Defect Process, Dopant Behaviour and Li Ion Mobility in the Li2MnO3 Cathode Material

Lithium manganite, Li2MnO3, is an attractive cathode material for rechargeable lithium ion batteries due to its large capacity, low cost and low toxicity. We employed well-established atomistic simulation techniques to examine defect processes, favourable dopants on the Mn site and lithium ion diffusion pathways in Li2MnO3. The Li Frenkel, which is necessary for the formation of Li vacancies in vacancy-assisted Li ion diffusion, is calculated to be the most favourable intrinsic defect (1.21 eV/defect). The cation intermixing is calculated to be the second most favourable defect process. High lithium ionic conductivity with a low activation energy of 0.44 eV indicates that a Li ion can be extracted easily in this material. To increase the capacity, trivalent dopants (Al3+, Co3+, Ga3+, Sc3+, In3+, Y3+, Gd3+ and La3+) were considered to create extra Li in Li2MnO3. The present calculations show that Al3+ is an ideal dopant for this strategy and that this is in agreement with the experiential study of Al-doped Li2MnO3. The favourable isovalent dopants are found to be the Si4+ and the Ge4+ on the Mn site.


Introduction
The next generation of high capacity energy storage systems require lithium ion cathode material exhibiting high energy density, low cost and non-toxicity. A variety of cathode materials have been examined in the past decade to improve the performance of the rechargeable Li ion batteries [1][2][3][4][5][6][7][8][9][10][11]. As very few of them exhibit promising results, there is a necessity to make breakthroughs in finding new materials.
"Layered" Li 2 MnO 3 was recently investigated as a potential cathode material for Li ion batteries due to its high theoretical capacity of 285 mAhg −1 and first charge plateau of~4.5 eV [12,13]. Furthermore, manganese is relatively safe, abundant and low-cost, making Li 2 MnO 3 a very promising cathode material. However, the material suffered from poor structural stability during cycling and electrical conductivity [14,15]. Li 2 MnO 3 was initially identified as an inactive material because the electrochemical activity of the material via the oxidation of Mn 4+ to Mn 5+ did not occur [16,17]. The electrochemical activity was reinvestigated later and it was determined that the extraction and reinsertion of Li is possible. Chen et al. [18] showed that theoretically Li extraction can be charge compensated by the formation of O 2 from O 2− ions in the lattice. Cho et al. [19] demonstrated that oxygen loss is energetically favourable during delithiation. Electrochemical performance was recently examined by doping Al on the Mn site, and it was shown that Al-doped Li 2 MnO 3 exhibits an enhancement on the rate capability and cycling stability [20].
To optimize the performance of Li ion batteries, a more detailed fundamental understanding of existing materials is necessary. Computational modelling techniques have significantly contributed to the characterization of experimental structures, prediction of pathways of migrating ions and identification of promising dopants in a variety of oxide materials [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. In the present study, we examine the intrinsic defects process, Li ion diffusion paths and the effect of dopants on the Mn site in Li 2 MnO 3 .

Computational Methods
Static atomistic calculations were performed on the crystal structure of Li 2 MnO 3 and its defect structures using the General Utility Lattice Program (GULP) code [37]. This method is based on the classical Born model of ionic crystals. Interactions between ions include the long-range (i.e., Coulombic) ionic interactions and the short-range (i.e., electron-electron repulsion and van der Waals interactions) ionic interactions, with both being considered. Short-range repulsive forces were modelled using the Buckingham potentials (refer to Supplementary Information). The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm [38] was applied to relax atom positions and lattice constants. In all optimized structures, forces on the atoms were smaller than 0.001 eV/Å. The point defects and migrating atoms were modelled using the Mott-Littleton method [39]. In this method, two spherical regions are defined, with the inner spherical region containing a number of ions greater than 700. In this region, ions are relaxed explicitly. Defect enthalpies in this simulation are expected to be overestimated as the ions are treated as spherical shapes with full charge at dilute limit. However, relative energies and trends remain consistent.
From a thermodynamic viewpoint, the defect parameters (for example, migration and formation energies) can be defined via the comparison of the real (defective) crystal to an isobaric or isochoric ideal (non-defective) crystal. These sets of defect formation parameters can be interconnected through thermodynamic relations as discussed in previous studies [40,41]. Here, the atomic scale calculations correspond to the isobaric parameters for the migration and formation processes [42,43]. Figure 1 shows the experimentally observed crystal structure of Li 2 MnO 3 . This structure belongs to the monoclinic structure of the C2/m space group (lattice parameters a = 4.937 Å, b = 8.532 Å, c = 5.030 Å, α = 90.0 • , β = 109.46 • and γ = 90.0 • ) as reported by Strobel et al. [44] in their single crystal X-ray diffraction. The crystal structure of Li 2 MnO 3 was subsequently reinvestigated by Boulineau et al. [45] and their reported structure was closer to the previous structure, with a small amount of cation mixing. Here, we used the crystal structure reported by Strobel et al. [44], as this model consisted of full occupancy atom positions. Both Li and Mn form edge-sharing distorted octahedral units with adjacent O atoms, as shown in the Figure 1.

