A theoretical approach to evaluate the rate capability of Li-ion battery cathode materials

Abstract

Charge–discharge rate capability is one of the most important properties of cathode materials for lithium batteries, in particular when envisaging high power density applications such as automotive applications. Efforts to modify rate have been carried out by carbon coating and decreasing particle size in order to modify electronic and ionic conductivity. However, this approach cannot justify all experimental data reported in the literature. Here, we investigated the rate capability of cathode materials by considering their density of states (DOS) calculated by several density functional theory (DFT) methods, in both the lithiated and the delithiated case. We suggested that these structures could be interpreted as n- or p-type semiconductors, depending on the DOS configuration. On this basis, if the lithiated structure acted as an n-type and the delithiated one as a p-type semiconductor, the resulting cathode will only be capable of achieving a “low rate”. If the opposite situation happened, the cathode would sustain high current rates. Li₂FeSiO₄, LiFePO₄, LiFeBO₃ and LiFeSO₄F were found to belong to the former class, whereas LiCoO₂, LiFeO₂ and LiMn₂O₄ were assigned to the latter one. On the basis of the proposed model, we suggested some general strategies related to the synthetic approach to improve cathode rate capability.

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1. Introduction

Ever-growing global demands for renewable energy storage have led to the need for development of more powerful rechargeable batteries.¹ At present, lithium-based batteries (LBs) outperform other systems.² Global ecological concerns, as well as recent fluctuations in crude-oil prices, have led to the acceleration of efforts for increasing the scope of LBs to large-scale applications, especially plug-in hybrid electric vehicles.³ In order to increase power density and push LBs towards large-scale applications, one of the most important parameters to be improved is the possible (dis)charge current rate, which is derived directly from the cathode rate capability. A high rate capability could even compensate for a low theoretical capacity. Nevertheless, the evaluation of its nature for different cathode materials is still lacking.

A number of well-known cathode materials can endure a high current rate, such as LiCoO₂ and LiMn₂O₄etc.⁴ On the other hand, a number of proposed cathode materials suffer from low tolerance for high current rates, including LiFePO₄, Li₂FeSiO₄, LiFeBO₃ and LiFeSO₄F etc.⁴ The latter category, in particular LiFePO₄ and Li₂FeSiO₄, are interesting cathode materials because of their low cost, environmental friendliness, and chemical and thermal stability.^5–7

So far, rate capability has been attributed to both electron and ion conductivity.⁴ Therefore, all investigations concerning the modification of rate have been focused only on these two parameters. The problem of low ionic conductivity might be overcome by decreasing grain size, and electron conductivity could be increased by coating the nano-grains with conducting carbon. However, as an example, carbon-coated ultrathin grains of Li₂FeSiO₄ did not allow high rate performances.^8–11 Carbon-coated grains of Li₂FeSiO₄ as small as 30 nm allowed charge–discharge measurements at C/20 (ref. 8) and C/16 (ref. 9 and 10) rates. Even ultrathin nanosheets of Li₂FeSiO₄ in a conductive matrix resulted in reported charge–discharge cycles at C/50 rate, although a high capacity was obtained.¹¹ By assuming that the highest reported rate is the highest possible one assuring good performance, it could be concluded that decreasing particle size and carbon coating did not remarkably modify the rate capability of Li₂FeSiO₄. Besides, the comparison between LiFeSO₄F and LiFePO₄ indicates the better rate capability of the latter material. For fine grain/particle sizes of cathode materials, much better rate capabilities have been reported for LiFePO₄^12–15 in comparison with LiFeSO₄F.^16–18 Also, for average grain/particle sizes, the rate capability of LiFePO₄^19–21 seems better than that of LiFeSO₄F^22,23 (more details can be seen in the ESI†). The ionic conductivity of LiFeSO₄F is much higher than that of LiFePO₄ (∼4 × 10⁻⁶ S cm⁻¹ for LiFeSO₄F vs. 2 × 10⁻⁹ S cm⁻¹ for LiFePO₄ at 147 °C), whereas their electronic conductivities are in the same range of magnitude.²² If ionic conductivity and electronic conductivity are the (main) parameters influencing rate capability, LiFeSO₄F would score much better than LiFePO₄, which indeed was not the case. On this basis, this investigation aims to assess the current rate capability of cathode materials by considering electronic contribution related to the behaviour of the lithiated–delithiated couple.

