Li2SnO3 as a Cathode Material for Lithium-ion Batteries: Defects, Lithium Ion Diffusion and Dopants

Tin-based oxide Li2SnO3 has attracted considerable interest as a promising cathode material for potential use in rechargeable lithium batteries due to its high- capacity. Static atomistic scale simulations are employed to provide insights into the defect chemistry, doping behaviour and lithium diffusion paths in Li2SnO3. The most favourable intrinsic defect type is Li Frenkel (0.75 eV/defect). The formation of anti-site defect, in which Li and Sn ions exchange their positions is 0.78 eV/defect, very close to the Li Frenkel. The present calculations confirm the cation intermixing found experimentally in Li2SnO3. Long range lithium diffusion paths via vacancy mechanisms were examined and it is confirmed that the lowest activation energy migration path is along the c-axis plane with the overall activation energy of 0.61 eV. Subvalent doping by Al on the Sn site is energetically favourable and is proposed to be an efficient way to increase the Li content in Li2SnO3. The electronic structure calculations show that the introduction of Al will not introduce levels in the band gap.

Lithium ion batteries with high-power densities for electrical vehicles and consumer electronics require high-performance cathode materials providing high concentration of Li + ions in the intercalation/ de-intercalation process, low cost, less hazard and their constituent elements being high abundance [1][2][3][4][5] . The search for such cathode materials generated considerable research activity and resulted promising new cathode materials such as Li 2 MSiO 4 (M = Fe, Mn and Co) [5][6][7][8][9][10][11][12][13] , Li 2 FePO 4 F 14 , and Li 2 FeP 2 O 7 15 . Several "Li-rich" materials such as Li 7 Mn(BO 3 ) 3 16 , Li 5 FeO 4 17,18 , Li 3 V(MoO 4 ) 3 19 and Li 4 Ti 5 O 12 20 have been reported as promising cathode materials producing high theoretical capacity. A key feature of "Li-rich" materials is that, in principle, extraction of more than one lithium per formula unit is possible. Thus, this can produce a higher capacity than the conventional cathode materials such as LiCoO 2 21 and LiFePO 4 22 . "Li-rich" Li 2 MnO 3 was recently suggested as a possible alternative cathode material due to its high capacity over 200 m Ahg -1 and high energy density [23][24][25] . However, this material showed poor structural stability during cycling and electronic conductivity. It was suggested that replacement of Mn by Sn could be a possible strategy to improve structural stability and thus cyclic performance of Li 2 MnO 3 26 . As both Li 2 MnO 3 and Li 2 SnO 3 crystalize in a monoclinic layered structure, these studies motivated to consider Li 2 SnO 3 as a viable cathode material for lithium ion batteries. Recently, Wang et al. 27 have used high-energy X-ray diffraction to determine the structure of Li 2 SnO 3 and determined that a singnificant amount of intra-layer Li-Sn intermixing is present in the as-prepared material. In another experimental study, Wang et al. 28 have used a hydrothermal route to prepare Li 2 SnO 3 and observed an electrochemical performance with high capacity and good cycling stability. Howard and Holzworth 29 have recently studied the Li-ion diffusion mechanism and the lithiation process computationally in both Li 2 SnO 3 and Li 2 SnS 3 . There are no further theoretical studies availble in the literature detailing the defect processes in this material. A greater insight into the defect properties of electrode materials is crucial to the full understanding of their electrochemical behaviour. Theoretical modelling can bridge this gap by providing detailed information of the key issues related to defect processes including cation mixing observed in experiment and doping strategies to increase the Li concentration in this material.
The present study extends our recent static atomistic simulation studies of the Li 5 FeO 4 30 and Li 2 CuO 2 31 battery materials where we examined the defect chemistry, lithium transport and dopants. We have carried out a detailed

Results and Discussion
Li 2 SnO 3 structure. Crystal structure of Li 2 SnO 3 exhibits a monoclinic crystallographic structure with space group C2/c (lattice parameters a = 5.290 Å, b = 9.190 Å, c = 10.030 Å, α = 90°, β = 100.1° and γ = 90°) as reported by Lang 32 . Figure 1 shows this structure and the chemical environments of Sn and Li (both forming octahedrons with six O atoms). This material has layers in the ab plane with an A-B stacking sequence. The starting point for the present study was to reproduce the experimentally observed monoclinic crystal structure to enable an assessment of the quality and efficacy of the classical pair potentials (refer to Table S1 in the Supplementary Information for the potentials parameters used and method section for the detailed description of the methodology) used in this study. The calculated equilibrium lattice constants (tabulated in Table 1) are in excellent agreement with experiment.

