Effects of cationic substitution on structural defects in layered cathode materials LiNiO2

The electrochemical properties of layered rock salt cathode materials are strongly influenced by defects. The three most common defects in LiNiO2-based compounds, namely extra Ni, Li–Ni anti-site and oxygen vacancy defects have been investigated. The calculated defect formation energies are very low in LiNiO2, consistent with the difficulty in synthesizing stoichiometric defect-free LiNiO2. A systematic study is conducted to examine the effect of Co, Mn and Al substitution on defect formation. It is shown that the presence of Ni in the Li layer can be rationalized using ideas of superexchange interactions. In addition, a correlation between oxygen vacancy formation energy and oxygen charge is noted. This explains the better thermal stability obtained by early transition metal or Al substitutions.


Introduction
Layered rock salt structure materials with the general formula LiMO 2 (where M is a transition metal) have been studied intensively due to their applicability as cathode materials in lithium ion batteries. LiCoO 2 is the prototype commercially used cathode. However, cobalt is toxic and expensive and therefore the search for replacements for cobalt-based cathodes has lasted for decades. LiNiO 2 is one of the potential cathode materials for lithium ion batteries. Although this compound has been studied for many years, the electronic, magnetic and local structures are still highly controversial. 1,2 Experimentally it is not yet possible to synthesize perfect, stoichiometric LiNiO 2 . A certain fraction of extra nickel ions occupy the lithium sites making the true formula of the material [Li 1Àx Ni x ]NiO 2 (ref. 3) (this is referred to hereaer as extra Ni defects on the Li site). A recent theoretical study on LiNiO 2 also predicts an unavoidable high concentration of Ni present in the Li layers at high temperature. 4 Besides, 11% of Li-Ni interlayer mixing (cation exchange between Li and Ni in the expected layered structure) is reported to occur in the LiNiO 2 -based material LiNi 1/2 Mn 1/2 O 2 and 6% in LiNi 1/3 Mn 1/3 Co 1/3 O 2 . 5, 6 The presence of Ni in the Li layers has a detrimental effect on the electrochemical performance of the material as a cathode. First, it disrupts the lithium diffusion by blocking the diffusion pathways. 7 Second, it has been suggested that the presence of nickel in the lithium layer is responsible for rst-cycle irreversibility. [8][9][10] During the rst charge, the Ni 2+ ions at Li sites are oxidized to smaller Ni 3+ ions. This causes a local shrinkage around those nickel ions and therefore it is difficult to insert lithium ions back into the positions around them.
Oxygen loss is another issue in layered cathode materials. A recent study on LiNi 0.8 Mn 0.1 Co 0.1 O 2Àd demonstrated that up to $12% oxygen loss occurs depending on the synthesis conditions and that there is a strong correlation between oxygen content and electrochemical performance. 11 Delithiated Li 1Àx NiO 2 is not thermally stable. It undergoes a phase transition accompanied by oxygen evolution. It has been shown that the extent of oxygen evolution increases as x increases. 12 This irreversible structural change is concomitant with oxygen loss and maybe responsible for the observed capacity fading. 13,14 In order to improve the electrochemical performance of LiNiO 2 , the strategy of partial substitution of Ni by other metal cations has been deployed. It is known that Co substitution gives better 2-D layered character. For LiNi 1Àx Co x O 2 with x > 0.3, nickel is no longer present in the lithium layer. 15 As a result, the irreversibility seen at the rst-cycle mentioned above disappears. By contrast, the interlayer mixing increases with Mn doping. 16 Nevertheless, Li x Ni 0.5 Mn 0.5 O 2 exhibits excellent structural stability against oxygen loss 17 at low Li content and therefore better safety. Al doping improves the thermal stability although Ni is still found in the Li layer. 18,19 Cycling tests show that 10% Al suppresses all the phase transitions observed for the Li x NiO 2 system. 19 Although the properties produced by partial cationic substitution are well studied, the reasons why these foreign dopants produce them are not clear. In this study, rst-principles calculations are performed to investigate the structural defects of Li-Ni anti-site, extra Ni and oxygen vacancy in LiNiO 2 and the effect of Ni substitution by Co (LiNi 0.5 Co 0.5 O 2 ), Al (LiNi 0.5 Al 0.5 O 2 ) and Mn (LiNi 0.5 Mn 0.5 O 2 ). The same structural defects in NaNiO 2 and LiCoO 2 are also calculated for comparison. defects in the supposedly perfect layered LiMO 2 . The extra Ni defect can be considered as occurring through the following defect reaction Similarly the interlayer mixing defect occurs through the reaction and the oxygen vacancy defect occurs through the reaction.
In this work we dene defect formation energies as the formation enthalpies of the above defect reactions at 0 K. Two assumptions are made here. First, in solid phases the volume term can be neglected and therefore the enthalpy corresponds to the internal energy. Second, defects are assumed to distribute evenly in the crystal. In the case of extra Ni defects in LiNiO 2 , the defect formation energy per defect is then given as where E(perfect) is the lattice energy of a perfect LiNiO 2 cell and E(defective) is the lattice energy of the cell containing one extra Ni defect. Similarly the defect formation energy of interlayer mixing is where E(perfect) is the lattice energy of the perfect cell and E(defective) is the lattice energy of the cell containing one interlayer mixing defect. The defect formation energy of oxygen vacancy is where E(perfect) is the lattice energy of the perfect cell and E(defective) is the lattice energy of the cell containing one oxygen vacancy. For LiNiO 2 , the concentrations of Ni present in the Li layers and oxygen vacancies are reported to be a few percent and are far beyond the dilute limit. However by an appropriate choice of the supercell size, the correct defect concentration can be simulated by substitution of the appropriate number of defects in the cell.

