MgFeSiO4 as a potential cathode material for magnesium batteries: ion diffusion rates and voltage trends

Developing rechargeable magnesium batteries has become an area of growing interest as an alternative to lithium-ion batteries largely due to their potential to offer increased energy density from the divalent charge of the Mg ion. Unlike the lithium silicates for Li-ion batteries, MgFeSiO4 can adopt the olivine structure as observed for LiFePO4. Here we combine advanced modelling techniques based on energy minimization, molecular dynamics (MD) and density functional theory to explore the Mg-ion conduction, doping and voltage behaviour of MgFeSiO4. The Mg-ion migration activation energy is relatively low for a Mg-based cathode, and MD simulations predict a diffusion coefficient (DMg) of 10 9 cm s , which suggest favourable electrode kinetics. Partial substitution of Fe by Co or Mn could increase the cell voltage from 2.3 V vs. Mg/Mg to 2.8–3.0 V. The new fundamental insights presented here should stimulate further work on low-cost silicate cathodes for Mg batteries.


Introduction
The Li-ion battery currently dominates the portable energy storage market, powering mobile phones, laptop computers and electric vehicles. But the next generation of electronics will rapidly overtake the limit of what is theoretically possible with traditional Li-ion systems. While there are new approaches, such as the development of Na-ion batteries and solid-state Liion batteries, that could potentially offer cost, specic energy and safety advantages, there are few options to improve energy density. One strategy to improve energy density beyond the capability of Li + systems is to utilise multivalent cations, specically the Mg 2+ ion, owing to its similar size to Li + . [1][2][3][4][5][6] Improvements in energy density originate from the ability to use a metal anode rather than an insertion structure. In addition, dendrite formation, which prevents the use of Li metal anodes for Li-ion batteries, does not occur with Mg metal anodes. 2 Due to the difficulty of Mg 2+ insertion/extraction in host structures, the choice of cathode materials for Mg batteries is limited. This is thought to be due to stronger ionic interactions and harder charge redistribution of Mg 2+ ions in comparison to Li + ions. 3 Approaches used to improve the diffusivity of Mg 2+ ions in cathode materials have included decreasing the particle size of the cathode, 7 charge shielding of the inserted Mg 2+ ions 8,9 and redistribution of the electrons donated by Mg to transition metal clusters. 3,[10][11][12] Various potential cathode materials for Mg batteries have been considered, such as V 2 O 5 , 13-17 polymorphs of MnO 2 , 18-24 molybdenum chalcogenides, 1,3,25 and spinel sulphides and oxides. [26][27][28][29] Recently, olivine-type Mg silicates have been reported to show promising cathode performance for Mg batteries, with some indication of reversible Mg intercalation. [30][31][32][33][34][35][36] This follows extensive work on lithium-based silicates, Li 2 FeSiO 4 and Li 2 MnSiO 4 , as possible low-cost and stable cathodes due to the high natural abundance of silicon and the strong Si-O bonds. 37 It has previously been reported that the olivine phase of MgFeSiO 4 exhibits a degree of mixing between octahedral Mg and Fe crystallographic sites. [38][39][40] However, ordered phases of the MgFeSiO 4 structure have been synthesised through high temperature methods. A synthesis temperature of up to approximately 900 C yields a structure where Mg 2+ occupies M2 octahedral sites and Fe 2+ prefers M1 octahedral sites. However above this temperature, the site preference switches, with Mg 2+ and Fe 2+ residing in M1 and M2 positions, respectively. 38 Therefore, above 900 C MgFeSiO 4 can be synthesised with a structure analogous to LiFePO 4 , where the Mg 2+ ions form one-dimensional channels along the c-axis.
In previous studies, Mg 2+ has been inserted into disordered olivine FePO 4 with a measured capacity of only $13 mA h g À1 . This poor performance was found to be linked to surface amorphisation that prevented the electrochemical reaction from penetrating the bulk, rather than poor Mg 2+ mobility in the structure. 41 A rst-principles study on the magnesium silicates reports the redox and thermodynamic behaviour of these compounds, 33 revealing a similarity between lithium-and magnesium-insertion processes. However, these calculations did not consider kinetic processes, such as the transport of Mg 2+ ions in the host lattice, which are essential to the performance of ion intercalation electrodes.
It is well established that the underlying transport and electronic properties of battery cathode materials are crucial to the greater understanding of their electrochemistry, but are not fully characterised for MgFeSiO 4 . Here we investigate the solidstate features that inuence the electrochemical performance of ordered MgFeSiO 4 (with a structure analogous to olivine LiFePO 4 ), by employing advanced modelling methods to probe the Mg-ion transport properties and voltage trends from transition metal doping.

