Essential Role of Spinel MgFe₂O₄ Surfaces during Discharge

DFT implemented in the Vienna ab initio simulation package (VASP)^24,25 was employed. The spin-polarized DFT+U calculations^26–28 were carried out with the PAW potential^25,29 using the PBE exchange-correlation functional³⁰ and a kinetic energy cutoff of 520 eV. A Hubbard U correction of U_eff = 5.3 eV was applied to the Fe d orbitals. This setup was successfully used to predict the discharging properties observed experimentally for bulk and surface MgFe₂O₄ according to our previous studies.^5,7 The Gaussian smearing method was used with the total energies converged better than 10⁻⁵ eV, and the final force on each atom is less than 0.02 eV Å⁻¹. The first Brillouin zone was sampled on 3 × 3 × 1 k-mesh. The 2 × 2 slab model was constructed to describe various MgFe₂O₄ surfaces. A 20 Å thick vacuum was added along the direction perpendicular to the surface to avoid the artificial interactions between the slabs. During geometry optimization, the top three layers were allowed to relax with adsorbed Li⁺ ions, while the rest were fixed at the bulk position.

The supercell of MgFe₂O₄ bulk was constructed with the Fd $\bar{3}\,$m primitive cell containing eight formula units in normal-spinel, mixed-spinel and inverse-spinel structures. According to the previous synchrotron X-ray powder diffraction (XPD) measurement,⁵ for the mixed-spinel structure, the formula of (Mg_0.25Fe_0.75)_8a(Mg_0.75Fe_1.25)_16dO₄ with the inversion degree of 0.75 was constructed. The DFT-optimized lattice parameters of 8.54 Å, 8.52 Å, 8.50 Å in normal-spinel, mixed-spinel and inverse-spinel, respectively (8.40 Å in experiments^5,8,14); and band gaps of 1.5 eV (1.5 ∼ 2.0 eV in experiments^16,17,31) in three systems are in reasonable agreement with the values measured experimentally.

The Li adsorption/binding energy is defined as³²

$$\begin{eqnarray*}&&{{\rm{E}}}_{{\rm{b}}}={{\rm{E}}}_{{\rm{xLi}}/{\rm{Surface}}}-{{\rm{E}}}_{{\rm{Surface}}}-{{\rm{xE}}}_{{{\rm{Li}}}^{+}}\end{eqnarray*}$$

where E_xLi/Surface, E_Surface, and E_Li+ correspond to the total energy of Li-adsorbed surface, bare surface and aqueous Li⁺ ion, respectively. x is the number of Li on the surface. Negative ${{\rm{E}}}_{{\rm{b}}}$ represents an energetically favorable adsorption.

The average intercalation voltage is calculated by³³

$$\begin{eqnarray*}&&{\rm{V}}=-\displaystyle \frac{{{\rm{E}}}_{\mathrm{xLi}/\mathrm{Surface}}-{{\rm{E}}}_{{\rm{Surface}}}-{{\rm{xE}}}_{{\rm{Li}}}}{{\rm{xF}}}\end{eqnarray*}$$

where E_Li stands for the total energy of Li bulk and F is Faraday's constant.

Magnesium ferrite was synthesized via a combination of co-precipitation and hydrothermal reaction with a subsequent calcination step modified from previously reported schemes.^34–36 Magnesium(II) nitrate, iron(III) nitrate, and sodium hydroxide reagents were used as received. The dry material was annealed in a tube furnace at 400 °C. X-Ray powder diffraction (XRD) of MgFe₂O₄ was collected with a Rigaku SmartLab X-ray diffractometer utilizing Cu Kα radiation, a Scintillation detector, and Bragg-Brentano focusing geometry. The XRD spectra were measured in a 2θ range from 5° to 90°. Rigaku PDXL2 software and the ICDD PDF-2 database was used for search-match analysis to identify the composition of the prepared material. Magnesium ferrite crystallite sizes were approximated by applying the Scherrer equation to the (3 3 1) reaction at a 2θ value of approximately 35° in the XRD pattern.

