Solvothermal synthesis of Sn3N4 as a high capacity sodium-ion anode: theoretical and experimental study of its storage mechanism

A new simple and scalable method to synthesise spinel-structured Sn3N4 has been developed using SnCl4 and LiNH2 precursors under solvothermal conditions. Nanocrystalline Sn3N4 with a crystallite size < 10 nm was produced and tested as anode material in sodium half cells, demonstrating a very high reversible (desodiation) capacity of 850 mA h g 1 measured over 50 cycles, the highest reported reversible capacity for a sodium anode apart from sodium itself. Ex situ X-ray absorption spectroscopy and X-ray diffraction show that the electrochemical reactions are reversible and that Sn3N4 is recovered upon re-oxidation. X-ray diffraction shows that the peaks associated with Sn3N4 reflections become narrower during discharge (reduction), evidencing that the smaller Sn3N4 particles are primarily involved in the electrochemical reactions, and broadening of the peaks is reversibly recovered upon oxidation. The analysis of the near edge X-ray absorption data (XANES) shows that the Sn oxidation state decreases during reduction and nearly recovers the initial value during oxidation. DFT calculations suggest that the insertion of Na into the Sn3N4 surface followed by substitution of tetrahedral Sn by Na is energetically favourable, and evidence of the removal of tetrahedral Sn from the spinel Sn3N4 structure is obtained from the analysis of the extended X-ray absorption fine-structure (EXAFS) measurements of reduced electrodes, which also show the recovery of the pristine structure at the end of oxidation. DFT also shows that Sn substitution by Na is only favourable at the Sn3N4 surface (not for bulk Sn3N4), in agreement with the electrochemical characterisation that shows that controlling the nanoparticle size is crucial to achieve full utilisation of Sn3N4 (and thus high capacity).


Introduction
Use of lithium-ion batteries (LIBs) in electrical energy storage is undergoing rapid growth due to their high energy density and long cycling stability. However, demand for battery grade lithium carbonate has up driven costs for manufacturing LIBs. 1,2 The renewed interest in sodium-ion batteries (SIBs) is in part due to the high abundance, low cost and wide geographical distribution of the alkali metal. Sodium is the sixth most abundant element and is found both in sea water and in various mineral forms. 3,4 The metal shares physico-chemical properties with lithium, and sodium analogues of LIB positive electrode (cathode) materials, including layered transition metal oxides (Na x MO 2 where M ¼ Ni, Co, Mn etc.) and polyanionic compounds such as NaFePO 4 , oen perform well. [5][6][7][8][9] For SIBs, the anode is still a considerable challenge. For LIBs, the standard anode material is graphite, however the larger ionic radius of sodium ions (1.02Å for Na + , 0.76Å for Li + ) leads to sluggish reaction kinetics, lower capacities and poor cycling stability in sodium-ion cells. Other carbon materials in the form of amorphous and hard carbon are able to accommodate sodium ions, delivering reversible capacities of up to $350 mA h g À1 . [10][11][12] Tin-based alloying materials have been studied as alternative anodes for SIBs. The full sodiation of Sn to Na 15 Sn 4 has a theoretical capacity of 847 mA h g À1 . 13,14 However, Sn undergoes a volume variation of 420% during alloying/ dealloying with Na. The large volume change imposed on the metallic Sn particles leads to pulverization, delamination and loss of conduction pathways, although nanostructuring does improve stability. Tin-based binary materials (e.g. SnO 2 , SnS, Sn 4 P 3 ) can mitigate the stresses imposed on the electrode by the formation of a matrix structure during initial reduction (Sn + Na x M y ), [15][16][17][18][19][20] as well as offering possible extra capacity by the combination of conversion and alloying processes. The most studied of these is SnO 2 , owing to its high theoretical capacity (1378 mA h g À1 ), low redox potential and ease of synthesis. 21,22 However, the material suffers from a large initial irreversible capacity loss, low electronic conductivity and poor cyclability. [23][24][25] Nano-structuring of conversion materials and formation of composites with carbon structures have yielded signicant improvements in their electrochemical performance. Some of the best of these are summarised in Table 1.
Even higher capacities are, in principle, obtainable with tin nitride (Sn 3 N 4 ). Sn 3 N 4 has a tuneable band gap and applications in photocatalysis, chemical sensing and solid state LIBs have been suggested. [32][33][34][35] As an anode material in SIBs, the conversion of Sn 3 N 4 to Sn and Na 3 N followed by full alloying of Sn to Na 15 Sn 4 would result in a capacity of 1512 mA h g À1 . Previously we produced bulk nanocrystalline Sn 3 N 4 by ammonolysis of a tin dialkylamide and demonstrated a reversible (de-sodiation) capacity of 270 mA h g À1 aer 50 cycles at 50 mA g À1 with a coulombic efficiency close to 95%. 36 Ex situ diffraction measurements on cycled electrodes suggested that a signicant fraction of the material was not involved in the electrochemical processes. Consequently, it was envisioned that smaller crystallite sizes could produce larger capacities. This is now demonstrated in this work, together with a theoretical and experimental study of the reaction mechanism.