Density functional theory (DFT) has generated unparalleled confidence in the possibility to apply quantum mechanics to solve exciting and challenging problems in chemistry by describing the electronic states of materials (ref. 6 and references therein). This study employs DFT calculations to define a simple model for evaluating the rate capability of cathode materials. This approach could help future modifications of known cathodes, or even help to find new candidates. Although only cathode materials for LBs are considered in this paper, the concept is inclusive and could be applied to other analogous systems.

2. Methodology

All the calculations in this work were performed using the full-potential linear augmented plane wave (FP-LAPW) method as implemented in the WIEN2K code²⁴ within the framework of density functional theory (DFT).²⁵ Inside the non-overlapping spheres of muffin tin radius (R_MT) around each atom, linear combinations of the radial solution of the Schrödinger equation times the spherical harmonic are used, and the plane wave basis set is used in the interstitial region. To expand the wave functions in the interstitial region a plane wave cut-off value of K_maxR_mt = 7.0 was used, where R_mt is the smallest atomic sphere radius in the unit cell and K_max is the magnitude of the largest K vector. The Fourier-expanded charge density was truncated at G_max = 12(Ryd)^1/2. The maximum value of the angular momentum (l_max) was set equal to 10 for the wave function expansion inside the atomic spheres. Convergence of the self-consistent iterations was performed within 0.0001 Ry.

Before calculating the density of states (DOS), full relaxation was performed for atomic positions and cell parameters using the Perdew–Burke–Ernzerhof generalized gradient approximation (PBE-GGA).²⁶ The references that the initial structures, initial cell parameters and relaxed cell parameters were obtained from are given in Table 1. For the assessment of density of states (DOS), the calculations were carried out using PBE-GGA²⁶ and generalized gradient approximations plus an on-site Coulomb self-interaction correction potential (GGA + U).²⁷ The U value was considered to be equal to 6 eV for Mn and Co and 5 eV for Fe atoms (based on ref. 6 and 28). For more comprehensive evaluation, the PBE-Fock-α method of Exact-exchange and Hybrid functionals²⁹ was also used. For a number of structures, PBE-GGA modified Becke–Johnson potential (mBJ),³⁰ local spin density approximation (LSDA) and local density approximation plus an on-site Coulomb self-interaction correction potential (LDA + U) were also considered. However, the results are similar to GGA(+U), and to avoid extending the text they are given in ESI.† Spin polarization was considered for transition metals, and the major spin was considered to be up. Integrals were calculated over the Brillouin zone with k-points based on the values given in Table 1.

Table 1 Space group (s.g.) and experimental cell parameters used as the initial structures, calculated cell parameters and Monkhorst–Pack mesh k-points used for calculation

Material	s.g.	Experimental cell parameters	Calculated cell parameters	k-points
Li2FeSiO4	Pmn21	(6.26615, 5.32955, 5.01484)^31	(6.278, 5.312, 4.987)	4 × 5 × 5
LiFePO4	Pnma	(10.227, 6.0048, 4.6918)^32	(10.164, 5.916, 4.6203)	3 × 5 × 6
LiCoO2	R3̄m	(2.8155, 2.8155, 14.0537; 120)^33	(2.840, 2.840, 14.090)	9 × 9 × 1
LiFeO2	R3̄m	(2.8155, 2.8155, 14.0537; 120)^33	(2.844, 2.844, 14.222)	9 × 9 × 1
LiMn2O4	Fd3̄m	(8.2444, 8.2444, 8.2444)^34	(8.156, 8.156, 8.156)	6 × 6 × 6
LiFeBO3	C2/c	(5.12901, 8.8402, 10.1002; 91.363)^35	(5.143, 8.837, 10.006; 90.75)	4 × 4 × 1
LiFeSO4F	C2/c	(13.03753, 6.39531, 9.84432; 119.7531)^18	(12.928, 6.342, 9.762; 119.753)	3 × 5 × 5