Coin-cell type batteries with lithium anodes were used to probe the electrochemistry of MgFe₂O₄, under an applied current density of 100 mA g⁻¹ between 0.2 and 3.0 V vs lithium. Galvanostatic measurements utilized MgFe₂O₄ electrodes prepared with 85% active material, 10% Super P carbon black, and 5% binder on a copper foil substrate. An electrolyte solution of 1 M LiPF₆ in 30/70 (v/v) ethylene carbonate/dimethyl carbonate solution was used. Electrochemical tests were done on two—electrode coin type cells assembled in an Ar-filled glove box with lithium as the counter electrode, polymer separator, and the MgFe₂O₄ working electrode.

Li⁺ ions were employed as a probe to evaluate the binding capability of each stable surface identified previously for pristine MgFe₂O₄.⁷ The adsorption of Li⁺ was considered at a low coverage, which described the situation at the very initial stage of discharge.

The stable (1 0 0) surfaces terminated by Mg or FeO₂, (1 0 0)-Mg or (1 0 0)-FeO₂ in our notation, and (3 1 1)-O or (3 1 1)-MgO₄ surfaces were considered for Li⁺ ion adsorption on pristine normal-spinel MgFe₂O₄, according to our previous study.⁷ Here, the topmost surface composition was used to label the surface termination. Various surface oxygen sites were tested (Figs. 1 and S1–S2 is available online at stacks.iop.org/JES/167/090506/mmedia). On (1 0 0)-Mg (Figs. 1a and S2), all the oxygen sites are able to provide the strong bindings to Li⁺ ion, among which the O₁O₂-Bridge site with the binding energy (E_b) of −2.59 eV (Table I), is the most favorable. The highly negative E_b indicates a strong thermodynamic preference to capture the Li⁺ ion from solution by (1 0 0)-Mg. However, this is not the case for (1 0 0)-FeO₂ (Figs. S1–S2), where the positive E_b for all surface oxygen sites are observed. The most preferred O₅O₆-Bridge site corresponds to E_b as high as 0.97 eV (Table I). That is, thermodynamically (1 0 0)-FeO₂ is not likely to attract the Li⁺ ion. In both cases, the Li⁺ ion interacts with two oxygen on adsorption. The difference is the local environment of the adsorption site. Compared to (1 0 0)-FeO₂, more Mg²⁺ ions are exposed on (1 0 0)-Mg (Figs. 1a and S2), which promotes the surface stability via the strong Mg-O interaction as shown previously.⁷ In the meantime, it also weakens the Fe-O bond on the surface. Upon discharge, Li is the electron donor. With the formation of Li–O bonds on the surfaces, one electron is transferred from Li to the surface, which is demonstrated by the limited states of Li 2 s and 2p right below the Fermi level according to the projected density of states (PDOS, Fig. 2a). As a result, the surface Fe³⁺ ions (Fe1–4, Fig. 1a), which interact directly to either O₁ or O₂ on the surface, are partially reduced to Fe²⁺, as the conduction bands are dominated by Fe 3d states with little contribution from Li⁺ and Mg²⁺.⁷ Consequently, the binding to Li⁺ ion is strengthened due to the weakened electrostatic repulsion from the Fe²⁺ ions as compared to Fe³⁺. However, little change was observed for (1 0 0)-FeO₂ (Fig. 2b) on Li⁺ ion. That is, the Fe³⁺ ions next to the O₅O₆-Bridge remains as 3 + instead. The strong repulsive force from Fe³⁺ hinders the approach of Li⁺ ion to the surface. In this case, the electron donated by intercalated Li results in the reduction of Fe³⁺ in the subsurface instead, so that the strong Fe³⁺–O²⁻ bonds on the surface and thus lower the surface energy can be sustained. For the same reason, all the adsorption sites on (1 0 0)-Mg can provide much stronger binding than that on (1 0 0)-FeO₂.

