77 K.
A standard catalyst containing 1 wt% Pt_NPs on a carrier of Al 2 O 3 particles (Catalysis Society of Japan) 25 was used to obtain comparative data for the catalytic reaction. The SSA of the Pt was 3.40 m 2 g cat À1 and the total SSA of the catalyst, including the Al 2 O 3 , was 176 m 2 g cat À1 . 25 A commercial mono WC particle (Kojundo Chemical Laboratory Co. Ltd, Japan; 99%) was also used as a reference sample. The WC-Co carbide , W-Co alloy , Pt_NPs, and WC samples were ushed in a H 2 atmosphere at 473 K for 2 h. Then, 20 mg of each sample was placed in a glass test tube with 1 ml of H 2 O. In addition, 0.5 mmol of NH 3 BH 3 (cr) was dissolved in 1.5 ml of H 2 O to form an aqueous solution of NH 3 BH 3 (aq) that was mixed with each of the aforementioned samples to evolve hydrogen by hydrolysis of the solution. Four repeat measurements of the hydrogen evolution volume (HEV) were performed for the WC-Co carbide , W-Co alloy, and Pt_NPs samples, whereas only one measurement was considered sufficient for WC as it showed no catalytic activity.
The HER rate for each sample was evaluated by determining the slope of the HEV curve as a function of time using the least squares method. The average HER rates of the four repeat measurements are presented here. The 1-sigma error (68% condence interval) 26 was calculated by dividing the standard deviation (s) of the four measurements by the average value.
To determine E a , the HEV over WC-Co carbide was measured at 308, 318, 328, and 338 K using a solution prepared with 1.0 mmol NH 3 BH 3 (cr) and 1.5 ml of H 2 O. A higher solution concentration than that used in the previous measurements was selected to achieve a longer reaction time and hence, more accurate Arrhenius plots. Three HER measurements were performed at each temperature and the average HER rate is presented. The 1-sigma error was evaluated by dividing 1s of the three measurements by the average value at each temperature. The 1-sigma error was evaluated from the standard deviation of the 12 total measurements.
To determine the value of M of WC-Co carbide , the magnetic hysteresis loop was measured using a SQUID instrument (QD, MPMS) under a magnetic eld increased to a maximum of 3 Â 10 4 Oe. Temperatures of 308 and 4 K were used to investigate the maximum value of M, 27,28 respectively.
The standard enthalpies of adsorption of H 2 (g), D ad H m , for WC-Co carbide , WC, and a commercial 99.9% Pt powder (Kojundo Chemical Laboratory Co. Ltd, Saitama) were measured at 423 K using a Calvet-type microcalorimetre (SETRAM, C80) in a H 2 atmosphere.

Results and discussion
Hydrogen evolution over WC-Co Fig. 1 shows a representative bright-eld TEM image of a WC-Co carbide sample. Co crystals with the fcc structure, [100] orientation, and diameter of 60 nm were observed in the WC matrix with [101] orientation. The atomic conguration was the same as that observed in our previous study. 24 The SSA values of the WC-Co carbide , W-Co alloy , and Pt_NPs samples are shown in Table 1. The WC-Co carbide exhibited an SSA $ 60% smaller than that of the Pt_NPs, whereas WC-Co carbide exhibited a smaller SSA than that of W-Co alloy . Fig. S1 (see ESI †) shows the XRD results. Only peaks related to the WC matrix and Co crystals were observed. Fig. S2 (see ESI †) shows the Co 2p XPS spectrum of WC-Co carbide . The peak at 778.4 eV was assigned to the metallic state Co 0 . Fig. S3 (see ESI †) shows representative EPMA/SEM images of W La, C Ka, and Co Ka for the WC-Co carbide particle. Because W, C, and Co were distributed homogeneously, HRTEM observation ( Fig. 1) was necessary to distinguish the Co crystals from the WC matrix. Fig. 2 shows the change in the average HEV over time (t) for hydrolysis of the NH 3 BH 3 (aq) over WC-Co carbide , W-Co alloy , Pt_NPs, and commercial WC samples. The slope of the HEV(t) curve for WC-Co carbide was steeper than that for Pt_NPs, indicating that WC-Co carbide exhibited singular catalytic activity, whereas W-Co alloy exhibited less activity.
The normalised HER rates per unit area, N HER (H 2 mol min À1 m À2 ), determined by normalising the HEV by the SSA values are shown in Table 1, along with their error values. The N HER of WC-Co carbide was $30% higher than that of Pt_NPs, indicating that it exhibits singular catalytic activity similar to Pt. The N HER of W-Co alloy was only approximately 10% of that of WC-Co carbide .