Recent years have expanded the list of tools capable of predicting new phases of materials using rst principles calculations. 37,38 Their application to the interaction of Na with Sn compounds has attracted considerable theoretical interest. An initial study in 2011 by Chevrier et al. used rst-principle calculations to predict the voltage prole of the process of sodiation of Sn by formation of Na x Sn y compounds. 39 Later experimental studies using X-ray diffraction and operando TEM corroborated the formation of Na 15 Sn 4 as the crystalline phase of maximum sodiation. [40][41][42] Further theoretical work combined with Mössbauer and X-ray absorption spectroscopies shed light into the reaction mechanism of Sn sodiation. 43,44 A decisive indepth examination of the reaction pathway by Stratford et al. using ab initio random structure searching and operando XRD, PDF and NMR characterization identied the structure of the intermediate Na x Sn y compounds and showed that the nal product Na 15 Sn 4 can store additional sodium atoms as an offstoichiometry product Na 15+x Sn 4 . 45 Theoretical studies have also been very useful for understanding the compounds formed with Na and N. The formation of metastable Na 3 N was predicted from theoretical considerations and later demonstrated in practice by synthetic routes using atomic co-deposition or reactions of sodium with active nitrogen, it was also shown that Na 3 N decomposes at $100 C. [46][47][48][49][50] On the other hand, sodium azide (NaN 3 ) is a wellknown stable compound of Na and N and it is manufactured at around 250 tonnes per year, with the main application in car airbags. 51,52 A theoretical study using global structure optimization identied a new compound, sodium azenide (Na 2 N 2 ), which was predicted to be stable (that is, it had a negative enthalpy of formation from the respective elements Na and N 2 ), 53 but the experimental synthesis of Na 2 N 2 has not been reported. Finally, theoretical and experimental studies on the tertiary compounds of Na x Sn y N z are currently limited, but ab initio calculations by Sun et al. showed that a phase of NaSnN is thermodynamically stable 54 and this was subsequently demonstrated experimentally. 55 Herein we report a joint theoretical and experimental study of the application of Sn 3 N 4 as a high capacity anode material in SIB, using a new synthesis method to make Sn 3 N 4 microcrystalline and nanocrystalline powders. The capacity achieved with nanocrystalline Sn 3 N 4 over 50 cycles exceeds those for anodes reported to date. The underlying mechanism is interrogated using rst principle methods and experimental characterization (XRD, EXAFS and XANES).

Experimental
Synthesis of Sn 3 N 4 was carried out under anaerobic conditions using either a nitrogen-lled glovebox or Schlenk line techniques. Benzene (Aldrich) was reuxed over sodium for 8 h, distilled and stored under nitrogen. SnCl 4 (Aldrich) was short-path distilled. LiNH 2 was obtained by reacting n BuLi (1.6 mol dm À3 in hexane, 500 cm 3 , Aldrich) with ammonia (distilled from a $100 cm 3 sodium/ liquid ammonia solution) at 0 C, ltering the white solid product and drying in vacuo. Solvothermal synthesis was performed in a 75 cm 3 autoclave (Parr 4740CH), with a silica liner reducing the internal volume to $60 cm 3 . SnCl 4 (0.60 g, 2.3 mmol) was placed in the silica liner and covered by 30 cm 3 of benzene. LiNH 2 (0.21 g, 9.2 mmol) was added and stirred. The autoclave was sealed and heated for 12 hours at temperatures as discussed later (300 to 430 C). Typically, $50 atm pressure was developed during heating. Aer cooling to room temperature, the autoclave was opened and the solid was washed with deionised water (50 ml) and MeOH (20 ml) to remove the LiCl by-product. The powder was then washed further with HCl (3 mol dm À3 , 30 ml) to remove any tin metal formed by thermal decomposition of the metal nitride. Electrode preparation involved homogenizing the Sn 3 N 4 active material (75%) with acetylene black (20%, Shawingan black, 100%-compressed, Chevron) and sodium alginate (5%, Aldrich) dissolved in deionised water. The slurry was cast onto Cu foil (17.5 mm thick, 99.9% purity, Goodfellow Ltd) using a K bar (wet thickness of 200 mm) and dried at room temperature. The coated foil was punched into circular discs (11 mm diameter) and pressed at 10 tonnes to obtain the Sn 3 N 4 electrode. Typical mass loadings of electrodes prepared in this way were 0.5-1.0 mg cm À2 . Swagelok cells were assembled in an argon-lled glove box. Sodium half-cells were prepared by cutting a fresh face of sodium metal (Aldrich, 99% purity) and rolling to produce sodium foil counter-electrodes, with two microber lter (Whatman, GF/F grade) separators soaked in 120 ml of 1 mol dm À3 NaPF 6 (Aldrich, anhydrous) in a 47.5 : 47.5 : 5 by wt mixture of ethylene carbonate (EC), diethyl carbonate (DEC) and uoroethylene carbonate (FEC) (all Aldrich, 99%, anhydrous or vacuum distilled before use). Electrochemical testing was performed with a BioLogic MPG multi-channel potentiostat. Galvanostatic cycling was carried out at 25 C at various rates of charge/discharge within the potential range of 10 mV to 2.5 V vs. the sodium metal counter-electrode.
Powder X-ray diffraction (XRD) measurements were recorded on a Bruker D2 Phaser using Cu-K a radiation (l ¼ 1.5418Å) in Bragg-Brentano geometry. The reections present were identi-ed by comparison with the ICSD database and patterns rened using the GSAS package. 56 Scale factor, background, lattice parameter, zero point correction, thermal displacement parameters, nitrogen atom positions, crystallite size broadening and isotropic strain. An Al 2 O 3 standard collected in the same geometry was used to dene the Gaussian instrumental peak shape, with the crystallite size obtained from the Lorentzian crystallite size broadening terms. 57 In two-phase ts containing two crystallite sizes, the tin thermal displacement parameters were constrained to a single value and the nitrogen thermal displacements were xed. Transmission electron microscopy (TEM) was carried out with a FEI Technai12 (120 kV) on samples that were dispersed into propanol with ultrasound and dropped onto carbon grids. Bulk elemental CHN combustion analysis was obtained from Medac Ltd, and the values are reported in weight percentages. The XRD patterns of the pristine electrodes show some small, unidentied impurity peaks, which are formed during the homogenizing process in electrode preparation, but additional diffraction studies with electrodes prepared without the homogenizing step show the same reactions (see ESI, Fig. S1 †).