Intrinsic defect processes.
To gain insights of the electrochemical behavior of an electrode material, we have calculated a series of isolated point defect (vacancy, antisite and interstitial) energies using classical pair potential method and combined them to calculate the formation energies for Frenkel, Schottky and antisite defects in Li 2 SnO 3 . The following equations represent the reactions involving these defects as written using Kröger-Vink notation 27 .    Figure 2 reports the reaction energies for these intrinsic defect processes. The most favorable intrinsic disorder is Li Frenkel and the formation of other Frenkel and Schottky defects is less favourable. The second most favorable defect process is calculated to be the anti-site indicating that there will be a small percentage of Li on Sn sites ( ′′′ Li Sn ) and Sn on Li sites ( ••• Sn ) Li particularly at higher temperatures. This is in agreement with the intralayer intermixing between Li and Sn found in the experiment 27 . Antisite defects have been observed in a variety of other Li ion battery materials during cycling 8,[33][34][35][36][37] . The formation enthalpy of Li 2 O via the Li 2 O Schottky-like reaction (relation 5) is a processes that requires an energy of 1.90 eV per defect (refer to Table S2). This is a process that can lead to further ′ V Li and •• V O but at elevated temperatures.
Lithium ion-diffusion. Promising high-rate cathode materials in lithium ion batteries require lithium ion diffusion with lower activation energy. Using classical pair potential method it is possible to examine various possible diffusion paths responsible for lithium ion diffusion and they provide experiment with complementary information. For the Li vacancy migration, we have calculated eight different local Li hops (refer to Fig. 3). Migration energies are reported in Table 2 together with the Li-Li separation, whereas energy profile diagrams are shown in Fig. 4. We have constructed long range paths connecting local Li hops with lower overall activation energy. We have identified two long range paths along the ab plane (refer to Fig. 3). The first long range path exhibits a zig-zag pattern (A → B → C → B → ttincluding a local Li hop with lower activation energy of migration of 0.16 eV (local hop C) but with overall activation energy of 0.65 eV (refer to Table 2). The second path exhibits a straight line (X → Y) with an activation energy of 0.63 eV. There are different possible long range Li diffusion paths can be constructed along the c-axis. Our examination reveals that the lower activation energy long range path along the c-axis plane is L → L → L (refer to Fig. 3) with overall activation energy of 0.61 eV. Other long range paths will have activation energies greater than 0.61 eV in this direction as their local Li hops show higher energies. The activation energy of Li-vacancy migration calculated along the c axis is reported to be 0.30 eV by Howard and Holzwarth 29 , which differs from our calculated value of 0.61 eV. The difference in activation energy can be due to difference in the c-lattice parameter calculated in their calculation (9.78 Å) and our calculation (10.059 Å). The experimental c-lattice parameter is reported to be 10.03 Å 32 . Here the activation energy of migration is defined as the position of the highest potential energy along the migration path.
Trivalent doping. Incorporation of extra lithium into the as-prepared material will enhance the capacity and further increase the applicability of Li 2 SnO 3 as a cathode material for rechargeable lithium batteries. A possible approach to increase the amount of lithium is by doping trivalent cations on Sn site through creating Li interstitials. Similar approach has been previously demonstrated in Li 2 MnSiO 4 cathode material 12 . Here we considered the solution of R O 2 3 (R = Al, Sc, In, Y, Gd and La) via the following process (in Kröger-Vink notation): 2 3 Sn X 2 S n i 2 Figure 5 reports the solution energies of R O 2 3 calculated using classical pair potential method and it can be observed that the most favorable dopant solution energy (0.60 eV) is for Al 3+ . This suggests a possible synthesis-doping strategy to introduce additional lithium into Li 2 SnO 3 , although the exact amount of Al  Figure 6 depicts the local coordination (including bond lengths and angles) with oxygen of the dopants occupying the Sn site and for comparison the octahedral SnO 6 unit in the relaxed structure of undoped Li 2 SnO 3 . The ionic radius of Sn 4+ in octahedral coordination is 0.69 Å. The ionic radius of Al 3+ is 0.16 Å smaller than that of Sn 4+ . In the AlO 6 unit, all six Al-O bonds are shorter compared to the Sn-O bonds present in the undoped Li 2 SnO 3 and the other R-O bonds. This is due to its smaller cation size of Al 3+ which strongly polarises the oxygen ions forming strong ionic bonds with O atoms. The second lowest solution energy is found for Sc 3+ . Its ionic radius is 0.05 Å and 0.20 Å longer than the Sn 4+ and Al 3+ respectively. Bigger size of the Sc 3+ compared to Al 3+ shows a higher solution energy. From In to La, dopant-oxygen bond distances increase and bond angles decrease gradually indicating the structural distortion and reflecting in the solution energies. In the relaxed structure of LaO 6 unit, La-O bond lengths are approximately the same but ~0.30 Å longer than Sn-O bond lengths present in SnO 6 unit. Furthermore, the ionic radius of La 3+ is 0.35 Å greater than Sn 4+ . Thus the solution energy is high. However, the current solution energy values are large and positive indicating that they are unfavorable.     The Li + p-states and Sn 4+ d-states are also contributing in the valence bands but with lower intensities as compared to O 2− . In the edge of the conduction band, the main contributions in the total DOS are attributed to the Li states and specifically to the Li + -s orbitals. The O 2− p-states in the conduction band correspond to a similar profile as the Li + p-states whereas the Sn 4+ orbitals are presented not to have a primary role in the total electronic structure of the material (refer also to Figure S1 in the Supplementary Information). In addition, the effect on the total DOS with the introduction of a lithium interstitial in the supercell is minimal. Specifically, no additional states are formed into the band gap, whereas the contribution of every element is not affected as shown in Fig. 7(b). The doping effect of trivalent dopants have been also considered and the impact of the • Al Sn and