Activation energy
To clarify the mechanism of the singular catalytic activity of WC-Co carbide , its E a value was investigated. Fig. 3 shows the HEV as a function of time during the hydrolysis of NH 3 BH 3 (aq) over WC-Co carbide at 308, 318, 328, and 338 K. Comparing the data measured at 308 K to the corresponding curve in Fig. 2, the HEV at the same time was consistent with doubling the NH 3 BH 3 concentration. Hence, a large number of reaction sites were available for studying the HER. The slopes of the HEV(t) curves increased with increasing temperature, indicating that the hydrolysis was a result of a thermally activated process.
The E a is dened by the Arrhenius equation: where k r is the reaction rate constant, R is the gas constant (8.3145 J K À1 mol À1 ), and A is the frequency factor indicating  the number of collisions of the reaction species. The N HER values summarised in Table 1 were regarded as k r which were plotted as an Arrhenius plot in Fig. 4 (ln k r vs. T À1 ). The ln k r values decreased linearly as a function of T À1 , where E a was calculated from the slope of this curve. The E a and A values for the HER over WC-Co carbide were 54.0 AE 13.0 kJ mol À1 and 1.01 Â 10 10 AE 2.44 Â 10 9 mol m À2 min À1 , respectively, where the uncertainty was evaluated as the error propagation 26 of the uncertainties of the N HER data at each temperature listed in Table 1. This E a value was larger than the literature value for Pt NPs (2 wt% Pt on an Al 2 O 3 support) 22 and similar to that of Co NPs (10 wt% Co on an Al 2 O 3 support), 21 indicating that the hydrogen was released from the surface of the Co nanocrystals in the WC matrix.
The catalytic activity of WC-Co carbide was evaluated considering the hydrogen overpotential (h H2 ). The h H2 of Pt is 0 V by denition, whereas for Co it is in the range of À0.25 to À0.47 V in 1 M H 2 SO 4 aqueous solution at 303 K under a current density of 0.3-10 mA cm À2 . 29 Chandra and Xu 22 determined E a (21 kJ mol À1 ) of the HER in NH 3 BH 3 (aq) over Pt NPs. 22 The difference in the activation energy, DE a , between WC-Co carbide and Pt NPs 22 was 33 kJ mol À1 , which corresponds to À0.34 V, consistent with the h H2 of Co. 29 This analysis indicated that the hydrogen release sites were the Co nanocrystals in the WC matrix. In general, h H2 is dened as the complex energies consisting of the elementary processes: (I) alignment of H + (aq) on the electrode; (II) accepting electrons to form the radical hydrogen atom H(rad.); (III) bonding two H(rad.) to form a H 2 molecule; (IV) convergence of the radicals to form hydrogen gas H 2 (g); and (V) desorption of H 2 (g) from the electrode. In this study, the separation of these elementary processes of h H2 was impossible as E a was determined only from a simple Arrhenius plot. Further computational simulations are necessary to clarify this point. The A value is discussed later with respect to the thermodynamic cycle.

Magnetic behaviour
The HER over the W-Co alloy powder was not enhanced as observed for WC-Co carbide (Fig. 2), indicating that H 2 (g) is not readily evolved over the Co atoms substituted into the bcc W lattice. However, the HER was enhanced in the case of the WC-Co carbide sample with Co atoms congured in the nanocrystal domain. The most likely difference between these congurations is related to their magnetic properties. Hence, M was investigated to clarify the different HER results. Fig. 5 shows M as a function of the magnetic eld (H) for WC-Co carbide and W-Co alloy at 4 K. WC-Co carbide showed a clear hysteresis loop, indicating that it is a ferromagnetic material. Assuming that the    Table S1. † value of M for WC-Co carbide resulted from the Co crystals, the maximum saturated value, M S , was 8.41 Â 10 3 emu (mol Co atoms) À1 . However, the value of M for W-Co alloy was close to zero, indicating that it had a spin glass state. 30 Similarly, the M (H) data were measured at 308 K, yielding similar results to those at 4 K for both samples.
