DFT and experimental studies of iron oxide-based nanocomposites for efficient electrocatalysis

Encapsulated iron oxide nanoparticles with g-C3N4 shells (Fex-NC) promote the hydrogen evolution reaction. The interactions between Fex-NC nanocomposites were investigated by DFT.


Introduction
Water electrolysis has attracted wide attention as a promising approach for generating high energy density hydrogen at high conversion efficiencies with zero CO 2 emissions. The hydrogen evolution reaction (HER) represents the cathodic half reaction of water electrolysis requiring electrocatalysts to simultaneously increase the reaction rate and efficiency, while lowering the overpotential. Among many electrocatalysts, the platinum group of metals remains as the first choice due to their fast kinetics, almost thermoneutral hydrogen binding energy (G B 0) and hydrogen evolution at values close to the reaction's equilibrium potential. 1 However, the high cost and scarcity of platinumbased materials have intensified the research of alternative low-cost electrocatalysts, to drive the transition to a viable hydrogen economy. Recent progress has focused on the development of traditional electrocatalysts and corresponding hybrids using metal/non-metal compounds of nitrides, selenides, phosphides, and carbides. The synthesis of low-cost, yet effective HER catalysts remains a major challenge. Some of the strategies for improving HER catalytic activity include heteroatom doping, particle size and morphology modification and incorporation of metal/oxide nanoparticles in carbon-based materials. Although much progress has been made in promoting higher HER activity, most of these materials are unstable under acidic and alkaline conditions, since they mainly rely on the interaction of metal-H bonds for the HER. 2 The encapsulation of nanosized electrocatalysts by carbonbased materials such as graphene has been proposed as a means of improving catalytic activity, efficiency, and stability, because graphitic carbon shells have high electrical conductivity, large surface area, good chemical stability, excellent structural tunability and particularly good insolubility in many solvents. These features are linked to improved electron transfer at exposed catalytic active sites under extreme operational conditions. 2 Furthermore, these graphitic carbon shells have also been reported to enhance HER activities by altering the Gibbs free energy of hydrogen adsorption through interaction between metal/metal oxide compounds and the surrounding carbon shell. These carbon shells can effectively prevent direct contact between metal atoms and electrolytes, so that the stability and corrosion resistance of electrocatalysts can be improved. Further introduction of single or multiple heteroatoms of nitrogen (N), 3 phosphorus (P), 4 and boron (B) 5 into the carbon shells can tune the electronic conductivity by offering improved charge transfer, thus influencing the electrocatalytic performance.
Iron and its derivatives are attractive for electrocatalysis due to their low cost and relative abundance. [6][7][8][9] However, their catalytic activity is limited due to instability and deactivation resulting from leaching of active nanoparticles from the reaction medium. Encapsulating iron and its derivatives in heteroatom-doped carbon shells prepared by the chemical vapor deposition and self-templating technique can influence the catalytic activity, while facilitating improved electron transfer, faster hydrogen desorption and better stability. 2 Herein, we use melamine as a nitrogen and carbon source to create such sheathed iron-oxide nanoparticles for electrocatalysis. The new process is an inexpensive and scalable method, which is realized via simple carbonization under an inert atmosphere. Experimental results show that iron oxide nanoparticles encapsulated in a graphitic carbon nitride shell can work as an efficient HER catalyst in an acidic medium with activities that are comparable to other reported carbon-encapsulated catalysts.

Experimental
Preparation of Fe x -NC nanocomposites Fe x -NC samples were prepared via dip coating and carbonization. Varying amounts of Fe(C 5 H 5 ) 2 (Sigma Aldrich) precursor were dissolved in ethanol (Sigma Aldrich) to obtain homogeneous solutions. Melamine-formaldehyde (MF) sodium bisulfite foams (Avocation Ltd) were then dip-coated in the precursor solutions of different concentrations (0.02-0.1 M). The dip-coated foams were dried overnight at 80 1C and then carbonized at 800 1C under a continuous argon flow of 50 mL min À1 . Approximately 50 mL min À1 of hydrogen gas was introduced into the furnace at the target temperature of 800 1C for 30 min to obtain the final samples. The as-prepared samples were denoted as Fe x -NC, where x represents the concentration of Fe, such that the precursor solution concentration varied at 0.02 M, 0.05 M, and 0.1 M, and the samples were named Fe 2 -NC, Fe 5 -NC and Fe 10 -NC, respectively.