For ex situ measurements before and aer galvanostatic cycling, microcrystalline tin nitride electrodes were cycled in Na half-cells to specic potentials of interest at 200 mA g À1 . The Swagelok cells were disassembled in an argon-lled glovebox as soon as the target potential had been reached. The electrodes were rinsed with anhydrous DEC solvent and allowed to dry. Ex situ X-ray diffraction patterns collected in a sealed XRD sample holder (Bruker, loaded in the glove box) were collected in grazing incidence geometry (1 incidence angle) with Cu-K a radiation (l ¼ 1.5418Å) using a Rigaku Smartlab with Hypix 2D detector. Near-edge (XANES) and extended ne-structure (EXAFS) X-ray absorption measurements in sealed polyfoil pouches were made at the B18 beamline of Diamond Light Source across the Sn K-edge region from 28.8 to 30.0 keV. Tin standards were produced by preparing inks with Sn, SnO 2 , SnO (Aldrich) and Na 4 Sn powders diluted with acetylene black to match the respective mass loadings of the tin nitride electrodes. The Na 4 Sn standard was prepared in a nitrogen-lled glovebox where a slight excess of Na (4.4 equiv., Aldrich, 99% purity) and Sn (Aldrich) was loaded into a furnace tube and sealed, following a previously reported synthesis method for Na 4 Sn. 58 The tube was placed into a furnace at 300 C and heated for 1 hour under owing N 2 . Aer heating, the sample was transferred to the glovebox before diluting with acetylene black to produce the Na 4 Sn standard. The Sn edge positions were obtained as the rst inexion point of the respective XANES absorption spectra, and the EXAFS data has been tted using two independent Sn-N coordination shells, similarly to previous studies of Sn 3 N 4 . 59 Targeted compounds of known composition and structure were simulated from rst principles as implemented in the Vienna Ab initio Simulation Program (VASP). 60 This approach is based upon density functional theory (DFT), and the PBE and HSE06 functionals were considered with the projected augmented waves method used for the pseudopotentials. 61,62 An energy cut-off of 600 eV and a minimum of a 4 Â 4 Â 4 (2 Â 2 Â 2) Monkhorst-Pack k-grid were used. The total energy of each system was minimised with respect to the internal coordinates and the lattice parameters, with a force tolerance of 0.01 eVÅ À1 . All charge analysis was performed using the Bader scheme. 63 Two functionals were considered here. PBE is a highly suitable functional for geometric considerations, whereas for chemical accuracy one would consider HSE06. In general, whilst broad trends can be extrapolated from a PBE result, the chemically accurate results require HSE06. To investigate the reaction pathways, we calculated the energies of the different compounds following the standard approach. 64 The reactions of Na with the Sn or N 2 can be written as: where Na x Sn 1Àx and Na y N 1Ày are compounds containing Na and Sn, and Na and N, respectively. The associated energy of the reaction is the energy of formation, E f , of the Na x Sn 1Àx and Na y N 1Ày compounds from the corresponding elements, which quantify the stability of the different compounds (negative formation energies indicate thermodynamic stability). The energies of formation are calculated from: where E(Na x Sn 1Àx ) and E(Na y N 1Ày ) are the total energy (per atom) of the structure, E(Na) and E(Sn) are the total energies of the bulk elements (per atom) and E(N 2 ) is the total energy of the nitrogen molecule. For Sn, the metallic beta phase was used in the calculations, following previous work, 45 since that is the stable phase at room temperature. To study the reaction of Na with Sn 3 N 4 , the associated reaction energies were computed: where E(Sn 3Àx N 4Ày Na z ) and E(Sn 3 N 4 ) are the total energies of the structure with and without the Na atom. These energies are given per Na atom. Raw data associated with gures in the manuscript and ESI † are available from ref. 99.

Results and discussion
Solvothermal synthesis of Sn 3 N 4 Solvothermal synthesis has become an effective, well-controlled route for the preparation of crystalline metal nitrides. [65][66][67] By heating reactants in a solvent medium inside a sealed autoclave, metathesis reactions can proceed at mild temperatures due to the solvent absorbing heat produced in the exothermic reactions. [68][69][70] Thermal decomposition of the formed metal nitrides is also signicantly reduced under solvothermal conditions, and the products are usually crystalline. 20,71,72 Sn 3 N 4 was synthesised via a simple and easily-scalable solvothermal method with dened particle size via a solvothermal metathesis reaction, with benzene employed as the solvent owing to its stability under solvothermal conditions: 73,74 XRD and TEM were employed to characterise the product of the solvothermal reaction. Sn 3 N 4 crystallises with the cubic spinel structure (Fd 3m) with a reported lattice parameter of 9.037(3)Å. 75 Powder X-ray diffraction (XRD) patterns of the brown products produced in solvothermal reactions at 300, 350 and 430 C are displayed in Fig. 1, all showing the peak positions of the Sn 3 N 4 reference. The good match of the XRD peak positions of the Sn 3 N 4 reference and the samples here produced, demonstrates the success in the synthesis of phase pure Sn 3 N 4 for all the reaction conditions here explored (the absence of other peaks demonstrate that no other crystalline impurities are present). In addition, for the sample produced at 430 C, all the XRD peaks are symmetrical and narrow, demonstrating that the sample is made of crystalline particles in the micron size range; this material will be referred to as microcrystalline Sn 3 N 4 in the following text. A Rietveld t to this XRD pattern (R wp ¼ 5.0%, R p ¼ 3.4%) yielded a lattice parameter of 9.0549(2)Å and an average crystallite size of 310(40) nm (ESI, Fig. S2 and Table S1 †). TEM micrographs corroborate this crystallite size (Fig. 2a).
In the XRD data for the sample prepared at 300 C, broad asymmetric peaks are present at similar positions to small sharp peaks, the latter resembling the microcrystalline sample obtained at 430 C. The asymmetric broadening feature is due to the fact that the sample is made of a mixture of nano-sized and larger crystallites. The presence of nano-size crystallites could be increased by sonicating the sample in HCl, the associated XRD pattern shows that the asymmetric broadening of the peaks is accentuated. The material obtained by heating at 300 C followed by sonication will be referred to as nanocrystalline Sn 3 N 4 in all that follows. A two-phase Rietveld t (R wp ¼ 9.4%, R p ¼ 7.4%) conrmed the presence of two distinct phases, both tting well as Sn 3 N 4 (ESI, Fig. S2 and Table S1 †). The lattice parameters of the two phases were 9.0514(4) and 9.139(2)Å, with average crystallite sizes of 137(13) nm (13.2(4)% of the material present) and 5.950(9) nm (86.8(2)%), respectively. TEM shows crystallites around both of these sizes, with a greater number of nanocrystalline particles present (Fig. 2b).