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Spheres of muffin tin radius (R_MT) around each atom were dictated by the structure of each material. In the case of Li₂FeSiO₄, LiFePO₄, LiCoO₂, LiFeO₂ and LiMn₂O₄, R_MT values of 1.76, 2.00, 2.00 and 2.02 a.u. were used for Li, Mn, Fe and Co, respectively, and 1.42 a.u. was used for the Si, P and O atoms. For LiFeBO₃, R_MT of Fe, Li, B and O atoms was set at 2.00, 1.75, 1.28 and 1.28 a.u., respectively. In the case of LiFeSO₄F, R_MT of Fe, Li, S, F and O atoms was equal to 1.96, 1.82, 1.35, 1.74 and 1.35 a.u., respectively. The electron and spin configuration of the atoms were software defaults, and were: Li: [He]2s¹, B: [He]2s²2p¹, O: [He]2s²2p⁴, F: [He]2s²2p⁵, Si: [Ne]3s²3p², P: [Ne]3s²3p³, S: [Ne]3s²3p⁴, Mn_up: [Ar]3d⁵(5↑, 0↓)4s²(1↑, 1↓), Fe_up: [Ar]3d^6.5(4.5↑, 2↓)4s^1.5(1↑, 0.5↓) and Co_up: [Ar]3d⁷(5↑, 2↓)4s²(1↑, 1↓).

3. Results and discussion

Two important polyanion cathode materials that suffer from low rate capability compared other commercial oxide cathodes are indeed LiFePO₄ and Li₂FeSiO₄. To evaluate their electronic conductivity, the density of states (DOS) diagrams calculated by the GGA + U method for the lithiated and delithiated structures of Li₂FeSiO₄ and LiFePO₄ are reported in Fig. 1. Each DOS diagram contains two main parts, one of which is mainly formed from the 3d orbitals of Fe atoms, whereas the other part is due to the remaining orbitals and atoms. Because of the proximity of the Fermi level to the states belonging to the 3d-Fe orbitals (Fig. 1), these indeed play the most relevant role in determining the electron conductivity of the investigated materials. Regarding the lithiated structures (Fig. 1a and d), the 3d-Fe filled orbitals are located at the highest energies below the Fermi level. One band, located exactly below the Fermi level, is formed in the spin down state (the major spin is up), and it is separated from the other parts of the valence band. The remaining empty orbitals of 3d-Fe are located above the Fermi level (spin down). For more details about the orbital contributions to the DOS, see the ESI.† In order to participate in the conduction process, firstly electrons from the spin down 3d band located below the Fermi level must move to the conduction band. The holes created in this band by the electron movement cannot contribute to the conduction because they are separated from the other part of the valence band. Therefore, in lithiated states, electrons will contribute more than holes to the conduction (Fig. 1a and d). In other words, the 3d-Fe orbitals act as donors, and the lithiated structure acts as an n-type semiconductor. On the other hand, in case of the delithiated structures (Fig. 1g and h) the spin down states of the 3d-Fe orbitals (5 orbitals) form empty bands above the Fermi level, and the states with the highest energy below the Fermi level are due to other atoms (mainly oxygen) rather than Fe. The other filled 3d-Fe orbitals (spin up) are located at low energies in Fig. 1g and h. Therefore, from the point of view of conduction, holes are created by the movement of electrons from the valence band to the empty 3d-Fe orbitals. In other words, delithiated structures will behave like p-type semiconductors. Thus, in the delithiated structures, holes play a more important role than electrons in conduction.

Fig. 1 Density of states (DOS) calculated by the GGA + U (= 5 eV) method for the initial lithiated and delithiated structures of Li₂FeSiO₄ and LiFePO₄ cathode materials.

To investigate the lithiation–delithiation process, we assume that all the charge carriers (Li⁺ ions, electrons and holes) could only move parallel to the electric field direction. Hence, the classic shrinking core model would not apply and, inside particles and far from the surface, one-dimensional progress of the lithiated–delithiated boundary should take place. Fig. 2 shows a scheme of the delithiation and lithiation processes. In this figure, the battery anode is located on the right. In the lithiation (delithiation) processes, the current/electric field direction inside the battery is from anode (cathode) to cathode (anode). As described, the majority of charge carriers in the lithiated structure are electrons (n-type) and in the delithiated one are holes (p-type). Given the p–n junction of a semiconductor material, if the arrangement of p and n parts with respect to the electric field will cause electrons and holes to move toward the junction (→|←), conduction will be favoured resulting in high current rates; in contrast, if the electric field direction keeps electrons and holes away from the junction (←|→), the conduction process will translate into low current rates. According to Fig. 2, the electronic field direction in both lithiation and delithiation processes leads to the majority of charge carriers moving away from the lithiated–delithiated junction. In other words, the lithiated–delithiated junction in this class of cathode materials acts as an inversely biased diode in both the lithiation and delithiation processes. On this basis, the rate capability of these materials will be low due to the low current rate across the material. In contrast, we will show that this phenomenon does not occur in high rate capability cathode materials such as LiCoO₂ and LiMn₂O₄ (see below).