Characterization and electrochemical testing
The morphology and structures of the samples were characterized using scanning electron microscopy (Hitachi S3200N, Oxford instrument -SEM-EDS) operated at 20 kV, and JEOL-2100 highresolution transmission electron microscopy (HR-TEM) operated at 200 kV. X-ray diffraction (XRD) patterns were acquired on a Bruker D8 Advance diffractometer (operated at 40 kV and 40 mA), with Cu Ka radiation, at a step size and dwell time of 0.021 and 1 s respectively. Raman spectra were recorded on a Renishaw RA800 series benchtop system with a 532 nm excitation length under a laser power of 6 mW. X-ray photoelectron spectra (XPS) were recorded using a VG ESCALab Mark II spectrometer with a non-monochromatic Al-anode X-ray source (1486.6 eV), operated at a 12 kV anode potential and a 20 mA filament emission current. N 2 adsorption/desorption was determined by Brunauer-Emmett-Teller (BET) measurements using a Quantachrome Autosorb-IQ surface area analyser. Information on the chemical bonding was obtained using attenuated total reflectance-Fourier transform infrared spectroscopy (ATR-FTIR, Bruker) over a wavelength of 400-4000 cm À1 . A CHI-760D electrochemical workstation with a three-electrode system was used to evaluate the electrocatalytic activity of the nanocomposites. The CHI-760D workstation was coupled with a rotating disk electrode (RDE) system where the reference, counter and working electrodes were Ag/AgCl/KCl, platinum wire and glassy carbon electrode (GCE) covered with catalyst ink, respectively. The catalyst ink was prepared via ultrasonification of a mixture of 5 mL of Nafion solution, 1 mL of ethanol/water solution and 3 mg of Fe x -NC sample. The measurements (cyclic voltammograms, linear sweep voltammograms and impedance spectroscopy) were carried out in a 0.5 M H 2 SO 4 (Sigma Aldrich) electrolyte solution at different potentials and scan rates varying from 0 to À0.8 V and 10-100 mV, respectively. The electrode was calibrated by a reversible hydrogen electrode (RHE) and acquired data were corrected for iR losses. The optimal sample was further subjected to a stability test for 5000 cycles.

Computational methodology
In order to support our experimental data, DFT simulation was performed on a QuantumATK, 10 while visualizations were achieved on a VESTA and vnl Version 2019.12. 11 To model the experimentally g-C 3 N 4 -encapsulated FeO x nanoparticles, two different strategies are employed; (I) g-C 3 N 4 is built where mixtures of Fe 3 O 4 and Fe 2 O 3 (collectively denoted as FeO) are encapsulated to form g-C 3 N 4 @FeO ( Fig. 1a and b), and (II) a single layer of g-C 3 N 4 is incorporated on the surface of Fe 3 O 4 ( Fig. 1c-e).