The microcrystalline and nanocrystalline Sn 3 N 4 samples were also characterised by XANES and EXAFS collected at the Sn K-edge. Fig. 2 shows the magnitudes of the Fourier transforms of the K 3 -weighted EXAFS data. A peak doublet at $1.5Å radial distance is present in both samples and corresponds to the distances between N sites and tetrahedral tin site (Sn tet -N) and octahedral tin site (Sn oct -N) at 2.05 and 2.20Å, as expected for the spinel Sn 3 N 4 structure and in agreement with previous studies. 59 Peaks between 2.5 and 4Å are attributed to other Sn-Sn interactions within the structure. 59 While XRD is suitable to characterise the composition of the microcrystalline sample, the nanocrystalline sample gives broad diffraction peaks. However, EXAFS shows that both samples have a very similar set of correlations with similar intensities (see results of the t in the ESI, Table S2 †), conrming structural similarities of Sn 3 N 4 in both samples. In addition, the analysis of the Sn K-edge XANES data enables the evaluation of the Sn oxidation state (see more details below), which were found to be 3.7 and 3.3 for the Sn 3 N 4 micro and nanocrystalline samples, respectively.
The estimation of the nitrogen content of the Sn 3 N 4 samples by combustion analysis gives values (10.1% and 8.2% for the microcrystalline and nanocrystalline samples) that are lower than the expected for pure, stoichiometric Sn 3 N 4 (13.6%). This can be ascribed, in part, to the presence of nitrogen vacancies, which is supported by the fact that the Sn K-edge XANES analysis provides values of the oxidation state of tin lower than 4. The elemental analysis also shows that the samples also contain carbon and hydrogen (12.4% C and 2.0% H for the microcrystalline sample and 1.0% C and 2.0% H for the nanocrystalline sample). The lower content of carbon in the nanocrystalline sample is expected, since less decomposition of the solvent (benzene) will take place at the lower temperature used for the solvothermal synthesis method. 68,69 Taking into account the presence of carbon and hydrogen residues and the nitrogen vacancies (calculated from the tin oxidation number), the expected values of the nitrogen content are 10.9% and 11.1% for the microcrystalline and nanocrystalline samples. The experimental values of the nitrogen content are somewhat lower (10.1% and 8.2% for the microcrystalline and nanocrystalline samples). The process of washing the samples in an HCl solution aer synthesis can produce a hydrolysis reaction producing a partial oxygen substitution of nitrogen sites at particle surfaces, forming a tin oxy-nitride, and this effect will be more severe for the nanocrystalline sample since it has a higher surface area. The XRD and EXAFS results show that the spinel structure is preserved aer the oxygen-nitrogen substitution. Incomplete combustion of the samples, as observed in other metal nitride studies, 76 could also contribute to the lower than expected nitrogen content obtained from the elemental analysis.

Electrochemistry of Sn 3 N 4 in sodium half cells
Sn 3 N 4 exhibits good stability in deionised water, hence water processable binders can be employed in electrode preparation, avoiding toxic organic solvents. In our previous study, Sn 3 N 4 electrodes prepared with sodium alginate as a binder demonstrated the best electrochemical stability during cycling and so we continued using sodium alginate for this work. 36 The binder is comparatively more rigid than the commonly used PVDF, a property that increases the electrode's ability to withstand large volume changes during cycling. [77][78][79] Na half-cells were constructed with 1 mol dm À3 NaPF 6 in EC/DEC with 5 wt% FEC electrolyte, again following previous work. 36 FEC was used as an additive that improves the electrochemical performance of tinbased electrodes. [80][81][82][83] Galvanostatic cycling of microcrystalline Sn 3 N 4 in Na halfcells was investigated at 50 and 200 mA g À1 (Fig. 3). At 200 mA g À1 , 671 mA h g À1 of capacity was passed on rst reduction (discharge, negative current) to 10 mV, of which 214 mA h g À1 was recovered on the rst oxidation (charge, positive current) to 2.5 V. This large initial capacity loss (32%) is tentatively attributed to irreversible processes such as the decomposition of the electrolyte and formation of an SEI. 20,36,84,85 Subsequent cycles demonstrated good cycling stability with a capacity fade of 7% between the 10th (268 mA h g À1 ) and 50th (250 mA h g À1 ) oxidations. The coulombic efficiency was 98% at the 50th cycle, indicating a stable, reversible electrochemical process. Greater capacities were achieved at a more modest current of 50 mA g À1 , with 520 mA h g À1 of capacity passed aer the 50th oxidation, with a coulombic efficiency of 97%. Capacity fade between the 10th (546 mA h g À1 ) and 50th (521 mA h g À1 ) oxidation was just 4%.
Galvanostatic cycling of nanocrystalline Sn 3 N 4 in Na halfcells (Fig. 4) shows greater capacities compared to the microcrystalline sample. At 200 mA g À1 , aer the initial irreversible capacity loss, a reversible (oxidation) capacity of 420 mA h g À1 was achieved. Capacity fade from the 10th (421 mA h g À1 ) to the 50th (416 mA h g À1 ) oxidation was only $1%. In addition, the coulombic efficiency rose to 98%, demonstrating the favourable reversibility of the charge/ discharge reactions on cycling. As expected, more capacity was achieved at the lower current of 50 mA g À1 . Reversible capacities of $850 mA h g À1 were obtained during cycling. The coulombic efficiency at the 50th cycle was 94%.