Al Li { :
Sn i } X pairs on the densities of states on Li 2 SnO 3 is presented in Fig. 7(c,d). Overall, the introduction of Al 3+ does not impact significantly the electronic structure as the Al -states contribution in the DOS is weak. Sn i } X pairs that correspond to the dopants of a large ionic radius, the DOS includes in-gap states ( Fig. S2  (g,h)) and a minor additional contribution next to the valence band ( Fig. S2 (i,j)).

Summary.
In the present study, we have used atomistic simulation techniques to provide detailed insights into intrinsic defects, lithium ion mobility and trivalent doping, which are relevant to the general electrochemical behaviour of layered Li 2 SnO 3 as a lithium battery cathode material. The Li Frenkel is the lowest energy and thus the dominant defect energy process. Anti-site disorder is only 0.03 eV higher than the Li Frenkel suggesting that there will be some Sn on the Li site and vice-versa and our calculation confirms this defect that has been experimentally observed. Considering the vacancy mechanism of diffusion the lowest activation energy migration path is along the c-axis plane with an activation energy of 0.61 eV. We have considered the solution energies of R O   Methods. In order to calculate the energetics for the formation of intrinsic defects and possible Li ion diffusion pathways, the classical pair potential method as implemented in the GULP package 38 was employed. This method is based on the classical Born model description of an ionic crystal lattice. All systems were treated as crystalline solids with interactions between ions consisting of the long-range attractions and short-range repulsive forces representing electron-electron repulsion and van der Waals interactions. The short range interactions were modelled using Buckingham potentials (refer to Table S1). Simulation boxes and the corresponding atom positions were relaxed using the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm 39 . The Mott-Littleton method 40 was used to investigate the lattice relaxation about point defects and the migrating ions. It divides the crystal lattice into two concentric spherical regions, where the ions within the inner spherical region (on the order of >700 ions) immediately surrounding the defect relaxed explicitly. Li ion diffusion was calculated considering two adjacent vacancy sites as initial and final configurations. Seven interstitial Li ions were considered in a direct linear route and they were fixed while all other ions were free to relax. The local maximum energy along this diffusion path is calculated and reported as activation energy of migration. As the present model assumes a full charge ionic model with the calculations corresponding to the dilute limit the defect enthalpies will be overestimated, however, relative energies and trends will be consistent.
The Li 2 SnO 3 supercells were modelled though the plane wave density functional theory code CASTEP 41,42 . The plane wave basis set was set to a cut-off of 480 eV and a 2 × 2 × 2 Monkhorst-Pack (MP) 43 k-point grid was used with a 98-atomic site supercell. For the exchange and correlation interactions in the crystal, we use the formulation with the corrected density functional of Perdew, Burke and Ernzerhof (PBE) 44 , within the generalized gradient approximation (GGA) with ultrasoft pseudopotentials 45 . All the calculations were under constant pressure conditions and the cells were relaxed in the minimum energy configuration before the investigation of the electronic structure. The Partial Density of States (PDOS) for the perfect and defective/doped structures is visualized through the OPTADOS tool 46,47 .