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The essential role of Mg²⁺ ions in enhancing the Li⁺ adsorption is also observed on (3 1 1) surfaces. Among the stable (3 1 1) surfaces with three different terminations, featured with the highest density of surface Mg²⁺ ions all oxygen sites on (3 1 1)-MgO₄ can provide strong bindings to the Li⁺ ion (Figs. S1–S2). Wherein, the most favorable is the O₁O₇O₁₂-Hollow(16c-Vacancy) site (E_b = −2.21 eV, Table I). When the surfaces are terminated by oxygen, neither the O-poor (3 1 1)-O¹ (E_b = 1.13 eV, Table I) nor the O-rich (3 1 1)-O² (E_b = 0.38 eV, Table I) favors the Li⁺ adsorption. The increased amount of O²⁻ ions on the surface, however, helps the binding by enhancing the symmetry of adsorption site from 2-fold to 3-fold. Among the five stable facets of normal-spinel MgFe₂O₄, only (1 0 0)-Mg and (3 1 1)-MgO₄ surfaces are active for adsorption of initial Li⁺ ions. Our results indicate that high density of Mg²⁺ ions exposed to the surface can strengthen the binding to the Li⁺ ions in addition to improve the surface stability as reported previously.⁷

For pristine mixed-spinel MgFe₂O₄, only the low-index (1 0 0)- Mg_1.5Fe_1.5O₄ and (0 0 1)-MgO₂, -FeO₂ surfaces are stable as shown previously (Figs. 1b and S1).⁷ On (1 0 0)-Mg_1.5Fe_1.5O₄ (Fig. 1b), the 16c-Vacancy site is highly favored for the Li⁺ adsorption (E_b = −8.81 eV). In the case of (0 0 1)-MgO₂ (Fig. S1), the Li⁺ ion can be stabilized at the O₅O₈-Bridge site (E_b = −7.51 eV, Table I); by comparison without the presence of surface Mg²⁺, the Li⁺ adsorption at the O₅O₇-Bridge of (0 0 1)-FeO₂ (Figs. S1, S3) is much weaker ( E_b = −3.91 eV, Table I). Again, the change of the termination from −FeO₂ to −MgO₂ results in a significant increase in Li⁺ binding activity, confirming the promotion of surface Mg²⁺ ions on the Li⁺ adsorption as seen in the case of normal-spinel MgFe₂O₄.

The pristine inverse-spinel MgFe₂O₄ has the most diversity in stable facets,⁷ all of which can stabilize the Li⁺ ions according to the current DFT calculations. With the presence of Mg²⁺ ions on (0 0 1)-Mg₂FeO₄ surface (Fig. 1c), the Li⁺ ion strongly interacts with the 16c-Vacancy site (E_b = −6.07 eV, Table I). While the binding is weakened with the decrease in surface Mg²⁺, going from the 16d-Vacancy site of (1 1 1)-O (E_b = −4.91 eV, Figs. S1, S4), the O₆O₇O₁₀-Hollow site (16c-Vacancy) of (3 1 1)-O (E_b = −3.96 eV, Figs. S1, S4) to the O₃O₇-Bridge site of (1 0 0)-MgFeO₄ (E_b = −3.37 eV, Figs. S1, S4). Here, we note that the variation from normal-spinel to inverse-spinel modifies the surface activity of (3 1 1)-O facets, making it energetically favorable for initial Li⁺ ion adsorption.

Our DFT calculations show that like the case of ZnFe₂O₄,⁴ the stability of MgFe₂O₄ surfaces correlates well with the capability to capture Li⁺ ions. As demonstrated previously, the high surface stability depends on the dense Mg²⁺ ions exposed to the surface.⁷ Accordingly, the statistics on densities of ions exposed for all the stable surfaces was performed, where a clear linear relationship between the density of Mg²⁺ ions and Li⁺ ions binding energy was observed (Fig. 3). That is, the higher density of Mg²⁺ ions correspond to the lower E_b or the higher capability to capture Li⁺ ions. While no clear correlation is observed between E_b and the densities of both Fe³⁺ and O²⁻ ions (Fig. S5). For each phase of MgFe₂O₄, the most active surfaces for Li⁺ ion capture feature the high Mg²⁺ ions density: 2.74 Mg nm⁻² for (1 0 0)-Mg of normal-spinel, 4.13 Mg nm⁻² for (1 0 0)-Mg_1.5Fe_1.5O₄ of mixed-spinel, and 5.54 Mg nm⁻² for (0 0 1)-Mg₂FeO₄ of inverse-spinel (Fig. 4 and Table I). The origin of the promoting effect is associated with the strong ionic nature of Mg-O bond. It enables the stabilization of the surface oxygen and thus the surface on one hand; on the other hand, the electrostatic repulsion from the surface to the approaching of Li⁺ ions is decreased by the preferential reduction of surface Fe³⁺ to Fe²⁺ during discharge, which enhances the capability of the surface to capture Li⁺ ions.