Model (I). DFT calculations are performed to understand the origin of the HER activity of g-C 3 N 4 @FeO. Although the sizes of the FeO nanoparticles and g-C 3 N 4 considered in the calculations are much smaller than those of the FeO nanoparticles and g-C 3 N 4 observed experimentally, the essential effect on the electronic structure, as shown below, can already be captured by this simple geometry. The supercell g-C 3 N 4 is in a rectangular lattice, which replicates four-unit cells of the bare tube in the c direction; the vacuum thicknesses in the a and b directions are set to B15 Å to avoid interactions between g-C 3 N 4 . A 1 Â 1 Â 5 Monkhorst-Pack k-point sampling for the structural relaxation has been employed, while a uniform k-point grid such as 5 Â 5 Â 5 is used for the electronic property simulations. The details of hydrogen adsorption and Gibbs free energy methodologies are given in the ESI. † Model (II). We also performed DFT simulations for the second model where magnetite Fe 3 O 4 with a cubic space group of Fd3m is considered. 12 The lattice parameters of magnetite Fe 3 O 4 are a/b/c = 8.394 Å and a/b/g = 90. After optimizing the lattice parameters of 56 atoms of bulk Fe 3 O 4 , an Fe 3 O 4 (001) slab was built. For the slab model calculations of surface energies and band edge positions, the thickness of the slab was kept as enough to ensure that the centre of the slab can be regarded as the bulk phase. A vacuum space of about 10 Å was kept between slabs, to eliminate the fictitious interaction between the periodically repeating slabs. After surface stability confirmation of Fe 3 O 4 (001), a single layer of g-C 3 N 4 is incorporated on its surface to build the Fe 3 O 4 (001)@g-C 3 N 4 , as shown in Fig. 1c. Hereafter, the Fe 3 O 4 (001) will be denoted as Fe 3 O 4 and Fe 3 O 4 (001)@g-C 3 N 4 as Fe 3 O 4 @g-C 3 N 4 . Finally, two water molecules were interacted on the optimized surfaces of Fe 3 O 4 and Fe 3 O 4 @g-C 3 N 4 , to determine the HER efficiency in the form of water adsorption energy. Generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) exchangecorrelation functional and double Zeta Polarized (DZP) basis set is used for the structural and energy optimization due to its superiority over hybrid pseudopotentials. 13 Moreover, a linear combination of atomic orbitals (LCAO) method is used for Fe, O, C, N, and H atoms. 14

Results and discussion
Structural and physicochemical properties Fe x -NC samples were evaluated by XRD to determine the phase purity and crystalline structure. Fig. 2 show the XRD patterns that confirm the presence of graphitic carbon nitride (g-C 3 N 4 ) and iron oxide. Two characteristic peaks of g-C 3 N 4 at 13.61 and 27.41 are indexed to the (100) and (002) planes, which are linked to the in-planar structure of the tri-s-triazine ring and interplanar stacking peak of C-N systems, respectively. 15 Besides g-C 3 N 4 , diffraction peaks of Fe x -NC samples are in good agreement with the standard pattern of cubic spinel The Raman spectra of Fe x -NC samples, presented in Fig. 3, show the characteristic peaks of graphene, a-Fe 2 O 3 and Fe 3 O 4 , and further confirm the successful formation of Fe x -NC nanocomposites. For carbon, the identified peaks of the D peak (B1350 cm À1 ), G peak (B1580 cm À1 ) and 2D peak (B2690 cm À1 ) are linked to defects, bond stretching of sp 2 graphitic carbon atom and a high-energy second-order process of graphene, respectively. The peak intensity ratios of the D band to G band are calculated to be 0.89, 0.88 and 0.94 for Fe 2 -NC, Fe 5 -NC and Fe 10 -NC, respectively. The higher peak intensity ratio of Fe 10 -NC depicts the presence of higher structural defects compared with other Fe x -NC samples. Characteristic peaks of Fe 2 O 3 and Fe 3 O 4 were also observed and marked in the spectra. Raman shifts at B212, 274, 389 and 586 cm À1 are assigned to A 1g and E g modes  of Fe 2 O 3 . 13 The two additional peaks at 329 and B497 cm À1 confirmed the presence of Fe 3 O 4 . 6 The ATR-FTIR spectra of Fe 5 -NC are shown in Fig. S1 (ESI †). Absorption peaks at the 2115 and 2350 cm À1 regions were observed, which were due to the CRN stretching. 17,18 The 1994 cm À1 peak is linked to bridge carbonyl groups. 16 The prominent bands at 462, 550 and 602 cm À1 are attributed to Fe-O vibrational modes in a-Fe 2 O 3 . 19 The weak peak at 630 cm À1 is attributed to the stretching vibration mode of the Fe-O bonds in the crystalline lattice of Fe 3 O 4 . 20 The SEM and TEM images of Fe x -NC samples are displayed in Fig. 4. As shown in the SEM images (Fig. 4a, c and e), the Fe x -NC consists of nanotubes of several micrometers in length with varying diameters, which were grown on the surface of carbon foams. Based on SEM elemental analysis, all Fe x -NC samples are composed of C, N, O and Fe elements, which are uniformly distributed. TEM images of single Fe x -NC nanocomposites prepared with varying precursor concentrations are shown in Fig. 4b, d and f. The outer diameter of the nanotubes was measured at about 47-117 nm with a wall thickness of 8.1-30 nm. The inner/outer diameter and wall thickness of the nanotubes were observed to decrease with increased precursor concentrations.