The magnetic moment b of a Co atom in the Co nanocrystals in WC-Co carbide at 4 K and 308 K were 1.50 and 1.42 m B per Co atom, respectively, where m B is the unit of the Bohr magneton. In the elemental Co crystal, the value of b for a Co atom is 1.7 m B . 27 Hence, the Co nanocrystals had a b value close to that of elemental Co. In contrast, the b value of a Co atom substituted into the bcc W lattice in the W-Co alloy measured at 4 K and 308 K was 6.79 Â 10 À2 and 7.48 Â 10 À3 m B , respectively. As described in our previous study, 24 the XRD pattern of W-Coalloy showed only the peaks of W. 24 The composition of W-Coalloy corresponds to the two phase equilibria region of the W phase and the intermediate phase of Co 7 W 6 in the phase diagram of the W-Co binary system. 31 Co 7 W 6 has complicated long-range periodic structure. 32 Formation of the complicated long-range periodic structures such as the sigma phase in the heatresistant alloys takes a lot of time to accomplish their atomic conguration. 33 Hence, the equilibrium phase of Co 7 W 6 was not formed during reduction with H 2 gas. The Co atoms are concluded to be supersaturated in the W lattice as a nonequilibrium state. Consequently, the spin conguration among isolated Co atoms was random (i.e., a spin glass state 30 ). Hence, the spin-ordered state of the Co in WC-Co carbide appears to be one of the factors determining the singular catalytic activity.
Cerri et al. 17 found that hydrogen chemisorption induced a disordering of electronic spin polarisation on the surface of ferromagnetic Gd, resulting in a change in M, and the Curie temperature, T C . It is likely that hydrogen chemisorption relaxes the spin conguration in the system. In aqueous solutions, the spin conguration of the protons is relevant. Here, the protons are likely to be absorbed on the ferromagnetic Co nanocrystals, such that their nucleus spin congurations are aligned to be antiparallel to relax the spin polarisation of the surface.

Thermodynamic cycle
The following equations show the thermodynamic equilibria among the species associated with the HER from hydrolysis of NH 3 BH 3 (cr), where the standard enthalpies of formation, D f -H m , at 298.15 K of the standard substances of NH 3 BH 3 (cr), 34 H 2 O(l), 35 ammonia (NH 3 (aq)), 35 orthoboric acid (B(OH) 3 (aq)), 35 ammonium (NH 4+ (aq)), 35 metaboric acid (BO 2 À (aq)), 36 and H 2 (g) 35 are summarised in Table S1. † Eqn (2) shows the hydration reaction of NH 3 BH 3 (cr), where the thermodynamic value is unknown. Eqn (3) shows the HER of the hydrolysis of NH 3 -BH 3 (aq). Eqn (4), rewritten as the sum of eqn (2) and (3), indicates the HER from the initial substance of NH 3 BH 3 (cr). Eqn (5) shows the formation of NH 4+ (aq). Eqn (6) shows the formation of BO 2 À (aq). Finally, eqn (7), rewritten as the sum of eqn (4)-(6), shows the nal state of the hydrolysis. Since eqn (5)-(7) are spontaneous reactions, the HER is given by eqn (4). As the standard entropy, S m , of NH 3 BH 3 (cr) has not yet been measured, the standard entropy of reaction, D r S , and the standard Gibbs energy of reaction, D r G , are unknown. However, D r G is more negative than D r H as the HER increases D r S . Therefore, when a driving energy is applied corresponding to the hydrogen overpotential of Co, the HER reaches equilibrium, as dened by eqn (7) via eqn (4).
In previous studies, Co NPs (10 wt% Co on an Al 2 O 3 support) 21 had an HER rate 10 times lower than that of Pt NPs (2 wt% Pt on an Al 2 O 3 support). 22 However, in the present study, the HER rate of WC-Co carbide was 30% higher than that of Pt_NPs, even if E a corresponds to the h H2 of Co. The excellent catalytic activity was a result of the high A value, as determined from the Arrhenius plot (Fig. 4). The WC matrix seems to facilitate the release of H + (aq) from NH 3 BH 3 (aq) and contribute to increasing A (i.e., the number of H + (aq) collisions). In accordance with the electron theory, the Pt-like high DOS near the E F of the surface of WC 7 can induce adsorption of NH 3 BH 3 molecules, which can promote the decomposition of B-N bonds to form NH 3 (aq), B(OH) 3 (aq), and H 2 (g) via highly unstable BH 3 (aq) close to the equilibrium states (see eqn (3)). Furthermore, considering the thermodynamic hierarchy, as shown in Table S1, † the D f G m of WB 37 is smaller than that of WC, 38 indicating that the chemical bonding between the W and B atoms is more stable than that between the W and C atoms. In addition, it is well known that natural tungsten ore consists of ammonium tungstate, 39 which is the starting material used in the present study, indicating the high affinity between tungsten and ammonia. Therefore, W in the WC matrix has a driving force for attracting NH 3 BH 3 (aq), resulting in preferential adsorption. Although a previous study 20 investigated the hydrolysis kinetics of NH 3 BH 3 using rst principles calculations based on the transition state theory and estimated the atomic distance of a B-N bond, the interaction between the WC matrix and NH 3 BH 3 (aq) should be further investigated by rst principles and molecular dynamics calculations. The BH 3 (aq) molecule can release three protons while bonding with three OH À ions to form B(OH) 3 . As shown in Table 1, when the amount of NH 3 BH 3 (aq) was doubled, N HER also doubled, indicating that there were sufficient HER reaction sites. Hence, the WC matrix played a crucial role in adsorbing NH 3 BH 3 molecules and decomposing B-N bonds, followed by supplying protons to the Co crystals.