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In addition to the density of surface Mg²⁺, the symmetry of oxygen sites for adsorption can also affect Li⁺ binding. In mixed-spinel, although (0 0 1)-MgO₂ features higher density of surface Mg²⁺ ions (5.51 Mg nm⁻²) than (1 0 0)-Mg_1.5Fe_1.5O₄, there is no highly O-coordinated octahedral 16c-Vacancy sites on/near surface and results in weaker binding to the Li⁺ ions. A similar situation is also observed for inverse-spinel, where the 16d-Vacancy site on (1 1 1)-O with the higher density of surface Mg²⁺ ions (6.40 Mg nm⁻²) is less active than that on (0 0 1)-Mg₂FeO₄ (Table I). The 16d-Vacancy site on (1 1 1)-O is located closer to Fe³⁺ ions than that on (0 0 1)-Mg₂FeO₄, which also contributes to the weakened Li⁺-surface interaction. Nevertheless, neither the site symmetry nor the distance to the neighboring Fe³⁺ as significant as the density of surface Mg²⁺ ions in determining the capability for the Li⁺ capture.

As the discharge progresses, more and more Li⁺ ions can be captured by the surfaces of MgFe₂O₄. Accordingly, we now extend our DFT calculations to study the sequential adsorption of Li⁺ ions on surfaces from low to high coverage. For each type of spinel MgFe₂O₄, only the surface that is the most active to bind Li⁺ ion was considered: (1 0 0)-Mg in normal-spinel, (1 0 0)-Mg_1.5Fe_1.5O₄ in mixed-spinel and (0 0 1)-Mg₂FeO₄ in inverse-spinel (Fig. 4).

On normal-spinel MgFe₂O₄(1 0 0)-Mg, the initial adsorption of Li⁺ ion at coverage of 1.37 li nm⁻² prefers the O₁O₂-Bridge site (Fig. 4). The additional Li⁺ ion at the equivalent O₁O₂-Bridge site is energetically favorable with an increase in energy gain going from 2.59 eV to 3.48 eV at coverage of 2.74 li nm⁻². Starting at 4.11 li nm⁻², the preferential adsorption position varies from the Bridge site to Hollow site, which increases the exothermicity to −4.74 eV. This is also accompanied with surface distortion, where the Fe ions on surface and in sublayers shift from the octahedral 16d sites to the less stable tetrahedral vacancies (Fig. 4). The saturation coverage of Li⁺ ions is 5.48 li nm⁻² corresponding an energy gain of 6.06 eV. After saturation, the adsorption of additional Li⁺ ion is hindered, which costs the energy of 4.01 eV. This is due to the strong repulsion from the existing Li⁺ ions on the surface. Moreover, the significant structural distortion under high Li⁺ coverage also indicates that the (1 0 0)-Mg surface of normal-spinel MgFe₂O₄ is not stable during the Li⁺ adsorption process and may lead to low cyclability.