The capacity of these Sn 3 N 4 electrodes is remarkable considering that other high capacity tin-based materials all incorporate a carbon architecture material such as graphene sheets, hollow spheres or nanotubes (see Table 1). In other Snbased conversion systems without a secondary support, capacity fading over multiple cycles is a problem. Wang et al. cycled SnO 2 at 50 mA g À1 with a capacity of 200 mA h g À1 achieved aer 50 cycles. 86 Ma et al. compared Sn 4 P 3 /hollow C core-shell composites (Table 1) with unsupported Sn 4 P 3 , and cycling the unsupported material delivered a capacity of just 104 mA h g À1 aer the 20th cycle at 100 mA g À1 . 31 The cycling of unsupported SnS electrodes was reported by Yu et al. with $200 mA h g À1 achieved aer 50 cycles at 100 mA g À1 . 87 In addition, further improvements could be achieved in full cell studies, since the reactivity of the sodium metal counter electrode has been shown to compromise cycling stability in studies in Na halfcells. 88,89 Similar to other conversion anode materials, 26-31 the rst cycle coulombic efficiency of the Sn 3 N 4 samples studied here (30-45%) is not suitable for commercial applications, but further improvements could be achieved by material development. For example, the use of a yolk-shell design, where the active material nanoparticles are sealed inside a carbon shell, has produced major performance improvements for other conversion materials, which has been attributed to the fact that the yolk-shell design enables the volumetric expansion associated with the electrochemical reactions while avoiding the direct contact of the active material with the electrolyte. 20,90 The investigation of alternative electrolytes is another highly promising route for improving performance and coulombic efficiency. 91 DFT study of the charge storage mechanism Previously, it was suggested that Sn 3 N 4 electrodes could undergo complete conversion to Sn metal and Na 3 N with subsequent alloying of Sn with Na to Na 15 Sn 4 . 36 Here, we exploit ab initio calculations to identify the candidate compounds involved in the reaction mechanism of sodiation of Sn 3 N 4 ; this is later analysed in view of the XRD, XANES and EXAFS results.
In order to construct the possible reaction pathways, we rst investigated the stability of the various phases of Na x Sn y and Na x N y compounds. We applied a similar approach to AIRRS, 45 except that for any stoichiometry where a known experimental structure exists, we only consider that structure. The PBE functional was used for an initial search, and we then studied the most stable candidates with the HSE06 functional. The HSE06 functional is necessary for considering nitrogen-based structures due to the difference in the N 2 molecule's binding energy in PBE and HSE06 (the binding energy of N 2 in HSE06 is 9.54 eV, whereas in PBE it is 8.44 eV and the experimental value is 9.79 eV). 92 Aer calculation of the formation energies of the different compounds, using eqn (3) and (4), the lines connecting the compounds of lower formation energy (known as convex hull) were calculated. When a candidate compound lies above the convex hull, it is concluded that the compound is not thermodynamically stable.
The results of the calculations of the formation energies of Sn-Na compounds are shown in Fig. 5a. The calculations made with the PBE functional agree with the results reported by Stratford et al. 45 To ensure chemical accuracy, additional calculations were made with the HSE06 functional. Whilst the formation energies are generally slightly smaller, the general trend in the convex hull is in good agreement with the previous PBE results. Our HSE06 calculations also show that all phases are metallic as expected. Our rst principles simulations combined Bader charge analysis which shows that Sn atoms are charge neutral (0.0|e|) in the b phase due to charge being evenly distributed. As the fraction of Na increases, the Sn atoms become increasingly negatively charged with the Na 15 Sn 4 phase Sn atoms possessing Bader charges of À3.7|e|.
The calculation of formation energies of Na-N compounds is shown in Fig. 5b. Due to the signicant error in binding energies of the N 2 molecule in PBE, only HSE06 results are discussed. Fig. 5b shows that NaN 3 is the only candidate compound that lies on the convex hull, which means that the other candidate compounds are not thermodynamically stable. For example, Na 3 N produces a positive energy of formation per atom (E f ¼ 0.29 eV in HSE06), which means that formation of Na 3 N from bulk Na and N 2 gas is not thermodynamically favourable. These ndings agree with the experimental enthalpy of formation of Na 3 N obtained by differential thermal analysis: 64 kJ mol À1 (or 0.66 eV), 48 which would correspond to a formation energy per atom of 0.66 eV/4 ¼ 0.17 eV. However, the fact that Na 3 N is metastable does not mean that it cannot be formed and remain stable: Na 3 N has been successfully synthesised by atomic co-deposition and the reaction of sodium with active nitrogen, [47][48][49] and it was stated that Na 3 N remained stable for weeks unless it was heated to $100 C. 48 At high pressures Na 3 N was also found to remain stable. 93 Our results of the metastability of Na 3 N are also in agreement with previous theoretical calculations. 46,50,53,94 For the elucidation of the energy storage mechanism of Sn 3 N 4 in sodium-ion cells, we studied the reaction of formation of Na interstitials and substitutional sites in bulk and surface Sn 3 N 4 (see ESI, Tables S3 and S4 †). For the study of surface reactions, slabs of material with [001] surface terminations were generated. The plane of cleavage was chosen based on the consideration that both surfaces must be (a) symmetric, (b) charge neutral and (c) stoichiometric. From these criteria four surfaces were created and relaxed. The most stable of these (see ESI, Fig. S3 †) was then considered for the surface reaction calculations. We considered slab systems with various thicknesses ranging from 0.3 to 2 nm to converge the energy calculations.
Three different mechanisms for the bulk sodiation of Sn 3 N 4 were considered: (a) the addition of interstitial Na ions into Sn 3 N 4 (with an associated reduction of the Sn oxidation state, reaction (7)), (b) the substitution of Na onto Sn sites (with an associated formation of Sn metal, reaction (8)), (c) or the substitution of Na onto N sites (with an associated formation of N 2 , reaction (9)). Na interstitial formation: Sn 3 N 4 + xNa / Na x Sn 3 N 4 (7) Substitution of Sn sites: Sn 3 N 4 + yNa / Na y Sn 3Ày N 4 + ySn (8) Substitution of N sites: Sn 3 N 4 + zNa / Na z Sn 3 N 4Àz + z/2N 2 (9) The associated reaction energies, per Na atom, are given in Table S3, ESI. † We found that, unsurprisingly, the least energetically favourable of these was Na substituting into the N site (reaction (9)). For the addition of Na interstitial sites (reaction (7)), we considered various sites for interstitial Na as shown in Fig. 6. The lowest energy conguration (shown in yellow: 16c interstitial forming a pseudo-octahedral Na site face linking to two SnN 4 tetrahedra and edge linking to four SnN 6 octahedra) was then considered in a larger supercell, corresponding to Na 0.0625 Sn 3 N 4 . This structure was found to be energetically favourable with a formation energy of À0.426 eV per Na atom. Apart from the formation of this energetically favourable Na interstitial, other Na interstitial sites considered (see Fig. 6 and ESI, Table S3 †) were found to have a positive formation energy, meaning that they were not thermodynamically stable with respect to bulk Sn 3 N 4 and Na. The energy of formation of Na interstitials ranged between 1.68 and 3.8 eV using PBE, and the values obtained with HSE06 were 0.3 eV lower. However, it is worth noting that the formation energy for inserting two Na interstitials into the structure was 1.28 eV (per Na atom) (compared to 1.68-3.8 eV for the rst interstitial considered here), indicating that the expansion of the structure to accommodate the rst Na atom results in a lower formation energy for subsequent Na intercalations. The third reaction pathway considered was Na substituting onto the Sn site (reaction (8)), which was also found to be energetically unfavourable. Substituting the Sn tetrahedra (Sn tet ) had a formation energy of 4.33 eV in PBE, and substitution at the Sn octahedral site (Sn oct ) was slightly less favourable at 4.47 eV in PBE (see sites in Fig. 6).