Bulk Li 2 MnO 3 Structure
Both atom positions and lattice constants were allowed to relax under constant pressure to obtain the equilibrium lattice structure. The calculated lattice constants were in excellent agreement with the experimental values, as reported in Table 1.

Intrinsic Defect Processes
Next, defect formation energies for the isolated vacancy, interstitial and anti-site defect were calculated, and were combined to calculate the Frenkel, Schottky and anti-site intrinsic defect reaction energies (Equations (1)-(8)). Intrinsic defect processes are useful to study the electrochemical behaviour of Li2MnO3. The following reactions, which were written by using Kröger-Vink notation [46], represent the Frenkel, Schottky and anti-site intrinsic defect processes: We report the reaction energies for these intrinsic defect processes in Figure 2. The Li Frenkel was calculated to be the most thermodynamically favourable intrinsic defect process. This process increases the concentration of Li vacancies that can enhance vacancy-assisted Li ion diffusion in Li2MnO3. Other Frenkel defect processes exhibit highly endoergic energies, suggesting that they are unlikely to occur at operating temperatures. The second most favourable defect process is the Li-Mn anti-site. In this defect, a small percentage of Li on Mn sites (Li ) and Mn on Li sites (Mn ⦁⦁⦁ ) would be observed at high temperatures. Anti-site defect has been observed in experimental and theoretical studies during the synthesis of as-prepared material and cycling [47][48][49][50][51][52]. The Li2O Schottky reaction (Equation (5)), leading to the formation of further and •• , is 5.16 eV per defect, indicating that this reaction can only take place at high temperatures.

Intrinsic Defect Processes
Next, defect formation energies for the isolated vacancy, interstitial and anti-site defect were calculated, and were combined to calculate the Frenkel, Schottky and anti-site intrinsic defect reaction energies (Equations (1)- (8)). Intrinsic defect processes are useful to study the electrochemical behaviour of Li 2 MnO 3 . The following reactions, which were written by using Kröger-Vink notation [46], represent the Frenkel, Schottky and anti-site intrinsic defect processes: Li/Mn antisite (cluster) : We report the reaction energies for these intrinsic defect processes in Figure 2. The Li Frenkel was calculated to be the most thermodynamically favourable intrinsic defect process. This process increases the concentration of Li vacancies that can enhance vacancy-assisted Li ion diffusion in Li 2 MnO 3 . Other Frenkel defect processes exhibit highly endoergic energies, suggesting that they are unlikely to occur at operating temperatures. The second most favourable defect process is the Li-Mn anti-site. In this defect, a small percentage of Li on Mn sites (Li Mn ) and Mn on Li sites (Mn ••• Li ) would be observed at high temperatures. Anti-site defect has been observed in experimental and theoretical studies during the synthesis of as-prepared material and cycling [47][48][49][50][51][52]. The Li 2 O Schottky reaction (Equation (5)), leading to the formation of further V Li and V •• O , is 5.16 eV per defect, indicating that this reaction can only take place at high temperatures.

Lithium Ion Diffusion
There is a necessity to understand the lithium ion diffusion paths together with activation energies to assess Li2MnO3 as a potential high-capacity cathode material for Li ion batteries. Determining Li ion diffusion paths is extremely challenging experimentally. Classical pair potentialbased simulation can provide valuable information about various possible Li ion diffusion paths and corresponding activation energies. Low activation energy is a key requirement for a promising highrate battery material. Possible Li vacancy-assisted diffusion paths were constructed. Six different local Li hops ( Figure 3) were identified for the Li vacancy migration. Table 2 reports the Li-Li separation, together with corresponding activation energies. Figure 4 shows the energy profile diagrams for activation energies of local Li hops.