The enlarged TEM image shows that nanoparticles are encapsulated within the nanotubes (Fig. 4b, d and f).
The high-resolution TEM (HRTEM) image shows that the outer layer of the nanotubes consists of graphitic layers with an interlayer spacing of 0.32 nm linked to the (002) plane of g-C 3 N 4 . Individual spots seen in the SAED patterns also indicate that Fe x -NC samples consist of mainly iron oxide nanoparticles.    Table S1 (ESI †). Comparison of the relative N and Fe elemental abundances indicates that Fe 10 -NC contains B4 wt% N and B14 wt% Fe on the surface. As shown in Fig. S3b (ESI †), the XPS spectra of C 1s are fitted into five components, assigned to C-C (284.5 eV), CQN (285 eV), CQO (287.6 eV), O-CQO (289.4 eV), and C p (291.3 eV). 23 The main peak at 284.5 eV is linked to sp 2 carbon, which shows that the carbon content of the samples is predominantly graphitic in nature. As shown in Fig. 6a, the high-resolution XPS spectra of Fe show peaks at 711.3 and 714.2 eV, which can be assigned to the binding energies of the 2p 3/2 orbitals of Fe 2+ and Fe 3+ species, respectively. For the 2p 1/2 orbital, the peaks at 723.5 and 727.6 eV are attributed to the binding energy of Fe 2+ and Fe 3+ species, respectively. The peak at 719.1 eV is a satellite peak, while an additional peak at 708.2 eV is linked to metallic Fe. The Fe 2p 3/2 peak at 711.3 eV indicates Fe-N bonding as Fe ions are coordinated to N. 24 XPS studies of Fe 5 -NC before and after testing in Fig. 6b show similar peaks; however, a negligible change in relative proportion of Fe species on the active Fe 5 -NC electrode after cyclic HER studies is observed.
Deconvolution of the high-resolution XPS O 1s peak confirmed the presence of oxygen related to the iron oxide catalyst (529.8 eV) and some carboxylic and hydroxyl species on the surface of the Fe 5 -NC sample at 533.1 and 531.5 eV, respectively (Fig. S3c, ESI †). N 1s spectra were deconvoluted into three peaks, which were assigned to the pyridinic N (398.3 eV), graphitic N (401.0 eV), and quarternary N + -O À (402.8 eV) with atomic contents of 26, 57 and 16 at% (Fig. S3d, ESI †), respectively. Pyridinic N served as metal-coordination sites due to its lone-pair electrons, while graphitic N was reported as catalytically active sites for electrocatalysis. 25 These two types of N species are of high content in Fe x -NC samples, which potentially lead to a high catalytic activity.

Model (I) g-C 3 N 4 -encapsulated Fe 2 O 3 /Fe 3 O 4 (g-C 3 N 4 @FeO).