In summary, ab initio calculations were applied to evaluate the energy of formation of bulk Na x Sn y N z compounds, of which only Na 0.0625 Sn 3 N 4 was found to be stable. Therefore, it can be proposed that the electrochemical sodiation of Sn 3 N 4 will produce the bulk formation Na 0.0625 Sn 3 N 4 . However, the capacity associated with such a process is very small: the theoretical capacity is only 4 mA h g À1 . Previous studies have also identied NaSnN as a stable compound, this phase contains Na ions intercalated in between two-dimensional layers of [SnN] À . 54,55 The sodiation of Sn 3 N 4 to form bulk NaSnN has an associated theoretical capacity of 65 mA h g À1 . However, the bulk conversion of the Sn 3 N 4 material into NaSnN is not supported by our experimental data: XRD data of the electrodes discharged to different potentials in Na half-cells (see discussion below, Fig. 9b) show that the diffraction pattern of the Sn 3 N 4 spinel structure is still clearly visible even aer polarization to 10 mV vs. Na + /Na, thus demonstrating that the core of Sn 3 N 4 particles undergoes little structural change. The absence of transformation of bulk Sn 3 N 4 into bulk NaSnN could be attributed to kinetic limitations. On the other hand, the sodiation of Sn 3 N 4 to form Na 0.0625 Sn 3 N 4 involves little structural rearrangement, so it is expected to be facile and the observed XRD patterns of the sodiated (i.e. reduced) electrodes are also consistent with Na 0.0625 Sn 3 N 4 . Thus, we conclude that sodiation of Sn 3 N 4 starts with the facile insertion of a small of amount of sodium in the Sn 3 N 4 structure, forming the identied stable compound Na 0.0625 Sn 3 N 4 . On the other hand, the surface of Sn 3 N 4 particles undergoes signicant reactions during cycling in Na half cells. To study the surface reactions, additional calculations were performed to evaluate the energy of formation of surface compounds.
By performing ab initio calculations with the PBE functional, we found that the insertion of Na into the Sn 3 N 4 surface (reaction (7)) was generally energetically favourable, resulting in a signicant energy gain (at the surface the formation energy is À3.5 eV for the adsorption of 1 Na atom). Further below the surface, this energy decreases but remains favourable for all the slabs we have considered (up to 2 nm thick). This indicates that, near the surface, the energetic cost of expansion and strain on Sn 3 N 4 associated with sodiation reactions is less than the energy gained from adsorbing Na. Furthermore, on the top surface layers of Sn 3 N 4 , the substitution of a Na into a Sn site, forming Na y Sn 3Ày N 4 + ySn (reaction (8)) becomes favourable, with formation energies of À1.9 eV for surface substitutions and À0.6 eV for subsurface (1 monolayer below) substitutions (both tin tetrahedral sites). As these represent the rst steps of conversion of the Sn 3 N 4 structure, this suggests a potential $1.9 V vs. Na + /Na for the surface process. However, we treat this with caution as it is heavily dependent on surface reconstructions and terminations. These ndings suggest that the electrochemical reaction of sodiation of Sn 3 N 4 is likely initiated by the insertion of Na on the surface followed by the substitution of Sn by Na at the Sn 3 N 4 surface, resulting in the formation of a Sn metal coating on top of the Sn 3 N 4 nanoparticle. Then, Sn metal could react further with Na forming different Na x Sn y alloys, with Na 15 Sn 4 as the nal product, as shown in previous studies of the sodiation of Sn in Na-ion cells. [39][40][41][42]45 It is reasonable to assume that the products of these surface reactions will grow as a shell around a core with Na y Sn 3 N 4 structure (possibly made of Na 0.0625 Sn 3 N 4 , according to our calculations). These ndings can explain the increase in the capacity values observed with the nanocrystalline tin nitride electrode, as the material will have a larger surface area compared with the microcrystalline material. Unfortunately, the larger surface also increases the electrolyte breakdown occurring in the rst charge cycle, which can explain the larger irreversible capacity loss witnessed on the initial cycle of the nanocrystalline material. 95 Fig. 6 A ball and stick representation of the Sn 3 N 4 structure. The large purple spheres are Sn; the smaller purple spheres are nitrogen. The Na interstitial in its lowest energy configuration is shown as a yellow sphere. Other sites considered are shown with green dots. The two substitutional sites for the substitution of Sn by Na are highlighted with orange dots (upper: octahedral, lower: tetrahedral). The unit cell is highlighted in red.

