Defects and lithium migration in Li2CuO2

Li2CuO2 is an important candidate material as a cathode in lithium ion batteries. Atomistic simulation methods are used to investigate the defect processes, electronic structure and lithium migration mechanisms in Li2CuO2. Here we show that the lithium energy of migration via the vacancy mechanism is very low, at 0.11 eV. The high lithium Frenkel energy (1.88 eV/defect) prompted the consideration of defect engineering strategies in order to increase the concentration of lithium vacancies that act as vehicles for the vacancy mediated lithium self-diffusion in Li2CuO2. It is shown that aluminium doping will significantly reduce the energy required to form a lithium vacancy from 1.88 eV to 0.97 eV for every aluminium introduced, however, it will also increase the migration energy barrier of lithium in the vicinity of the aluminium dopant to 0.22 eV. Still, the introduction of aluminium is favourable compared to the lithium Frenkel process. Other trivalent dopants considered herein require significantly higher solution energies, whereas their impact on the migration energy barrier was more pronounced. When considering the electronic structure of defective Li2CuO2, the presence of aluminium dopants results in the introduction of electronic states into the energy band gap. Therefore, doping with aluminium is an effective doping strategy to increase the concentration of lithium vacancies, with a minimal impact on the kinetics.

Li 2 CuO 2 is an attractive material with many interesting characteristics, already considered for CO 2 chemisorption 15,16 . In battery applications, a phase transition during the first circle of charge/discharge is confirmed and attributed to oxygen loss and delithiation. Recently, Ramos-Sanchez et al. 17 , have reported on this phase transition control and proposed Li 2 CuO 2 for future applications due to its high capacity in pre-charge conditions as well as fast Li + mobility. The partial pressure chemisorption has been also investigated by Lara-Garcia and Pfeiffer 18 . In essense, it was found that for low pressures the material's behavior is not affected while increase of pressure combined with additional oxygen source enhances the CO 2 chemisorption 18 . Furthermore, The Li + and O 2ion-diffusion can also affect the CO 2 chemisorption by means of an extra layer that forms on the surface which limits the process as the CO 2 cannot easily reach the bulk material.
In previous studies, the electronic structure of Li 2 CuO 2 has been investigated using the local density approximation (LDA) 19 , LDA-LCAO 20 and the generalized gradient approximation (GGA) 21 , however, there is lack of clarity in the literature for the exact contributions of each element (and their orbitals) in the valence and conduction band. Ramos-Sanchez et al. 17 report on the band gap formation with higher oxygen states close to the Fermi level. To further examine the electronic structure and the defect processes of Li 2 CuO 2 , atomistic simulations are required. These can identify the defect engineering processes which are able to lead to the improvement of the material properties and accelerate progress 22-25 . In the present study, we investigate the intrinsic defect processes, electronic structure and lithium vacancy self-diffusion in Li 2 CuO 2 using static atomistic simulations and density functional theory (DFT).
Intrinsic defect processes. The study of the intrinsic defect processes of energy materials is important in order to understand their electrochemical behavior and their propensity to form intrinsic defects. The intrinsic defect reactions in Kröger-Vink notation are: (1) (3) The reaction energies for these intrinsic defect processes are reported in Table 1. Typically to most oxides, the formation of all Frenkel and Schottky defects is unfavourable and this suggests that the formation of vacancies and interstitial defects will be hindered at equilibrium conditions. Therefore, these intrinsic defects will be present only at low concentrations in undoped Li 2 CuO 2 . The lithium Frenkel is a lower energy process compared to the other Frenkel and Schottky processes considered. 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 2.57 eV per defect (refer to Table 1). This is a process that can lead to further ′ V Li and •• V O however at elevated temperatures far from room temperature. We also considered the formation of antisite defects ( ′

Li
Cu and Cu Li ) both when the defects are apart (isolated form, relation 6) and when they form a defect pair (cluster, relation 7). For the isolated case, the defect energies of the two antisites were calculated independently in order to calculate the energy of the defect process applying relation 6 (i.e. the effect of defect association is not included), which is 0.88 eV per defect (refer to Table 1). For the antisite pair (relation 7) the energy per defect drops considerably (0.31 eV per defect, refer to Table 1) mainly due to the binding of the oppositively charged defects and relaxation effects. Lithium self-diffusion. The present static atomistic simulation enabled the examination of possible Li vacancy migration paths and calculated the corresponding activation energies of migration. For the Li vacancy migration, we identified three paths between adjacent Li sites (refer to Fig. 1(b)). The zig-zag diffusion path (path A in Fig. 1(b)) in the ab-plane is the lowest energy process with an activation energy of migration of 0.11 eV (refer to Fig. 2). Here the activation energy of migration is defined as the position of the highest potential energy along the migration path.