Lithium Ion Diffusion
There is a necessity to understand the lithium ion diffusion paths together with activation energies to assess Li 2 MnO 3 as a potential high-capacity cathode material for Li ion batteries. Determining Li ion diffusion paths is extremely challenging experimentally. Classical pair potential-based simulation can provide valuable information about various possible Li ion diffusion paths and corresponding activation energies. Low activation energy is a key requirement for a promising high-rate battery material. Possible Li vacancy-assisted diffusion paths were constructed. Six different local Li hops ( Figure 3) were identified for the Li vacancy migration. Table 2 reports the Li-Li separation, together with corresponding activation energies. Figure 4 shows the energy profile diagrams for activation energies of local Li hops.
Five possible long-range paths consisting of local Li hops with lower overall activation energies were identified ( Table 3). The first long-range path (intra layer along the b axis) exhibited a slightly distorted linear pattern (A→E→E→A), with an overall activation energy of 0.59 eV. The second path connected local hops B and F, forming a curved trajectory (F→B→B→B) along the ab plane (intra layer), with an overall activation energy of 0.47 eV. The third long-range path (C→C→C→C) lay between layers (inter layer), with the Li local hops of C. The activation energy for this migration was calculated to be 0.44 eV. This was the lowest activation energy of the four intra layer Li migration paths. In the fourth long-range path (D→D→D→D), the Li ion migrated in the bc plane (intra layer), with an overall migration energy of 0.45 eV. Finally, the fifth long-range path (D→D→D→D) was located in the ab plane (intra layer) and the activation energy for this path was 0.47 eV. The current results show that the Li ion would diffuse fast in Li 2 MnO 3 via intra layers or inter layers. Determining Li ion diffusion paths is extremely challenging experimentally. Classical pair potentialbased simulation can provide valuable information about various possible Li ion diffusion paths and corresponding activation energies. Low activation energy is a key requirement for a promising highrate battery material. Possible Li vacancy-assisted diffusion paths were constructed. Six different local Li hops (Figure 3) were identified for the Li vacancy migration. Table 2 reports the Li-Li separation, together with corresponding activation energies. Figure 4 shows the energy profile diagrams for activation energies of local Li hops.  Table 2. Calculated Li-Li separations and activation energies using classical pair-potential method for the lithium ion migration between two adjacent Li sites (as shown in Figure 3).

Li-Li Separation (Å)
Activation Energy (eV) A 2.65 0.27  Table 2. Calculated Li-Li separations and activation energies using classical pair-potential method for the lithium ion migration between two adjacent Li sites (as shown in Figure 3). Five possible long-range paths consisting of local Li hops with lower overall activation energies were identified ( Table 3). The first long-range path (intra layer along the b axis) exhibited a slightly distorted linear pattern (A→E→E→A), with an overall activation energy of 0.59 eV. The second path connected local hops B and F, forming a curved trajectory (F→B→B→B) along the ab plane (intra layer), with an overall activation energy of 0.47 eV. The third long-range path (C→C→C→C) lay between layers (inter layer), with the Li local hops of C. The activation energy for this migration was calculated to be 0.44 eV. This was the lowest activation energy of the four intra layer Li migration paths. In the fourth long-range path (D→D→D→D), the Li ion migrated in the bc plane (intra layer), with an overall migration energy of 0.45 eV. Finally, the fifth long-range path (D→D→D→D) was located in the ab plane (intra layer) and the activation energy for this path was 0.47 eV. The current results show that the Li ion would diffuse fast in Li2MnO3 via intra layers or inter layers.

Long-Range Path Direction Overall Activation Energy (eV)
A→E→E→A

Trivalent Doping
The capacity of Li2MnO3 can be increased by incorporating additional Li in the form of interstitials into the as-prepared crystal structure. This would increase its applicability in rechargeable lithium batteries. Doping trivalent cations on the Mn site is an efficient engineering strategy to create Li interstitials in the lattice. In previous work, this strategy has been applied to Li and Na ion battery materials. In this work, we considered some trivalent dopants from different parts of the periodic table (early transition elements, post-transition elements and lanthanide elements).