Methods
The methods used here are well established and detailed elsewhere. 42,43 Previous studies on inorganic solids have successfully applied these potential-based methods, including olivinestructured LiFePO 4 and NaFePO 4 (ref. [44][45][46] and Li and Na silicate cathode materials. [47][48][49][50] Interactions between ions in the silicate framework were described using the Born-model framework, with a long-range coulombic term and a shortrange term to model electron-electron repulsions and van der Waals interactions. The inclusion of a three-body term was necessary in order to model the angle-dependent nature of the SiO 4 unit. 47 The shell model 51 was used to account for the ionic polarisability effects. The interatomic potentials used here (listed in Table S1 in ESI †) were taken from previous studies on related oxides and silicates. 47,49,52 The Mott-Littleton approach is used to simulate the lattice relaxation around defects and migrating ions, which is incorporated within the GULP code. 53 Molecular dynamics (MD) calculations, which introduce kinetic energy to the system by solving Newton's equations of motion for an ensemble of ions at nite temperatures, were performed using the LAMMPS code. 54 The calculations were carried out on a simulation box, with periodic boundary conditions, made up of 12 Â 6 Â 10 unit cells, consisting of 20 160 atoms. The initial conguration of the structure contained 10% Mg vacancies (and corresponding Fe 3+ species), which were randomly distributed. The Pedone model 55 was used for the MD simulations, which was employed successfully in recent studies on Na-ion conducting battery materials. 50,56 Three initial congurations were investigated and the results of the three structures were averaged. Simulation runs were carried out using the NVT ensemble and a time step of 2 fs for long runs of 6 ns, at temperatures in the range 300-1500 K. Preequilibrium runs of 4 ps with NVE and NPT ensembles were rst used for stable congurations. Computer simulations have been used to investigate a range of materials for lithium and sodium batteries. 40,42,[56][57][58][59] Density functional theory (DFT) calculations were performed using a plane wave basis set implemented in the VASP code. 60 A cutoff energy of 440 eV and k-point mesh of 2 Â 4 Â 5 were needed to converge the forces and energies. PAW potentials 61,62 and the spin-polarized generalised gradient approximation (GGA) with the PBEsol functional 63 were used. DFT+U methodology was used to account for the metal d-orbitals with an effective Hubbard U eff ¼ U À J ¼ 4.3, 3.9, 3.3 and 6.0 eV (J ¼ 1.0 eV) for Fe, Mn, Co and Ni, respectively. 56 A ferromagnetic arrangement of the unpaired 3d electrons was assumed. The Mg 2+ /Mg cell voltage for the Fe 2+ /Fe 3+ redox couple was calculated using the following equation: The chemical potential of magnesium (m{Mg}) was calculated using Mg metal. Such DFT techniques have been applied to other battery materials 29,42,57,59 including Li-ion silicate cathodes. 58,64

Structural modelling
The olivine-type structure of the cation-ordered MgFeSiO 4 belongs to the Pmnb space group (Fig. 1), 34 and consists of corner sharing FeO 6 octahedra along the bc plane. SiO 4 tetrahedra share corners and edges with the FeO 6 octahedra. Mg ions are located in channels along the c-axis. The starting point of the study was to reproduce the experimentally observed structure of MgFeSiO 4 . A comparison between the calculated unit cell parameters based on effective potentials and those of the experimental structures is given in Table 1 (and further details on potential models are given in Table S2 †).
The lattice parameters were computed to within 1% of the experimental values. Reproduction of the lattice parameters adds validity to the interatomic model used for simulating defects and Mg-ion migration.