Fig. 2 Schematic illustration of junction behavior during: (a) lithiation and (b) delithiation processes, if the delithiated (lithiated) structure behaves as a p (n)-type semiconductor. Charge carrier displacement inside the cathode material under an electric field is considered.

GGA + U calculations also show two significant differences between Li₂FeSiO₄ and LiFePO₄ in the lithiated state (Fig. 1): (i) the energy gap between spin down 3d and the other states located below the Fermi level for LiFePO₄ (Fig. 1f) is less than that of Li₂FeSiO₄ (Fig. 1c); (ii) in the case of Li₂FeSiO₄, the 3d band above the Fermi level is positioned completely within the conduction band created by the other atoms (Fig. 1b), whereas the first state above the Fermi level for LiFePO₄ is formed by just the 3d-Fe orbitals (Fig. 1e). The second point is likely to be more important because it means that the 3d orbitals form an acceptor band, and the contribution of holes to the conduction process would be increased in comparison with Li₂FeSiO₄. Therefore, we can conclude that the GGA + U method predicts a better rate capability for LiFePO₄ than Li₂FeSiO₄. It is noteworthy that this discussion is relevant if the anisotropic shrinking core model³⁶ can be assumed for LiFePO₄. However, it was established that the classic shrinking core model³⁷ does not describe the experimental observations.³⁸ In contrast, by assuming the domino-cascade model for LiFePO₄,³⁹ electrons would not move across the material, so this discussion could not be applied. However, there is still some controversy about the possible application of the domino-cascade model to this material.⁴⁰

The above discussion is based on the results obtained from GGA + U calculations. However, in order to make our conclusions more robust, we also used other DFT methods. DOS diagrams of Li₂FeSiO₄ and LiFePO₄ obtained from the PBE-Fock-α method of Exact-exchange and Hybrid Functionals, GGA + U modified Becke–Johnson potential, LSDA and LDA + U methods are reported in the ESI.† However, they lead to the same conclusion as the GGA and GGA + U methods. Using the GGA method without the U potential would complete our considerations of the cathode materials. At the same time, it is well known that the GGA + U method is more useful for the prediction of band-gap values. Regarding the Fermi level position in the DOS diagrams (or band structures), the GGA method is indeed more useful for the recognition of n- and p-type materials. In Fig. 3, states belonging to 3d-Fe orbitals below and above the Fermi level are evidenced by red and green, respectively. The remaining parts formed by all the other orbitals are indicated in grey. It is assumed that Fe-ions act as dopants in a semiconductor matrix. Therefore, the real band gaps may be considered as the distances between the grey parts of each diagram. On this basis, the real band gaps for Li₂FeSiO₄ and LiFePO₄ are about 5.5 eV and 6.1 eV, respectively. Based on this assumption, the Fermi levels in the lithiated structures (Li₂FeSiO₄ and LiFePO₄) are located closer to the conduction band than the valence band. Thus, the lithiated structures could be considered as n-type semiconductors. On the other hand, in delithiated structures the Fermi levels are located nearer to the valence bands, identifying them as p-type semiconductors. Accordingly, for a delithiated–lithiated junction at equilibrium, the GGA method predicts a bias voltage of 1.8 V and 2.5 V for Li₂FeSiO₄ and LiFePO₄, respectively.

Fig. 3 DOS calculated by the PBE-GGA method for initially lithiated and delithiated structures of Li₂FeSiO₄ and LiFePO₄ cathode materials.

The DOS diagrams for two other well-known cathode materials, LiCoO₂ and LiMn₂O₄, in the lithiated and delithiated states are illustrated in Fig. 4. For a better comparison with Li₂FeSiO₄ and LiFePO₄ materials, LiFeO₂ (obtained by replacing Co with Fe in LiCoO₂ and the relaxing the structure) is also given. LiFeO₂ was previously proposed as a cathode material. However, it suffers from several problems, including a complex synthetic process,² low potential range,⁴¹ low stability⁴² and the presence of many polymorphs.⁴³ Based on the previous discussion, and according to Fig. 4(a), (c), (d) and (f), we can conclude that the related materials would act as p-type semiconductors, because conduction would take place by the movement of holes (created by the movement of electrons to the acceptor band of 3d orbitals) in the valence band. From Fig. 4(b) and (e), GGA + U calculations predict the occurrence of conductivity assisted by both electrons and holes. Therefore, in LiCoO₂, LiMn₂O₄ and also LiFeO₂ materials, holes are able to move through all lithiated and delithiated structures, and so through lithiated–delithiated interfaces. Also, the DOS diagrams obtained by the GGA method for these materials (Fig. 5) show that the Fermi level is closer to the valence band than to the conduction band (p-type character) for both lithiated and delithiated structures. Therefore, holes are responsible for the conductivity in these materials, and their lithiated–delithiated junction would not behave as an inversely-biased diode. Consequently, their rate capabilities should be adequate, at least from the electronic conductivity point of view.