Structural and chemical change during cycling
In order to elucidate the reactions undergone by Sn 3 N 4 materials in Na half-cells, electrodes were extracted from the cell at potentials chosen from features observed in the potential prole (Fig. 7, also see differential capacity plots in the ESI, Fig. S4 †). These were 1.6, 1.2, 1.0, 0.5 and 0.01 V vs. Na/Na + during reduction and 0.1, 0.75, 1.5 and 2.5 V vs. Na/Na + during oxidation. Samples were then characterised by XRD, XANES and EXAFS. These experiments utilised the microcrystalline Sn 3 N 4 in order to obtain more useful diffraction data, although it is recognised that the nanocrystalline material has the larger capacity. On rst reduction, there is a sloping plateau over 1.6 V (Fig. 7) followed by a small plateau at 1 V. We attribute this process to the insertion of Na ions into the Sn 3 N 4 structure via surface reactions such as the substitution of Na to Sn sites which produces Sn metal coatings. These reactions were found to be energetically favourable (negative formation energies) at the Sn 3 N 4 surface by DFT calculations. At lower potentials the formation of Na x Sn y phases is expected, which likely requires some Sn to have already formed. A large, sloping plateau is observed at 0.5 V, that could be ascribed to the alloying reaction (Sn / Na x Sn). This alloying process continues to 10 mV, as described in SnO 2 and Sn 4 P 3 systems. [96][97][98] Since the sodiation of Sn produces a series of Na x Sn y compounds at potentials in between 0.5 V and 0 V vs. Na + /Na, these last processes have been assigned to the Sn alloying reactions (Sn / Na x Sn y ). [39][40][41][42]45 Sn K-edge XANES analysis was performed to probe changes in the oxidation state of Sn in the cycled electrodes. For that purpose, prior to the measurements, Sn-K edges were calibrated against Sn standards with dened oxidation states (Sn, SnO 2 , SnO and Na 4 Sn with oxidation states of 0, +4, +2 and À4, respectively, see ESI, Fig. S5 †). The XANES spectra (Fig. 8) show the edge energy shiing to lower energy values during the rst reduction and a decrease in the intensity of the white line position at the fully reduced state (10 mV vs. Na + /Na), corresponding to an average oxidation state of À0.1 (ESI, Table S5 †). Whilst a negative oxidation state implies that Na-Sn alloying has taken place, it also suggests incomplete conversion of Sn 3 N 4 to Na-Sn alloys, as we would expect a much lower oxidation state (À1.25) for the fully sodiated Na 15 Sn 4 phase. Fig. 8 also shows an increase in the edge energy shi and intensity of the white line position in the XANES spectra during the rst oxidation of the Sn 3 N 4 electrode. The average oxidation state of Sn was 3.5 in the fully charged state (2.5 V vs. Na + /Na), very close to the average oxidation state of the pristine sample (3.7). This provides strong evidence that reformation of Sn 3 N 4 occurs. Fig. 9b shows the ex situ XRD data of Sn 3 N 4 electrodes cycled to the same set of potentials as in the XANES measurements in Fig. 8. It is observed that the reections corresponding to Sn 3 N 4 become sharper on reduction of the electrode, this suggests that the smaller crystallites are reacting more readily and hence the average crystallite size increases. At 0.5 V, clear reections for Sn metal appear in the pattern. This is in agreement with the ndings from the DFT calculations, which predict that sodiation would induce the insertion of Na into the surfaces of the Sn 3 N 4 particles, thus ejecting Sn metal, followed by the growth of a Na-Sn alloy shell around the Sn 3 N 4 particles. Formation of Na-Sn alloys is not clearly visible in the XRD data, indicating poor crystallinity or small particle size of the Na-Sn alloys.  During the initial stages of the re-oxidation, the intensity of the Sn metal reections diminishes but small Sn diffraction peaks are still visible at the end of charge (2.5 V), suggesting incomplete reversibility of the conversion process. At the end of oxidation, the Sn 3 N 4 peaks become broader, similar to the pristine samples, indicating that the electrochemical reactions are reversible and the small crystallites reoxidise recovering the spinel Sn 3 N 4 structure. The pristine electrode exhibits a reection at 37.5 that disappears upon reduction and it is not recovered aer oxidation. This peak appears due to the use of a homogeniser for the electrode preparation: Fig. S1 in the ESI † shows that electrodes prepared without homogenization do not have this peak and exhibit the same changes in the XRD pattern induced by the electrochemical reactions. Unfortunately, the assignment of this peak is unclear: NiO and CrO 2 show reections close to that position, but at higher angles, and they show other reections that are not observed in the experimental patterns (see ESI, Fig. S6 †). The pattern of the electrode at the end of oxidation (2.5 V) shows a very small peak at 26.2 , which could be ascribed to the formation of small amounts of SnO 2 , but again, the position of the peak is not exactly as expected for SnO 2 and other reections of SnO 2 are not observed (ESI, Fig. S7 †).
The EXAFS spectra during the rst cycle (Fig. 9a) show a peak doublet at 1.5Å radial distance corresponding to Sn-N bonds. The intensity of the lower radial distance peak within the doublet, corresponding to the tetrahedral Sn tet -N bond distance, decreases greatly during reduction compared to the octahedral Sn oct -N site ( Fig. 9a and expanded in ESI, Fig. S8 †) suggesting that Na substitution has taken place preferentially on the tetrahedral Sn sites. This is in agreement with the rst principle calculations that showed substitution of Na onto tetrahedral Sn sites to be slightly more favourable than on octahedral sites (ESI, Table S3 †). It is worth mentioning that the decrease in the intensity of the peak related to the tetrahedral Sn tet -N bond distance starts at very high potentials (1.6 V), supporting our interpretation of the electrochemical data that the rst sloping plateau centred at 1.6 V is due to sodiation surface reactions of substitution of a Sn tetrahedral site by Na. Then, as the potential is further reduced, a new environment starts to emerge from 1 V to 10 mV which could be assigned to the formation of Na-Sn alloys. The intensity of the tetrahedral Sn tet -N peak increases in the EXAFS spectra during the subsequent reoxidation of the electrode suggesting that the spinel Sn 3 N 4 is reforming. This is in agreement with the increased oxidation state calculated from the XANES analysis (ESI , Table  S5 †).