Specic enthalpy of hydrogen adsorption
The D ad H m values of WC-Co carbide, and commercial WC and Pt powders at 423 K were À22.42 AE 0.90, À21.87 AE 0.87, and À109.72 AE 4.39 J m À2 , respectively. We found that the D ad H m of WC was less exothermic than that of Pt, implying that the desorption of H 2 (g) from the surface of WC was not difficult. Previous studies have investigated the catalytic activity of WC 13 and related carbide composites 11,12 under an external voltage. When an external voltage is applied, the H + (aq) ions align on the surface of WC, followed by hydrogen evolution. However, when no external voltage is applied, such an alignment of H + (aq) is unlikely to be signicant. In contrast, on the surface of WC-Co carbide , the H + (aq) ions seem to align as a result of the magnetic eld of the Co nanocrystals, followed by hydrogen evolution. The D ad H m of Pt is extremely high, indicating that hydrogen was stored in its lattice. Pt simultaneously achieves the adsorption, storage, and desorption of hydrogen species, although the specic mechanism is still unknown. Fig. 6 shows a schematic of the catalytic HER over WC-Co carbide , which involves the following steps. (1) The NH 3 BH 3 molecules are absorbed on the WC matrix by the attractive interaction of W-B bonds; (2) the B-N bonds in NH 3 BH 3 (aq) are broken to form stable NH 3 (aq) and unstable BH 3 (aq); (3) the B atoms in BH 3 (aq) with a signicantly short lifetime release three quasistable protons and coordinate three OH À (aq) ions from the surrounding H 2 O molecules to form stable B(OH) 3 molecules, wherein the H 2 O releases three protons; (4) sufficient amounts of protons from BH 3 (aq) and H 2 O are adsorbed on the ferromagnetic Co nanocrystals in the WC matrix, resulting in antiparallel alignment of the nucleus spin congurations of the two H + (aq) to relax the spin polarisation of the system; (5) hydrogen molecules are evolved as the protons accept electrons, e À , such that E a is consistent with h H2 of Co, wherein Co is protected by galvanic protection; 40 (6) one e À is released during the decomposition of BH 3 , along with a proton, while the other e À is released from OH À (aq) during coordination to form B(OH) 3 (aq), i.e. the origin of charge transfer is the B atom adsorbed on the W atom, wherein the charge is transferred to Co via the WC matrix; (7) the WC matrix decomposing NH 3 BH 3 (aq) and generating H + (aq) applies a driving energy corresponding to the necessary hydrogen overpotential, wherein the WC matrix supplies excess protons to the Co sites.

Mechanism of a singular catalytic behaviour of WC-Co carbide
The relative volume ratio of the WC matrix vs. Co nanocrystals is estimated to be 100 : 13 from the densities of pristine WC and Co. When the relative SSA ratio of the WC matrix vs. Co nanocrystals is hypothetically equal to the relative volume ratio, the SSA of the Co nanocrystals is 0. 15   Co and Ni. 29 These E a results support the mechanism depicted in Fig. 6.