Fig. 4 DOS calculated by the GGA + U method for initially lithiated and delithiated structures of LiCoO₂, LiFeO₂, LiMn₂O₄, LiFeBO₃ and LiFeSO₄F cathode materials.

Fig. 5 DOS calculated by the GGA method for initially lithiated and delithiated structures of LiFeO₂, LiMn₂O₄, LiFeBO₃ and LiFeSO₄F cathode materials. The LiCoO₂ diagrams are similar to the LiFeO₂ ones, and are given in the ESI.†

Other cathode materials which were recently proposed for lithium batteries are LiFeBO₃ and LiFeSO₄F. Considering the configurations of Fig. 4(g)–(j), and the Fermi level positions in Fig. 5(e)–(h), low rate capability is expected for both these materials, in comparison with the high performing oxides previously examined. However, due to the existence of an acceptor band of 3d-Fe in the lithiated state (Fig. 4(i)), the rate capability of LiFeSO₄F should be better than that of LiFeBO₃ (Fig. 4(g)) and Li₂FeSiO₄ (Fig. 1b), whereas it should be worse than LiFePO₄, according to the parts below the Fermi level in Fig. 4(i) and 1(f). It is noteworthy that this ordering is made according to the electronic conductivity in the material, although ionic conductivity should also be considered.

Actual rate capability is indeed one of the most important properties for a cathode material, especially if intended for high power density applications such as automotive applications. However, it is very difficult to extract reliable data from the literature to compare different cathode materials from a rate capability point of view. This quantity, in fact, could be affected by synthesis methods, primary particles and aggregate size, carbon amount, test temperature, etc. Moreover, different investigators report their results at different current rates. Therefore, a reliable comparison is very difficult. It could be assumed that the highest rate reported by an investigator is the highest possible/acceptable rate for his/her own material. Nevertheless, comparison between the experimental data of different cathodes remains very difficult, because each synthesis method is optimized for a given material, and comparison between cathodes synthesized by different methods is not unswerving.

Considering the rate capability of LiFePO₄ is likely to be the most difficult task, because it is the most intensively investigated polyanion cathode material⁵ and many experimental methods/recipes have resulted in different data.^4,5 As an example, using 1.5 wt% of graphene nanosheets in LiFePO₄ delivered 94% (160 mA h g⁻¹) of the theoretical capacity (C_th) at C/5 rate, and the capacity value was kept at 65% even at the high rate of 10 C.⁵ For Li₂FeSiO₄, charge–discharge measurements at C/16 (ref. 9, 10, 31, 44 and 45) and C/20 (ref. 8, 46 and 47) were considered in many investigations. However, good performances at rates as high as 1 C have rarely been reported.^48,49 The first report on LiFeBO₃ considered measurements at C/250, at which only 4% of its C_th was delivered (C_th is 220 mA h g⁻¹).⁵⁰ In a subsequent work, 72% of C_th at C/44 and 56% of C_th at C/4.4 were obtained.⁵¹ However, achievements of the theoretical capacity (C_th) at C/20 and more than 75% of C_th at 2 C rate were also reported.⁵² In the case of LiFeSO₄F, a rate of C/20 was considered in many investigations,^{16–18,53–56} and resulted in the delivery of 56–81% of C_th. Also, the achievement of ∼85% of C_th at a C/10 rate was reported in two investigations,^22,23 and ∼72% of C_th at 1 C rate in one investigation.²²

According to our picture, we propose four strategies to improve the rate capability of cathode materials which suffer from low rate capability. (1) Coating the material with carbon would be partially helpful, because a layer of conductive carbon would connect lithiated and delithiated regions. However, experimental works showed that this strategy only partially solves the problem. (2) Doping would be helpful due to changes of DOS configuration. For example, replacing transition metals with each other could change DOS configurations.⁶ (3) Coating cathode particles with another material that acts as an n- or p-type semiconductor. (4) Coating the cathode particles with a layer of solid material containing lithium ions.