Trivalent Doping
The capacity of Li 2 MnO 3 can be increased by incorporating additional Li in the form of interstitials into the as-prepared crystal structure. This would increase its applicability in rechargeable lithium batteries. Doping trivalent cations on the Mn site is an efficient engineering strategy to create Li interstitials in the lattice. In previous work, this strategy has been applied to Li and Na ion battery materials. In this work, we considered some trivalent dopants from different parts of the periodic table (early transition elements, post-transition elements and lanthanide elements). The selection of the prominent dopant Al 3+ is due to its small size and low cost. Furthermore, there is an experimental report on the doping of Al 3+ on the Mn site [20]. The solution of R 2 O 3 (R = Al, Co, Ga, Sc, In, Y, Gd and La) was considered via the following process (in Kröger-Vink notation): The selection of the prominent dopant Al 3+ is due to its small size and low cost. Furthermore, there is an experimental report on the doping of Al 3+ on the Mn site [20]. The solution of R2O3 (R = Al, Co, Ga, Sc, In, Y, Gd and La) was considered via the following process (in Kröger-Vink notation):  Xiang et al. [20] synthesised both Li2MnO3 and Al-doped Li2MnO3 and examined their rate capacities. Their study shows that there is a greater improvement in the Al-doped Li2MnO3 compared with that of pristine Li2MnO3. The second most favourable dopant is the Co 3+ and its solution enthalpy is calculated to be 0.52 eV, only 0.07 eV higher than that of Al 3+ . Solution enthalpy increases gradually with the ionic radius of M 3+ ions reflecting in the bond lengths and bond angles. The optimised bond lengths and bond angles of trivalent dopants occupying the Mn site and the octahedral MnO6 unit in the relaxed structure of undoped Li2MnO3 are shown in Figure 6. The highest solution enthalpy is calculated for La 3+ . This is due to the larger ionic radius difference between the La 3+ and the Mn 4+ . The current solution enthalpy values for Sc 3+ , In 3+ , Y 3+ , Gd 3+ and La 3+ are highly endoergic, suggesting that they are unfavourable at operating temperatures.
Density functional theory calculations performed by Hoang et al. [53] show that Al and Fe are energetically favourable dopants on the Mn site, which agrees with our calculations. Kong et al. [54] used ab initio simulations to examine the thermodynamical stability of a variety of aliovalent dopants, including trivalent dopants Al 3+ and Fe 3+ on the Mn site. In their study, charge introduced by cation doping was compensated by anion doping (F and N) on the O site. In our study, negative charge introduced by trivalent dopants on the Mn site was compensated by positively charged Li interstitials, creating a Li2MnO3 material with a high capacity. Xiang et al. [20] synthesised both Li 2 MnO 3 and Al-doped Li 2 MnO 3 and examined their rate capacities. Their study shows that there is a greater improvement in the Al-doped Li 2 MnO 3 compared with that of pristine Li 2 MnO 3 . The second most favourable dopant is the Co 3+ and its solution enthalpy is calculated to be 0.52 eV, only 0.07 eV higher than that of Al 3+ . Solution enthalpy increases gradually with the ionic radius of M 3+ ions reflecting in the bond lengths and bond angles. The optimised bond lengths and bond angles of trivalent dopants occupying the Mn site and the octahedral MnO 6 unit in the relaxed structure of undoped Li 2 MnO 3 are shown in Figure 6. The highest solution enthalpy is calculated for La 3+ . This is due to the larger ionic radius difference between the La 3+ and the Mn 4+ . The current solution enthalpy values for Sc 3+ , In 3+ , Y 3+ , Gd 3+ and La 3+ are highly endoergic, suggesting that they are unfavourable at operating temperatures.

Tetravalent Doping
Here, we consider some isovalent dopants (Si 4+ , Ge 4+ , Ti 4+ , Sn 4+ , Zr 4+ and Ce 4+ ) on the Mn site. The following reaction equation was used to calculate the solution enthalpy: Solution enthalpy increases with ionic radius. Exoergic solution enthalpy was calculated for Si 4+ and Ge 4+ (Figure 7). This was due to the smaller ionic radius of Si 4+ (0.40 Å) compared with Mn 4+ (0.53 Å). The higher charge density of Si 4+ forms stronger Si-O bonds, as reported in Figure 8. The ionic radii of Ge 4+ and Mn 4+ are the same. This is reflected in the exoergic solution enthalpy. The optimised structures of MO6 units together with bond lengths and bond angles are shown in Figure 8. Endoergic solution enthalpies are observed for the other dopants. Solution enthalpy for CeO2 is highly endoergic, meaning that doping Ce on the Mn site is highly unlikely to occur.  Density functional theory calculations performed by Hoang et al. [53] show that Al and Fe are energetically favourable dopants on the Mn site, which agrees with our calculations. Kong et al. [54] used ab initio simulations to examine the thermodynamical stability of a variety of aliovalent dopants, including trivalent dopants Al 3+ and Fe 3+ on the Mn site. In their study, charge introduced by cation doping was compensated by anion doping (F and N) on the O site. In our study, negative charge introduced by trivalent dopants on the Mn site was compensated by positively charged Li interstitials, creating a Li 2 MnO 3 material with a high capacity.