To determine the Gibbs free energies (DG H* ) of hydrogen adsorption, we choose the first model of g-C 3 N 4 @FeO. First principles DFT calculations are employed to simulate the DG H* adsorption on g-C 3 N 4 @FeO ( Fig. 1a and b), and the clusters of  Fig. 7 leads us to predict that the DG H* value at position (2) is optimum (À0.22 eV), responsible for the dissociation reaction, and shows higher catalytic activity. The reason behind this activity is due to the electrostatic bonding of H with the C atom of g-C 3 N 4 @FeO. On the other hand, the DG H* value at position number (4) is maximum (À0.61 eV), which is due to the strong adsorption energy of the H atom over the surface of the catalyst. This higher adsorption energy does not dissociate the hydrogen bonding and decreases the overall catalytic activity. Moreover, the DG H* value at position (1) is positive (1.33 eV) and here the H is also attached to N of g-C 3 N 4 @FeO. However, the N atom of g-C 3 N 4 @FeO has no bonding with Fe of FeO. In this case, no association takes place and consequently, there will be no HER as well. Furthermore, the DG H* values of H adsorption at position (3) are À0.48 eV, which is also higher and does not allow dissociation reaction. In summary, the H-N interaction at position (4) is stronger, which is due to the direct contact of Fe of FeO with N of g-C 3 N 4 . The DG H* value at position (2) exhibits high activity toward the HER, which is close to the thermodynamic limit value of 0 and even far better than that of the Pt (111) surface, which is B0.09 eV. 26 The reason behind this is the encapsulation of FeO with g-C 3 N 4 and to avoid its direct contact with the H atoms, which slightly minimizes the adsorption energy. So, we propose that g-C 3 N 4 @FeO-based electrocatalysts are promising candidates for highly efficient HER. Furthermore, we suggest that the enhanced HER activity  of g-C 3 N 4 @FeO is due to the encapsulation of FeO nanoparticles with the g-C 3 N 4 shell, which has affected the properties of the wall where H is adsorbed (see Fig. 7). The density of states (DOS) of pristine g-C 3 N 4 is compared with that of g-C 3 N 4 @FeO and shown in Fig. 8, where the interaction of Fe-C, Fe-N, O-C, and O-N in g-C 3 N 4 @Fe can be identified. DOS of g-C 3 N 4 @FeO is enhanced especially near the valence band (0 to À1.8 eV), which is due to the interaction of C and N atoms with FeO clusters and exhibits extra features near the Fermi level. Moreover, charge transfer also occurred from the FeO cluster to the g-C 3 N 4 , which raises the Fermi level by about 0.12 eV. This effect is further illustrated by the electron difference density (EDD) distribution as shown in the inset of Fig. 8. The charge transfer creates a local dipole near the interface, which consequently decreases the local work function and increases the chemical reactivity of the functionalized region of the g-C 3 N 4 @FeO exterior. So, this accounts for the optimum value of DG H* (hydrogen adsorption) over the C in the region where FeO is sitting below and has no direct contact. Finally, this can further increase the DOS near the Fermi level and reduce the work function of the doped g-C 3 N 4 (see Fig. 9).
Model (II): Fe 3 O 4 @g-C 3 N 4 . As evident from our experimental results and discussion, the performance of the g-C 3 N 4 @Fe 3 O 4 system is superior to pristine g-C 3 N 4 ; to correlate and confirm our observation, periodic DFT calculations are further carried out for Fe 3 O 4 , g-C 3 N 4 , and the Fe 3 O 4 @g-C 3 N 4 heterostructure. A lower lattice mismatch of 5.6% is present in the Fe 3 O 4 @g-C 3 N 4 system, which also validates the coexistence between Fe 3 O 4 and g-C 3 N 4 . The optimized structures of monolayer Fe 3 O 4 , g-C 3 N 4 , and Fe 3 O 4 @g-C 3 N 4 are given in Fig. 1c-e. It is found that g-C 3 N 4 forms a non-covalent type interaction with the surface atoms of Fe 3 O 4 through N-Fe with a simulated distance of B2.2 Å, which reveals the strong electrostatic interaction in the Fe 3 O 4 @g-C 3 N 4 system. The simulated adsorption energy of g-C 3 N 4 nanosheets over Fe 3 O 4 is À0.73 eV, which further confirms the stability of the Fe 3 O 4 @g-C 3 N 4 heterojunction. This interface adhesion formation energy was calculated according to eqn (1). These extra bands can be called flat bands, which work as charge trapping centres and consequently increase the overall catalytic performance of Fe 3 O 4 @g-C 3 N 4 . Interestingly, in either spin states, the Fermi energy level is diffused in the valence band (Fig. 10).
The simulated electrostatic potential maps of Fe 3 O 4 , g-C 3 N 4 , and Fe 3 O 4 @g-C 3 N 4 along the Z-direction are displayed in Fig. 12, where the g-C 3 N 4 monolayer has shared its electronic cloud density with a surface of Fe 3 O 4 in Fe 3 O 4 @g-C 3 N 4 . The work functions of Fe 3 O 4 , g-C 3 N 4 , and Fe 3 O 4 @g-C 3 N 4 are 5.86, 4.24, and 5.55 eV, respectively. We can see that the Fig. 8 Comparative density of states plots of g-C 3 N 4 and g-C 3 N 4 @FeO. The Fermi energy level is aligned at 0 eV. Insets show the electron difference density (EDD) of pristine SWNCNT and g-C 3 N 4 @FeO. Fig. 9 Averaged electrostatic potential profiles on the plane perpendicular to the b-axis as a function of the b-axis of the supercell of g-C 3 N 4 and g-C 3 N 4 @FeO, respectively. The relaxed structure of g-C 3 N 4 @FeO is also shown in the background.