Regarding the third strategy, by using an n-type semiconductor coating on the surface of the cathode particles, the electrons of the coating layer would increase the diffusion (leakage) of electrons through the cathode material and modify its electronic conductivity. Also, coating the cathode with a p-type semiconductor would lead to a similar mechanism by the leakage of holes. The superior rate capability (85.4% of C_th at a rate of 2 C and ∼59% of C_th at 30 C)⁵⁷ of LiFePO₄ in presence of Fe₂P could be explained by this mechanism.

Coating cathode materials with a Li-rich material, surprisingly, would improve electronic conductivity by increasing the leakage of electrons through the delithiated structure. The interface between the delithiated material and the Li-rich coating would act as a lithiated structure (n-type character). Notably, this does not mean the probable progression of the Li ions in the delithiated structure (Li concentration gradient), but the existence of Li ions at the interface would lead to it becoming a lithiated structure itself. Forming an n-type layer at the interface would lead to the mechanism explained above. For a schematic illustration of the mechanism, see the ESI.† Experimental data showed a remarkable increase in rate capability by coating amorphous lithium phosphate on LiFePO₄ particles: a capacity as high as 76% of C_th at 50 C was achieved.⁵⁸ Also, a similar scenario for Li₂FeSiO₄ (using nanocrystalline Li₂FeSiO₄ surrounded by amorphous Li₂SiO₃ and C) resulted in remarkable modification of its performance, and up to 90% of C_th was delivered at a 3 C rate.⁵⁹ Interestingly, a simple coating process should not change Li ion migration inside the bulk material; however, this phenomenon has been attributed to the modification of Li migration at the boundary of coated particles and the coating layer.⁵⁸ Nevertheless, it has to be yet explained how a solid–solid interface could allow better Li migration than a solid–liquid one. This study suggests a mechanism through which a Li-rich layer could modify the electronic conductivity inside the cathode material. Therefore, in this scenario, coating cathode particles by a Li-rich layer will cause enhancement of current rate capability by the modification of the electronic, not ionic, conductivity.

4. Conclusions

This study proposed a simple but powerful qualitative approach to recognize high/low rate capable cathode materials from the point of view of electronic conductivity. The suggested mechanism was based on the electronic conduction at the junction of the lithiated–delithiated structures of the cathode. We established that if the delithiated structure acted as an n-type and the lithiated structure acted as a p-type semiconductor, the lithiated–delithiated junction would behave as an inversely-biased diode in both delithiation and lithiation processes. A number of DFT methods were employed to evaluate the character of cathode materials in lithiated–delithiated states. The GGA + U was more helpful for a qualitative comparison between cathode materials, however, GGA method could be more useful for the recognition of p-/n-type semiconductors due to the relative location of the Fermi level in the band gaps. This approach predicted excellent rate capabilities for LiCoO₂, LiFeO₂ and LiMn₂O₄. In the case of Li₂FeSiO₄, LiFePO₄, LiFeBO₃ and LiFeSO₄F, our analysis showed that they are low rate cathode materials. However, qualitatively, according to DOS configurations calculated by the GGA + U method, the rate capabilities of LiFePO₄ and LiFeSO₄F are better than those of Li₂FeSiO₄ and LiFeBO₃.

Acknowledgements

The authors are grateful for access to WIEN2k code. One of the authors (S. Asgari) acknowledges partial support provided by INSF.

Notes and references

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Footnote

† Electronic supplementary information (ESI) available: Comparison details between the rate capability of LiFePO₄ and LiFeSO₄F (Table 1S); 3d-Fe orbital contributions of Fig. 1 (Fig. 1S); DOS calculated by the PBE-Fock-α method for Li₂FeSiO₄, LiFePO₄ (Fig. 2S), LiCoO₂, LiMn₂O₄, LiFeBO₃ and LiFeSO₄F (Fig. 7S); DOS of Li₂FeSiO₄ and LiFePO₄ calculated by mBJ (Fig. 3S), LDA + U (Fig. 4S) and LSDA (Fig. 5S) methods; DOS of LiCoO₂ calculated by GGA (Fig. 6S); schematic illustration of 3rd (Fig. 8S) and 4th (Fig. 9S) proposed modification methods. See DOI: 10.1039/c3ta13387g

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