Another denition of h H2 in electrochemistry is the HER current density, i 0 , determined by extrapolating the cathodic Tafel line to the reference hydrogen electrode. 41 Fig. S4 † shows the correlation between magnetic susceptibility, X, 42 and log i 0 41 of the transition metals of the fourth, h, and sixth periods (rows) of the periodic table of the elements. In the sixth period, the log i 0 value of Pt was large, consistent with the high HER catalytic activity, while X was large, corresponding to a high log i 0 . Similarly, in the h period, the log i 0 values and X values of Rh and Pd were large. In the fourth period, the log i 0 values of Fe, Co, and Ni were high. As these metals are ferromagnetic with spontaneous magnetisation, their X values are not relevant. However, their spin-ordered ferromagnetic state likely increased their log i 0 values. In contrast, the diamagnetic transition metals of Au and Hg in the sixth period, Ag and Cd in the h period, and Cu and Zn in the fourth period with negative X values showed small log i 0 values consistent with their lower HER catalytic activities. Therefore, we conclude that the magnetic properties of the transition metals are related to the HER catalytic activity. Materials with high X values are likely to interact readily with the nucleus spin of H + (aq). Ferromagnetism seems to induce alignment of the nucleus spin of H + (aq) on the ferromagnetic metal surface, as discussed with regard to the contribution of the Co nanocrystals in this study. Aer formation of two radical H atoms by donation of electrons, the spin conversion of the two H atoms should form the 1s g molecular orbital of a H 2 molecule. The magnetic properties of metals are likely to contribute to the spin conversion. Aer H 2 molecules are formed, they are released from the surface of the metals with a high positive X value or ferromagnetism because H 2 is diamagnetic with a negative X value (À19.7 Â 10 À9 m 3 kg À1 ).
Recently, it was shown that an external magnetic eld enhanced the oxygen evolution reaction (OER) during electrolysis of a KOH aqueous solution. 19 A Pt plate was used as the cathode and ferrite NiZnFe 4 O x (deposited on Ni foam by direct magnetic interaction between the materials) was used as the anode. An external magnetic eld of 0.45 T was applied to the anode using a rare-earth permanent magnet, which resulted in the OER current almost doubling (from 24 to 40 mA cm À2 at $1.65 V). 19 They hypothesised that the external voltage accelerated the spin conversion to form the paramagnetic triplet of O 2 (g). Li et al. 43,44 prepared a series of metal-organic frameworks (MOFs) composed of the Fe-Ni binary 43 and W-Co-Fe ternary system 44 as electrocatalysts. Their superior catalytic properties appear to result from the magnetic elements of Fe, 43,44 Ni 43 , and Co. 43,44 These ndings are highly relevant to the present study.
There have been many investigations of the electronic states of HER. 29 However, the interaction between the nucleus spin of H + (aq) and electronic spin of metals has not yet been investigated. Thomas et al. 45,46 calculated the energy eigenvalues of the electrons and nuclei of hydrogen atoms (protons) by considering the wave functions of both protons and electrons, and describing the zero-point motion of the protons by a Slater-type wave function. This approach could be applied to the HER catalytic reaction.
As described above with respect to the thermodynamics, the WC matrix appears to facilitate the release of H + (aq) from NH 3 BH 3 (aq) and contribute to increasing A (i.e., the number of collisions between H + (aq) ions). However, H 2 (g) appears to be barely formed by such collisions. The alignment of H + (aq) on the catalyst surface and the donation of an electron to the ion are necessary. When an external electric voltage is applied to WC, these requirements are likely to be satised, resulting in the catalytic activity observed in previous studies. [11][12][13][14][15][16] The internal magnetic eld is considered sufficient to induce catalytic activity without requiring an external voltage.
Pt seems to easily adsorb NH 3 BH 3 (aq) with the highest DOS at the E F of all elements, and easily evolves H 2 (g) from its surface with the smallest h H 2 of any known element. A study of the interaction between Pt with a high magnetic susceptibility and protons with a nucleus spin appears to be a necessary future work to consider the effect of the magnetic eld from the earth on the spin alignment of the protons.
Pt catalysts have low reusability in HER from HCOOH due to CO poisoning. WC-Co carbide is advantageous for avoiding CO poisoning due to that it is prepared by carburizing with CO via CO 2 . Reusability of WC-Co carbide should be further investigated.

Conclusion
The catalytic activities of WC and its composites had previously only been observed under the conditions of an applied external voltage, and the predicted intrinsic catalytic activity of mono WC without an external voltage had not been veried. We hypothesised that the introduction of an internal magnetic eld would provide conditions similar to those provided by the external voltage to enhance the catalytic performance of WC. To this end, the WC lattice was doped with ferromagnetic Co nanocrystals to introduce an ordered-spin conguration as an internal magnetic eld. The internal magnetic eld successfully increased the HER rate during hydrolysis of NH 3 BH 3 to a value even higher than that of the Pt nanoparticles. The enhanced catalytic activity was attributed to the synergistic effect of the WC matrix promoting hydrolytic cleavage of NH 3 BH 3 and the ferromagnetic Co crystals interacting with the nucleus spin of the protons. Our new strategy for enhancing the catalytic performance by introducing an internal magnetic eld is expected to provide new opportunities for developing novel catalysts, such as those for hydrolysis of NH 3 BH 3 and the electrodes of fuel cells.

Conflicts of interest
There are no conicts to declare.