Tetravalent Doping
Here, we consider some isovalent dopants (Si 4+ , Ge 4+ , Ti 4+ , Sn 4+ , Zr 4+ and Ce 4+ ) on the Mn site. The following reaction equation was used to calculate the solution enthalpy: Solution enthalpy increases with ionic radius. Exoergic solution enthalpy was calculated for Si 4+ and Ge 4+ (Figure 7). This was due to the smaller ionic radius of Si 4+ (0.40 Å) compared with Mn 4+ (0.53 Å). The higher charge density of Si 4+ forms stronger Si-O bonds, as reported in Figure 8. The ionic radii of Ge 4+ and Mn 4+ are the same. This is reflected in the exoergic solution enthalpy. The optimised structures of MO 6 units together with bond lengths and bond angles are shown in Figure 8. Endoergic solution enthalpies are observed for the other dopants. Solution enthalpy for CeO 2 is highly endoergic, meaning that doping Ce on the Mn site is highly unlikely to occur. and Ge 4+ (Figure 7). This was due to the smaller ionic radius of Si 4+ (0.40 Å) compared with Mn 4+ (0.53 Å). The higher charge density of Si 4+ forms stronger Si-O bonds, as reported in Figure 8. The ionic radii of Ge 4+ and Mn 4+ are the same. This is reflected in the exoergic solution enthalpy. The optimised structures of MO6 units together with bond lengths and bond angles are shown in Figure 8. Endoergic solution enthalpies are observed for the other dopants. Solution enthalpy for CeO2 is highly endoergic, meaning that doping Ce on the Mn site is highly unlikely to occur.

Conclusions
In conclusion, we have used atomistic simulation techniques to examine intrinsic defects, Li ion diffusion pathways with activation energies and favourable trivalent and tetravalent dopants on the Mn site in Li2MnO3. The lowest defect energy process was calculated to be the Li Frenkel, which will ensure the number of Li vacancies that are necessary for vacancy-assisted Li diffusion. The second most favourable defect process was found to be the cation mixing. Diffusion of lithium with the low activation energy of 0.44 eV suggests that high ionic conductivity would be observed in Li2MnO3. Doping of Al on the Mn site is an efficient strategy to increase the Li content, as reported in the experiment. The favourable isovalent dopants were calculated to be the Si 4+ and Ge 4+ . These theoretical predictions require experimental verification.
Supplementary Materials: The following are available online at www.mdpi.com/xxx/s1, Table S1: Interatomic potential parameters used in the atomistic simulations of Li2MnO3.

Funding:
The research leading to these results received funding from the European Union's H2020 Programme under Grant Agreement no 824072-HARVESTORE.

Acknowledgments:
We acknowledge the computational facilities and support provided by the High Performance Computing Center at Imperial College.

Conflicts of Interest:
The authors declare no conflict of interest.

Conclusions
In conclusion, we have used atomistic simulation techniques to examine intrinsic defects, Li ion diffusion pathways with activation energies and favourable trivalent and tetravalent dopants on the Mn site in Li 2 MnO 3 . The lowest defect energy process was calculated to be the Li Frenkel, which will ensure the number of Li vacancies that are necessary for vacancy-assisted Li diffusion. The second most favourable defect process was found to be the cation mixing. Diffusion of lithium with the low activation energy of 0.44 eV suggests that high ionic conductivity would be observed in Li 2 MnO 3 . Doping of Al on the Mn site is an efficient strategy to increase the Li content, as reported in the experiment. The favourable isovalent dopants were calculated to be the Si 4+ and Ge 4+ . These theoretical predictions require experimental verification.