On (1 0 0)-Mg_1.5Fe_1.5O₄, the active 16c-Vacancy site has already been occupied at coverage of 1.38 li nm⁻²; while at 2.75 li nm⁻² the additional Li⁺ ions are forced to adsorb at the less active 16c-Vacancy sites which are closer to Fe³⁺ ions (Fig. 4). This is a slightly endothermic process, with a low energy cost of 0.08 eV. The further increase in coverage to 5.51 li nm⁻² with Li⁺ ions filled in the O₄O₅-Bridge site is thermodynamically preferred with energy release of 10.57 eV (Fig. 4). The adsorption at coverage of 6.89 li nm⁻² is not likely corresponding to an energy cost of 0.64 eV and the increase in structural distortion, which is again associated with the lateral repulsion from the neighboring adsorbed Li⁺ ions. Accordingly, the (1 0 0)-Mg_1.5Fe_1.5O₄ surface can be saturated by Li⁺ ions up to coverage of 5.51 li nm⁻², where the active 16c-Vacancy and O₄O₅-Bridge sites are all occupied. Here, we assume the highly exothermic adsorption of Li⁺ ions at 1.38 li nm⁻² (−8.81 eV) likely overcome the small endothermicity (0.08 eV) to reach the coverage of 2.75 li nm⁻². During this process, the Fe³⁺ ion in subsurface is very mobile, displacing from the tetrahedral 8a site to octahedral 16c-Vacancy in the 1st sublayer and partially blocking the typical 16c → 16c pathway for Li⁺ transport from surface to bulk.

On (0 0 1)-Mg₂FeO₄ surface, the Li⁺ ions locate at the 16c-Vacancy site at coverage of both 1.38 li nm⁻² and 2.77 li nm⁻², with the energy gain of 6.07 eV and 8.88 eV, respectively (Fig. 4). After the 16c-Vacancy sites are saturated, the O₂O₄-Bridge sites are occupied by Li⁺ ions at coverage of 4.15 li nm⁻² and 5.54 li nm⁻², which is unlikely to occur due to the endothermicity of 1.92 eV and 3.64 eV, respectively. Thus, the saturation coverage in this case is as low as 2.77 li nm⁻².

The capability of three spinel MgFe₂O₄ surfaces to capture Li⁺ is different. Both the mixed-spinel (1 0 0)-Mg_1.5Fe_1.5O₄ and inverse-spinel (0 0 1)-Mg₂FeO₄ with higher density of Mg²⁺ ions exposed to the surface are able to bind Li⁺ more strongly than normal-spinel MgFe₂O₄(1 0 0)-Mg surface ranging from the low Li coverage to the saturated coverage (Fig. 4). This is also demonstrated by the PDOS (Figs. 2 and 5). More obvious change in Fe 3d state on discharge is observed as compared to that for other ions on the surface when going from mixed- and inverse-spinel to normal-spinel. Specifically, the delocalization of surface Fe 3d states is enhanced when the Li⁺ ions are adsorbed on mixed-spinel (1 0 0)-Mg_1.5Fe_1.5O₄ (Fig. 5a) and inverse-spinel (0 0 1)-Mg₂FeO₄ (Fig. 5b). That is, the reduction of surface Fe³⁺ and thus the binding of Li⁺ ions can be promoted on phase transition of MgFe₂O₄ from normal to mixed or inverse spinel. In term of saturation coverage, though, the inverse-spinel surface cannot accommodate Li⁺ ions as much as that for normal- and mixed-spinel surfaces (Fig. 4). Overall, among the three phases of MgFe₂O₄ the mixed spinel is likely the most active, where the active (1 0 0)-Mg_1.5Fe_1.5O₄ surface not only allows active capture of Li⁺ ions and thus likely high discharge voltage at the initial stage, but also enables the accumulation of Li⁺ ions at high coverage, and thus likely high capacity. However, compared to ZnFe₂O₄ surfaces (12.66 li nm⁻²),⁴ the saturation coverage (up to 5.51 li nm⁻²) for MgFe₂O₄ is significantly lower. The high density of Mg²⁺ ions in MgFe₂O₄ does improve initial Li⁺ ions adsorption with lower E_b in comparison with ZnFe₂O₄ (E_b < −5 eV); however, the drawback is that the existing surface Mg²⁺ ions block some of the active sites for adsorption, and limits the high saturation by Li⁺ ions.