Discussion of reaction mechanism
Previously we proposed that the electrochemical reactions of Sn 3 N 4 in Na-ion cells could proceed via a conversion and alloying mechanism: 36 Conversion: Sn 3 N 4 + 12Na + + 12e À / 4Na 3 N + 3Sn (10) Alloying of Sn: 4Sn + 15Na + + 15e À / Na 15 Sn 4 Combination of reactions (10) and (11) has an associated theoretical capacity of 1512 mA h g À1 . This reaction mechanism is, thus, consistent with the observed reversible capacities of up to 850 mA h g À1 . The fact that the experimental capacity is lower than the theoretical capacity could be ascribed to incomplete conversion of Sn 3 N 4 and alloying to produce Na 15 Sn 4 . Indeed, many battery materials undergoing conversion reactions do not reach the full theoretical capacity. Nanostructuring of the material (that is, decreasing the particle size) oen results in signicant improvements in the practical capacity, due to a better utilisation of the whole material. This is also observed in the present work by comparing the reversible capacities of the microcrystalline and nanocrystalline samples. Furthermore, the XRD characterisation evidences the presence of unreacted Sn 3 N 4 throughout the whole discharge and charge process for the lower capacity microcrystalline sample.
The analysis of XANES to quantify the variation of the Sn oxidation state following reduction and oxidation is also consistent with reactions (10) and (11). The Sn oxidation state in microcrystalline Sn 3 N 4 is found to become negative (ca. À0.1) aer reduction, which demonstrates the formation of Sn-Na alloys. While the expected Sn oxidation state in Na 15 Sn 4 is more negative, the XANES data provides an average measurement for the whole sample, and some unreacted or partially reacted Sn 3 N 4 at the end of discharge is demonstrated by XRD. On charge, the Sn oxidation state increases to +3.5, which suggests that the original Sn 3 N 4 material is recovered aer charge, and further support is obtained from the XRD characterisation, which shows the re-growth of broad Sn 3 N 4 reections upon oxidation.
However, reaction (10) involves the formation of Na 3 N which is metastable and decomposes at around 100 C. We then considered the possibility that reaction (10) was not reversible due to decomposition of Na 3 N and the associated loss of N 2 , if that was the case, the electrochemical reactions would only involve the Sn-Na alloying reaction (reaction (11)), except for the rst discharge (reduction) of the cell which would also include reaction (10). However, reaction (11) of Na alloying of Sn to Na 15 Sn 4 has a theoretical capacity of 732 mA h g À1 when referred to the mass of the initial Sn 3 N 4 material. This capacity value is lower than the observed values of the reversible capacities and it is also inconsistent with the high Sn oxidation state obtained by XANES at the end of oxidation (ca. 3.5) and the recovery of Sn 3 N 4 observed in XRD measurements. All these measurements suggest that the electrochemical reactions on oxidation largely recover the original compound, Sn 3 N 4 . That would not be possible if N 2 was lost in the form of gas. Insertion of additional Na beyond Na 15 Sn 4 has been suggested from the analysis of operando NMR measurements of Sn reactions in Naion cells, 45 but such additional Na insertion on the Na-Sn alloy is insufficient to explain the experimental capacities observed in this work. The discharge prole of Sn 3 N 4 in Na-half cells is also distinct from that observed for Sn, which again supports the hypothesis that the electrochemical reactions are not simply Na-Sn alloying (reaction (11)). 14 The results of DFT calculations concur that Na 3 N is not stable against decomposition to Na and N 2 , in agreement with experimental observations. On the other hand, NaN 3 and Na 2 N 2 are stable or potentially stable. Considering the formation of NaN 3 or Na 2 N 2 in the rst conversion reaction, the following possible reaction mechanisms can be proposed: Conversion with NaN 3 formation: 3Sn 3 N 4 + 4Na + + 4e À / 4NaN 3 + 9Sn (12) Overall with NaN 3 formation: 12Sn 3 N 4 + 151Na + + 151e À / 16NaN 3 + 9Na 15 Sn 4 (13) Conversion with Na 2 N 2 formation: Sn 3 N 4 + 4Na + + 4e À / 2Na 2 N 2 + 3Sn (14) Overall with Na 2 N 2 formation: 4Sn 3 N 4 + 61Na + + 61e À / 8Na 2 N 2 + 3Na 15 Sn 4 (15) The theoretical capacity of conversion and alloying is 818 mA h g À1 with azide formation (reaction (13)) and 992 mA h g À1 with azenide (reaction (15)). Of the phases considered the highest reversible capacity of $850 mA h g À1 aer 50 cycles can only be explained by the azenide (Na 2 N 2 , reaction (15)). The Raman spectrum of fully sodiated Sn 3 N 4 electrodes does not show evidence of formation of NaN 3 or Na 2 N 2 , although this could be ascribed to the poor sensitivity of Raman measurements to detect small amounts of these compounds (ESI, Fig. S9 †).

Conclusions
Microcrystalline and nanocrystalline Sn 3 N 4 were prepared using solvothermal conditions at 430 C, or at 300 C followed by ultrasound treatment in aqueous HCl. Sn 3 N 4 electrodes of both materials were cycled in Na half-cells, with the nanocrystalline electrode providing a higher capacity and good cycling stability over 50 cycles. Indeed, the capacity exceeds those reported for other tin-based materials, and good cycling stability with other tin-based materials has only been achieved with carbon supports or composite structures. The results presented here bring a deeper understanding of the Sn 3 N 4 reaction mechanism in Na-ion cells. They provide evidence for the formation of Na-Sn alloys at the end of discharge and of reformation of Sn 3 N 4 at the end of charge. DFT calculations combined with ex situ X-ray diffraction and X-ray absorption spectroscopy indicate that the N from Sn 3 N 4 remains in the electrode in the form of some sort of Na-N compound. Na insertion into the Sn 3 N 4 nanoparticles, ejecting some Sn which forms Sn x Na y phases on the surface, has been shown to be energetically feasible from DFT calculations and is also consistent with the observed changes in the Sn-N and Na-Sn bond distances obtained from EXAFS spectra and with the change in the oxidation state obtained from XANES. The new solvothermal synthesis here developed is a simple and low cost synthesis route that enables an unprecedented control of the Sn 3 N 4 particle size, which is critical to achieve full utilization of Sn 3 N 4 and thus high capacity.

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