Trivalent doping.
Although there is a very low migration activation energy the diffusion of lithium will be constrained by the high Li Frenkel energies, since there will only be a limited concentration of ′ V Li that act as  vehicles mediating Li self-diffusion via the vacancy mechanism. A defect engineering strategy to introduce a high ′ V Li is by doping with trivalent ions. This can be described in the Kröger-Vink notation as: It should be noted that similar defect engineering strategy has been successfully employed in other energy materials such as materials for solid oxide fuel cells 27,28 . Here we have examined a number of R O 2 3 oxides, namely those with R = Al, Sc, In, Y, Gd and La, to find the oxide with the minimum solution enthalpy. The results of our calculations are shown in Fig. 3 where it can be observed that the solution energy of Al 2 O 3 is the lowest one (0.97 eV/Al 3+ ). Therefore, doping with Al will result in the formation of ′ V Li with energies significantly lower than those required by the Li Frenkel reaction. This will lead to a non-equilibrium concentration of ′ V Li . These vacancies will in turn act as vehicles for Li self-diffusion, increasing the Li diffusivity.
It is shown here that the Al 2 O 3 solution enthalpy is considerably lower than the enthalpies for Schottky and Frenkel disorder. Therefore, vacancy and interstitial concentrations will be primarily due to the extrinsic impurity compensation processes. Similar processes have been previously considered in ceramic materials for energy applications (solid oxide fuel cells), such as Y 2 O 3 or doped CeO 2 28,29 . It should also be noted that the defect enthalpies are expected to be overestimated (although relative energies will be very reliable) as (a) we assume a fully ionic model (refer to Table S1 in the Supplementary Information) and (b) the calculations correspond to the dilute limit.
The introduction of substitutional dopants in the lattice may also impact the migration energies of lithium. Figure 4(a) represents the different energy profiles in the vicinity of an Al dopant atom. It can be deduced that the introduction of dopants in the vicinity of the migrating ′ V Li will increase the migration energy barriers from 0.22 eV (for the smallest dopant, Al) to 0.88 eV (for the largest dopant, La) (refer to Fig. 4 (b) and Figure S1    Li } X . The valence band maximum (VBM) is set at zero energy level. For the perfect structure (refer to Fig. 5(a)), the band gap of Li 2 CuO 2 is calculated at 1.05 eV. It is shown that Cu and O mainly contribute to the DOS of the valence band, driven by the Cu-d and O-p orbitals, while Li and Cu are the main contributors to the conduction band, driven by the Li-p and Cu-p orbitals (refer also to Figure S2 in the Supplementary Information). We also observe the high states of Cu and O just below the VBM and the non-uniformity of the band as presented by two separated contributions, in agreement with a previous study 17 . The effect on the DOS of the introduction of a lithium vacancy in the supercell is minimal (refer to Fig. 5(b)) as no additional states are created into the band gap, wheras only a small increase in the DOS in the conduction band due to Lithium is observed. (for oxygen vacancies refer to supplementary material Figure S3).
The impact of the • Al Cu and • ′

Al V { :
Cu Li } X pairs on the densities of states on Li 2 CuO 2 was also considered (refer to Fig. 5(c,d)). It is shown that the • Al Cu introduces a distribution of states in the band gap with a simultaneous minor narrowing of the gap itself (to 0.80 eV). Similar picture is observed in Fig. 5 Supplementary Information). Therefore, the introduction of Al (and other) dopants has an effect on the electronic structure, mainly with the introduction of states in the band gap but also with a minor narrowing of the gap. Although for battery applications, the leading conduction mechanism is the diffusion of ions, the effect of the energy levels in the band gap have to be considered as well.

Summary
In the present study, the intrinsic defect processes and the Li vacancy diffusion in Li 2 CuO 2 were investigated. Lithium vacancy diffusion with a very low migration energy (0.11 eV) along zig-zag diffusion path in the ab-plane is the lowest energy process. The high lithium Frenkel energy in essense implies a low concentration of lithium vacancies. We propose here doping Li 2 CuO 2 with aluminium to introduce a higher concentration of lithium vacancies. The aluminium dopants will impact the activation energy of migration increasing the barrier to 0.22 eV. The combination of low solution enthalpy and low increase in the migration energy of lithium as compared to the intrinsic processes or the other dopants considered here, constitutes doping with aluminium the preferential doping strategy to increase the lithium diffusivity in Li 2 CuO 2 . The DOS analysis reveals that the introduction of aluminium will introduce electronic states into the energy band gap. It is anticipated that the present study will motivate further experimental and theoretical work [30][31][32] to determine the diffusion properties of Li 2 CuO 2 and its potential application in batteries. Additionally, it will generate further interest in lithium cuprate materials for energy storage applications.

Methods
Atomistic simulations employing interatomic potentials method were used to investigate the relative energetics for the formation of intrinsic defects and the possible pathways for lithium ion migration. In particular Buckingham-type interatomic potentials as implemented in the general utility lattice program (GULP) 33 were used, within the Born model of solids. The interactions between ions consist of a long-range Coulombic term and a short-range component, which aims to represent electron-electron repulsion and van der Waals interactions. Short-range interactions were modeled using the Buckingham potentials. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm 34 was employed to relax the simulation boxes and atomic positions. Lattice relaxation around point defects and the migrating ions were considered using the Mott-Littleton method 35 . This divides the system into two concentric regions, where the ions within the inner spherical region (>700 ions) surrounding the defect relaxed explicitly. The defect calculations were performed in supercells containing 720 ions. Li diffusion was investigated by considering two adjacent vacancy sites as initial and final configurations. The Li interstitial ion was placed along the direct pathway between the initial and final vacancy configuration. We have considered seven intermediate (interstitial) positions which were fixed while all other ions were free to relax. The energy difference between the saddle point position and the system in its initial state is effectively the activation energy of migration.
To calculate the DOSs for pure and defective Li 2 CuO 2 , density functional theory simulations were employed using the plane wave code CASTEP 36,37 . The exchange and correlation interactions are modelled by using the corrected density functional of Perdew, Burke and Ernzerhof (PBE) 38 in the generalized gradient approximation (GGA), with ultrasoft pseudopotentials 39 . The kinetic energy cut-off of the plane wave basis is 500 eV, in conjunction with a 3 × 2 × 3 Monkhorst-Pack (MP) 40 k-point grid and a 60-atomic site supercell. To consider correlation effects of localized electrons onsite Coulomb repulsions in the range of 4-8 eV is set for the Cu 3d orbitals. We have tested this value to establish that the trends are not affected by the specific choice of U-parameter. The calculations were under constant pressure conditions. The system has been treated as spin polarized. For the PDOS analysis/imaging, the OPTADOS code is employed 41,42 .