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To evaluate the contribution of Li⁺ adsorption on the surfaces to the discharge of MgFe₂O₄, the DFT-calculated E_b (Fig. 4) on the stable surfaces were used to estimate the average cell voltages. Here, the active MgFe₂O₄ in mixed spinel was taken as a case study. Using the bulk model,⁵ it was shown previously that the DFT-estimated discharge voltage agreed reasonably well with the experimental value at x > 0.5 (Fig. 6); however, at x < 0.5 the theoretical estimation is much lower, particularly at the very early stage with x < 0.25. Following our previous study of ZnFe₂O₄ surfaces,⁴ the coverage of Li⁺ on the surface was converted to the x value in the form of Li_xMgFe₂O₄, according to the number of Li⁺ ions adsorbed and therefore the number of electrons transferred in addition to the corresponding surface areas for the particles measured experimentally.⁵ Our results show that at x < 0.25 the estimated discharging voltage based on the DFT-calculated E_b for mixed-spinel (1 0 0)-Mg_1.5Fe_1.5O₄ are much higher than that based on the bulk materials and describes well the experimental measurements (Fig. 6). Such an observation again confirms the important contribution from surfaces to the initial lithiation as seen for ZnFe₂O₄ surfaces.⁷ Compared to bulk, the surface is able to provide the lower-coordinated oxygen sites for Li⁺ and enable the less structural distortion driven by intercalated Li⁺ ions, which help in enhancing the stability of intercalated Li⁺ ions.

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To experimentally verify the voltage profile, MgFe₂O₄ material was synthesized and electrochemically evaluated. X-ray powder diffraction was consistent with a MgFe₂O₄ spinel (Fd $\bar{3}\,$m) reference pattern indicating no crystalline impurities. A crystallite size of 10 nm was determined by applying the Scherrer equation^37,38 to the (3 3 1) reflection at a 2θ value of approximately 35°. Rietveld refinement showed good agreement of lattice parameters compared to crystalline MgFe₂O₄ group (8.3674 Å)³⁹ and our DFT calculations (8.52 Å), with a = b = c of 8.7345⁹ Å and an R_wp of 0.76% (Fig. S7). The material was electrochemically evaluated in two electrode cells. The voltage profile showed a difference in cycle 1, with consistent profiles for cycles 5 and 10 (Fig. 7a). The cycle 1 discharge capacity exceeded the theoretical capacity of MgFe₂O₄, 804 mAh g⁻¹, with values above 1200 mAh g⁻¹. The excess cycle 1 capacity is attributed to the decomposition of the electrolyte and the formation of the SEI and Li₂O on the surface of the pristine electrode at the electrolyte interface, a process that coincides with the irreversible capacity loss between cycles 1 and 2.^20,40–44 Subsequent cycle discharge capacities realized were ∼85% of the theoretical capacity (Fig. 7b).

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Besides the Li⁺ capture, the transport from surface toward bulk is also key to the discharge performance. To gain better understanding, we investigated Li⁺ ion transport from surface to subsurface on three stable and active surfaces, normal-spinel MgFe₂O₄(1 0 0)-Mg, mixed-spinel MgFe₂O₄(1 0 0)-Mg_1.5Fe_1.5O₄ and inverse-spinel (0 0 1)-Mg₂FeO₄. Three sublayers, 1st, 2nd, and 3rd sublayers in addition to the surface layer, were defined (Fig. S6) to open a path for Li⁺ transport. Finally, both low and saturated coverage of Li⁺ ions were considered to account for the coverage effect (Figs. 8 and S8–S9).