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heterojunction Fe 3 O 4 @g-C 3 N 4 has optimum work; lower than that of Fe 3 O 4 but higher than that of g-C 3 N 4 . So, the HER performance of the Fe 3 O 4 @g-C 3 N 4 heterojunction can be calculated from the difference of work functions. It is also inferred that charge transfer occurred between Fe 3 O 4 and g-C 3 N 4 . Finally, this type of charge transfer creates a local dipole near the interface, decreases the work function (from 5.86 to 5.55 eV) and enhances the HER activity over the surface of g-C 3 N 4 @FeO. The charge transferring phenomenon at the Fe 3 O 4 @g-C 3 N 4 heterojunction is calculated from the electron difference density (EDD) of the heterostructure, and the results are shown in Fig. 13 and Fig. S7 (ESI †). In Fig. 13, the charge difference at the interface is clearly depicted where the green and yellow shaded areas represent the charge accumulation and depletion, respectively. It is found that charge distribution mainly occurs at the interface region of the Fe 3 O 4 @g-C 3 N 4 heterostructure, whereas almost no perturbation was observed in the rest of Fe 3 O 4 @g-C 3 N 4 , especially in those parts, which are far away from the interface. We can predict that this type of charge distribution may result in a non-bonding interaction, 27 between g-C 3 N 4 and Fe 3 O 4 (vide supra). A slice of the planaraveraged EDD along the Z-direction of Fe 3 O 4 and Fe 3 O 4 @ g-C 3 N 4 is depicted in Fig. 13  The adsorption energy of a water molecule was calculated by subtracting the energies of the optimized water molecule and adsorbent-bare slab (E surface ), from the optimized water-slab complex (surface@H 2 O), using eqn (2).
The strength of hydrogen bonding in these species is calculated from inter-bonding distance and adsorption energy. As can be visualized from      The stronger the hydrogen bonding, the higher the water splitting ability will be. The high adsorption energy of water can be correlated to the experimentally lower overpotential of the HER. In summary, Fe 3 O 4 @g-C 3 N 4 has higher catalytic activity (in terms of strong water adsorption energy) than that of pristine Fe 3 O 4 . Again, these results and discussion strongly corroborate our experimental data, presented below.

Electrochemical properties
As shown in Fig. 15a, Fe 5 -NC exhibits a small onset potential of 73 mV and low overpotential (Z B 10) of 191 mV to achieve a current density of 1 and 10 mA cm À2 , respectively, which is lower than the onset potentials and overpotentials of both Fe 2 -NC and Fe 10 -NC samples. Fe 2 -NC and Fe 10 -NC require overpotentials of 215 mV and 233 mV, respectively, to reach 10 mA cm À2 . The LSV curves also indicate that Fe 5 -NC exhibits better activity with higher catalytic currents compared with those of the other samples. These results are comparable to recently reported metal-encapsulated nanocomposites of P-doped Ni@CNTs/NF, FNC-MoS 2 and Co/Co 2 P@ACF/CNT HNCs. 4,28,29 Corresponding Tafel plots derived from polarization curves were used to deduce the HER mechanism of the samples (Fig. 15b). Fe 5 -NC has a small Tafel slope of 69 mV dec À1 , compared to that of Fe 2 -NC (77 mV dec À1 ) and Fe 10 -NC (91 mV dec À1 ), which indicates its faster kinetics towards the HER. Based on the Tafel slope values, the HER with Fe x -NC samples likely proceeded via the Volmer-Heyrovsky mechanism in which the rate limiting step is usually the electrochemical discharge step. The Tafel slope of the Volmer reaction (H 2 O + e À -H ads + OH À ), which represents the initial discharge step is 120 mV dec À1 , while the electrochemical desorption, Heyrovsky reaction (H ads + H 2 O + e À -H 2 + OH À ) and recombination (Tafel reaction: -H ads + H ads -H 2 ) occur at lower values of 40 and 30 mV dec À1 , respectively. 30 Tafel slopes of the Fe x -NC samples lie within this range, which suggests that the Volmer-Heyrovsky mechanism must have occurred during hydrogen evolution.