Energetics and pathways for Na-ion migration
Examination of the intrinsic Mg-ion mobility in MgFeSiO 4 is of interest when considering its use as a cathode material for magnesium batteries. In the olivine structure there are three potential pathways for Mg-ion migration, as shown in Fig. 2a. The activation energies of Mg migration along these pathways in MgFeSiO 4 are listed in Table 2, along with the Mg-Mg distances. The activation energy is signicantly lower for pathway A (parallel to the c-axis) than for pathways B and C. This is similar to the results obtained for olivine LiFePO 4 , 44 where the lowest energy pathway is along open channels that run parallel to the b-axis. The activation energies for pathways B and C are both prohibitively high and so Mg ion migration is not likely in these directions. This can be rationalised by considering the structure of MgFeSiO 4 ; the distance between neighbouring Mg 2+ ions in pathways B and C is greater than pathway A. In addition, pathway B has a smaller channel size than pathway A. Pathway C would involve migration directly past both Fe-O and Si-O bonds, both of which would contribute to the high migration energy found. Fig. 2b shows the curved pathways along which Mg-ion migration is predicted to take place in MgFeSiO 4 . These same migration pathways have also been simulated in olivine LiFePO 4 , 44 and subsequently conrmed by diffraction measurements and maximum entropy studies. 65 The calculated migration energy for this pathway was 0.60 eV, just 0.05 eV higher than that calculated for LiFePO 4 . 44 A previous rst-principles study carried out by Rong et al. 66 reports the migration energies of different multivalent ions in olivine FePO 4 , layered NiO 2 and spinel Mn 2 O 4 . Here Mg 2+ diffusion in the olivine structure was calculated to require approximately 0.7 eV, lower than multivalent cation diffusion in the layered and spinel structures, calculated at approximately 1.1 and 0.8 eV, respectively. The relativity low migration energies predicted for both olivine FePO 4 and MgFeSiO 4 suggest favourable Mg 2+ ion transport in the olivine structure.
MD techniques, used here at long timescales, are well suited to examine ion motion. The curved pathways predicted using energy minimisation techniques were also generated using MD, as shown in the energy density plot in Fig. 2c.
A small degree of anti-site defects (the exchange of Mg 2+ /Fe 2+ on neighboring sites) is found in the MD calculations; an example can be seen in Fig. 2c, where Mg-ion density is found near the Fe sites. These defects were anticipated given the high levels of Mg/Fe mixing in the thermodynamically stable form of MgFeSiO 4 . [38][39][40] This type of defect has been reported to cause blocking of the 1D migration pathways in olivine LiFePO 4 . 67 However, major blocking of the Mg channels was not observed in our MD simulations, which is likely to be important for reversible Mg intercalation. Hence, we predict that while antisite defects may form causing a localised blocking effect, the Fe 2+ ions are able to migrate back into their original sites allowing Mg 2+ ions to diffuse through uninterrupted channels. Also there was no evidence of inter-channel hopping of the displaced Mg 2+ ions.
The mean squared displacement (MSD) of Mg ions, [r(t)] 2 , for MgFeSiO 4 is shown in Fig. 3. The MSD data can be used to derive the Mg-ion diffusion coefficient (D Mg ) using: At 300 K a D Mg value of 1.1 Â 10 À9 cm 2 s À1 was calculated. To our knowledge there no experimental or calculated diffusion coefficients for ordered MgFeSiO 4 for direct comparison. A previous study on tavorite FeSO 4 F as a potential cathode for Mg batteries, quoted an estimated D Mg in the range of 10 À9 cm 2 s À1 , the same order of magnitude as observed for Li diffusion in the same structure. 68 Interestingly, Mg batteries may be more suitable for high temperature environments where the diffusion rate (and electrode kinetics) would be higher.
An Arrhenius plot for Mg 2+ diffusion in MgFeSiO 4 is shown in Fig. 4, which can be used to estimate the activation energy of migration. An activation energy of 0.79 eV was derived. While this value is slightly higher than that predicted using energy minimisation, it is still relatively low for a Mg-based cathode material. This result and the prediction of D Mg in the range of Li-ion cathode materials, suggests favourable Mg 2+ intercalation kinetics for ordered MgFeSiO 4 .

Dopant substitution
Previous dopant studies on lithium-ion battery cathodes have suggested that the incorporation of dopants on certain sites could potentially improve the capacity of the material by increasing the amount of lithium available for extraction through formation of lithium interstitial defects. 47 Doping strategies could also be benecial for magnesium-ion cathode materials. While the divalent nature of the magnesium ion offers increased energy density over monovalent lithium, many structures only allow for the de/intercalation of half of the available magnesium. The incorporation of dopants could create Mg interstitial defects that could consequently improve the capacity of the cathode material.
Here we investigate trivalent doping (Al, Ga and V) on the Si site within the MgFeSiO 4 structure. The doping process is described using the following equation (where M ¼ Al, Ga or V): M 3+ doping on the Si site is charge compensated by the formation of an Mg interstitial. We note that the alternative charge-compensation mechanism involving oxygen vacancies is less favourable by more than 4 eV. Trivalent doping on other sites in the structure would yield Fe vacancy as compensation, which would not improve the capacity or Mg diffusion in the material.
The dopant substitution reaction energies were calculated by combining the appropriate defect and lattice energy terms, listed in Table 3. Interatomic potentials used to model the corresponding binary oxides of the dopant cations were used in each case (Table S3 †). This systematic approach to dopant incorporation has been applied successfully to other silicate systems. 47 The large incorporation energies (in Table 3) for trivalent Al, Ga and V doping in MgFeSiO 4 to create Mg interstitials are unfavourable, and suggest a low degree of dopant solubility. Therefore, we conclude such trivalent doping of MgFeSiO 4 is not a viable method to improve its capacity or Mg diffusion properties.

Cell voltage trends
One challenge to overcome when developing new cathode materials for magnesium-ion batteries is to establish an adequate operating voltage (in the range of approximately 2.0-3.0 V) while simultaneously retaining a high reversible capacity. 69

Conclusions
Our fundamental study of olivine-structured MgFeSiO 4 as a potential cathode material for Mg batteries shows good reproduction of the experimentally observed structure and reveals key atomic-scale insights into its electrochemical properties. First, we derive an Mg-ion migration energy of 0.6 eV along the 1D channel through a curved pathway (similar to LiFePO 4 ), and a diffusion coefficient (D Mg ) of 10 À9 cm 2 s À1 at 300 K from large-scale MD. These ion transport results suggest favourable Mg 2+ intercalation kinetics.
Secondly, doping of trivalent Al, Ga or V ions on Si sites is unfavourable and suggests low dopant solubility.
Finally, the DFT derived cell voltage for MgFeSiO 4 of 2.35 V vs. Mg/Mg 2+ agrees well with the available electrochemical data. Mn or Co doping of this structure on the Fe site is predicted to increase the cell voltage to greater than 2.70 V. However, in the case of Ni doping this brings the voltage outside of the useable electrochemical stability range of current electrolytes. Overall, the fundamental insights presented here will inform the future optimisation of silicate electrodes for magnesium batteries.