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At low coverage, (1 0 0)-Mg is too stable to allow the Li⁺ transport from the O₁O₂-Bridge on the surface to the 16c position of the 1st sublayer, which shifts back to surface site after geometry optimization (Figs. 8a, 8b). The following Li⁺ transport to 16c-Vacancy site in the 2nd sublayer (Fig. 8c) is also unfavorable, with an energy loss of 4.23 eV. From the 2nd to the 3rd sublayer (Fig. 8d) the process is energetically preferred with an energy gain of 2.73 eV. That is, at low coverage the Li⁺ ion transport is very unlikely from the normal-spinel MgFe₂O₄(1 0 0)-Mg surface to bulk. When comparing the energetics, the surface saturation by Li⁺ ions is more favorable than the Li⁺ transport (Fig. 4). That is, Li⁺ ions prefer to accumulate on the surface at the initial lithiation stage to a saturated coverage prior to the transport to subsurface, as we observed in previous study in ZnFe₂O₄.⁴ On the saturated (1 0 0)-Mg (Fig. 8e), the adsorption of additional Li⁺ ions is hindered due to the electrostatic repulsion from the saturated Li⁺ ions (Fig. 8f) and the corresponding binding energy is positive (E_b = 2.05 eV); however, it facilitates the transport toward the 2nd sublayer (Fig. 8g) corresponding to an energy gain of 4.90 eV; while the further displacement toward the 3rd sublayer (Fig. 8h) costs energy of 2.29 eV. Nevertheless, the transport of Li⁺ ions from the Li⁺-saturated surface is thermodynamically more feasible than that from the bare surface (Fig. 8).

At low coverage, the initial adsorption of Li⁺ ion at the octahedral 16c-Vacancy site at the 1st sublayer is favorable with an energy gain of 8.81 eV (Figs. 8 and S6a, S6b). The further transport to the 2nd sublayer (Fig. S6c) is also exothermic by 1.45 eV. During this process, the transport from the 2nd sublayer to the 3rd sublayer (Fig. S6d) is the only endothermic step, which costs energy of 3.00 eV. Thus, at low coverage the Li⁺ ion transport along the mixed-spinel MgFe₂O₄(1 0 0)-Mg_1.5Fe_1.5O₄ surface is likely feasible, driven by the significant energy gain in adsorption and transport to the 2nd sublayer. On the Li⁺-saturated surface, which is more likely to occur than transport according to the energetics (Figs. 4 and 8), the existing Li⁺ ions occupy all the active surface sites (Fig. S6e). Yet, he sequential adsorption (0.64 eV, Fig. S6f), the transport from surface to the 2nd sublayer (−3.98 eV, Fig. S6g) and from the 2nd to the 3rd sublayer (2.27 eV, Fig. S6h) likely proceeds smoothly with no highly endothermic step involved (Fig. 8).

The Li⁺ transport along (0 0 1)-Mg₂FeO₄ surface shows similar behavior as mixed-spinel (1 0 0)-Mg_1.5Fe_1.5O₄ (Figs. 8 and S8) under both the low coverage and saturate coverage. Again, at low coverage the initial Li⁺ adsorption on 16c-Vacancy site at the 1st layer (−6.07 eV, Figs. S8a, S8b) and the transport to the 2nd sublayer (−1.07 eV, Fig. S8c) are both downhill; while the displacement from the 2nd to the 3rd sublayer is uphill (3.01 eV). At saturation coverage, the Li⁺ ion adsorption is highly hindered (E_b = 5.56 eV); while the sequential transport to the 2nd sublayer (−2.18 eV) is more favorable.

According to our DFT calculations, upon electrochemical discharge the stable MgFe₂O₄{1 0 0} surfaces in three spinel structures are likely saturated by Li⁺ ions first, which is followed by the Li⁺ transport from the surface to subsurface. All saturated surfaces studied feature an endothermic adsorption of Li⁺ ion on the surface, a sequential exothermic transport to the 2nd sublayer and eventually an uphill transport to the 3rd sublayer. Wherein the 16c-Vacancy site is preferred in the sublayers in all cases. Energetically, the mixed-spinel (1 0 0)-Mg_1.5Fe_1.5O₄ displays the lowest endothermicity along the adsorption and transport path (Fig. 7), which is followed by the inverse-spinel (0 0 1)-Mg₂FeO₄ and the normal-spinel (1 0 0)-Mg in a decreasing sequence. Overall, the mixed-spinel (1 0 0)-Mg_1.5Fe_1.5O₄ surface is the most active among the diverse MgFe₂O₄ surfaces studied, which likely displays the high capacity, the high voltage and Li⁺ transport at initial discharging stage. Our study implies that the controlled synthesis toward maximization of such facet should enable a significant promotion in stability and discharge performance of MgFe₂O₄.