Cyclic voltammetry at different scan rates (5-50 mV s À1 ) was applied to study the electrochemical properties of the Fe x -NC samples and the results are presented in Fig. 15c. The reaction profile was capacitive rather than faradaic during the volumetric scan within the range of À0.1-0 V (vs. RHE). The electrochemically active surface areas (ESCAs) of the three samples were evaluated by measuring the double layer capacitance (C dl ) obtained from fitting of the difference in current densities versus the scan rates. From Fig. 15d, the C dl values of Fe 2 -NC, Fe 5 -NC and Fe 10 -NC were determined to be 11.12, 23, and 15 mF cm À2 , respectively. The improved C dl value for Fe 5 -NC is linked to its improved electrocatalytic performance due to the presence of intrinsically more catalytically active sites. The reaction kinetics of the Fe x -NC samples at the electrode/ electrolyte interface was evaluated by EIS. The Nyquist plots in Fig. 15e reveal that the charge transfer resistance (R ct ) of Fe 5 -NC (8 O) is much lower than that of the other samples (Fe 2 -NC, 14 O and Fe 10 -NC, 44 O), which indicates a faster kinetics and reaction process, due to easier charge transfer at the electrode/ electrolyte interface. Stability of Fe 5 -NC was measured by chronoamperometric curves and taking continuous linear potential sweeps on the electrode at a scan rate of 50 mV s À1 for 5000 cycles. As shown in Fig. 15f, the current density of Fe 5 -NC exhibits negligible changes after 5000 cycles compared with the initial curve, with only minimal loss of activity at a current density of 10 mA cm À2 . The chronoamperometric curve recorded at À0.3 V in Fig. S9 (ESI †) also indicates that Fe 5 -NC retains 94% of its relative current density after 5 hours of testing. This result demonstrates the improved stability of Fe 5 -NC as a HER electrocatalyst. Although Fe 5 -NC shows good stability, the dissolution of Fe ion concentration in electrolyte cannot be ruled out and will be investigated via inductively coupled plasma mass spectrometry in the future to further validate its long-term stability. The morphology and crystal structure of Fe 5 -NC exhibit negligible changes after 5000 cycles (Fig. S8, ESI †), which is indicative of its good stability. These results confirm that the present carbon nitride shell indeed can protect the oxides from acidic bubble corrosion during the cycling test, which highlights its application potential.
To sum up, the enhanced catalytic activity of Fe 5 -NC can be attributed to the following reasons: (1) synergy between iron oxide nanoparticles and the graphitic carbon nitride shell, which promotes HER activity by facilitating faster charge transfer and weakening strong hydrogen adsorption to obtain improved hydrogen desorption; (2) uniform distribution of all elements and creation of abundant defect sites from the N-doping into carbon frameworks, which would improve interfacial adsorption and electronic interaction, while creating catalytically active sites for HER activity; (3) the introduction of high ESCA, which allows for enhanced accessibility of exposed active sites for the HER; and (4) the smaller charge transfer resistance linked to the faster kinetics and higher current density.

Conclusions
Fe x -NC nanocomposites were successfully prepared via a simple method using melamine as the simultaneous nitrogen and carbon source. The resulting Fe x -NC consists of iron oxide nanoparticles sheathed by graphitic carbon nitride shells of 8.1-30 nm thickness. The observed data of g-C 3 N 4 encapsulated iron oxide nanoparticles were successfully reproduced with the help of periodic density functional theory (DFT) simulations. Both theory and experiment strongly correlate to each other, where the g-C 3 N 4 @FeO has superior performance compared to pristine g-C 3 N 4 and Fe 3 O 4 . It is found that the catalytic activity of g-C 3 N 4 @FeO arises from the electron transfer from FeO >particles to the g-C 3 N 4 , which forms an electrostatic interaction, leading to a decreased local work function on the surface of g-C 3 N 4 , which consequently enhanced the HER activity.

Conflicts of interest
The authors have no competing interest to declare.