Computational approach
In this study, rst-principles calculations are performed to investigate the structural defects of interlayer mixing, extra Ni and oxygen vacancy in layered LiNiO 2 and the effect of Ni substitution by Co (LiNi 0.5 Co 0.5 O 2 ), Al (LiNi 0.5 Al 0.5 O 2 ) and Mn (LiNi 0.5 Mn 0.5 O 2 ). The structural defects in layered NaNiO 2 and LiCoO 2 are also calculated for comparison.
All calculations are based on Density Functional Theory (DFT) in combination with the projector augmented wave (PAW) method. 20 The generalized gradient approximation (GGA) is used with the Perdew-Burke-Ernzerhof functional 21 and a Hubbard model U correction 22 is incorporated for the d electrons to give a better description of this strongly correlated system. The U parameters used for Ni, Co and Mn are 6.5, 4.9 and 4.5 eV, respectively. These parameters are adapted from a self-consistent calculation. 23 The plane wave energy-cutoff is set to 500 eV. For all cells, the k-point spacing is less than 0.05Å À1 in the Brillouin zone. Structural optimizations were performed until the residual force acting on each ion was less than 0.01 eV A À1 . All calculations were carried out using the Vienna ab initio simulation package (VASP). 24 For the calculation of perfect layered LiNiO 2 , a possible ground state cell with space group symmetry P2 1 /c is used as the starting structure. The interlayer mixing defects and extra Ni defects in such a supercell correspond to a concentration of 3.125%, which is well within the experimentally reported range of defect concentration in LiNiO 2 . Therefore the size of the cell is adequate for simulating the observed defects in LiNiO 2 and there is no need for extrapolation to the innite limit.
The interlayer mixing defect in layered AMO 2 (A ¼ Li, Na) is constructed by swapping one Ni (Co in the LiCoO 2 case) in the MO 2 slab with the nearest A ion. The extra Ni defect is constructed by replacing one A ion by Ni in the supercell. The oxygen vacancy defect is constructed by removing one oxygen atom from the supercell.

Properties of undoped compounds
Before proceeding to the defect structure calculations, the crystal and electronic structures of perfect LiNi 0.5 Co 0.5 O 2 , LiNi 0.5 Al 0.5 O 2 and LiNi 0.5 Mn 0.5 O 2 are rst determined. In LiNi 0.5 Co 0.5 O 2 and LiNi 0.5 Al 0.5 O 2 the linear ordering of cations with space group symmetry P2/m is found to be more energetically favorable than the zigzag ordering and is therefore used for subsequent defect calculations. In LiNi 0.5 Mn 0.5 O 2 , the zigzag ordering of Ni and Mn with space group symmetry P2/c is energetically more favorable, in agreement with a previous theoretical study. 25 Fig . 2 shows the calculated density of states for each material. The insulating behaviour of these compounds is well reproduced with band gaps of about 0.7 eV, 0.9 eV and 1.1 eV for LiNi 0.5 Co 0.5 O 2 , LiNi 0.5 Al 0.5 O 2 and LiNi 0.5 Mn 0.5 O 2 , respectively. The local density of states (DOS) of Ni in LiNi 0.5 Co 0.5 O 2 shows one empty spin-up and two empty spin-down states which indicates that the electronic conguration of Ni is t 6 2g e 1 which is low-spin Ni 3+ , in accordance with the calculated magnetic moment 1.12 m B . A Jahn-Teller distortion occurs as expected for low-spin Ni 3+ as shown from the Ni-O bond lengths in Table 1. Cobalt ions are therefore anticipated to be Co 3+ for the sake of charge neutrality. Indeed the empty spin-up and empty spin-down states from the local density of states of cobalt indicate that its electronic conguration is t 6 2g e 0 g (S ¼ 0) implying low-spin Co 3+ , along with its calculated zero magnetic moment. Likewise, nickel ions are determined to be low spin Ni 3+ in LiNi 0.5 Al 0.5 O 2 with a Jahn-Teller distortion. Nevertheless, from the Ni 3+ -O bond lengths in Table 1, it is clear that Ni 3+ displays two different modes of Jahn-Teller distortion, Q 2 and Q 3 in LiNi 0.5 Co 0.5 O 2 and LiNi 0.5 Al 0.5 O 2 respectively, as shown in Fig. 3. The Q 3 mode of Jahn-Teller distortion is the one observed in LiNiO 2 . 26 In LiNi 0.5 Co 0.5 O 2 , the low-spin Co 3+ ions are very stable in the isotropic octahedral environment with 6 identical Co 3+ -O 2À bond lengths. The structural constraint imposed by the presence of rigid Co 3+ octahedra makes the more distorted Q 3 mode less favourable and results in the Q 2 mode for distorted Ni 3+ . This result is in agreement with an EXAFS study that in LiNi 1Ày Co y O 2 the Jahn-Teller distortion of NiO 6 octohedra is suppressed with increasing y. 27 In LiNi 0.5 Mn 0.5 O 2 , two empty spin-down e g states seen in the local density of states of nickel and fully-occupied spin-down t 2g states seen in the local density of states of manganese indicate that their electronic congurations are t 6 2g e 2 g and t 3 2g e 0 g corresponding to Ni 2+ and Mn 4+ , in agreement with previously reported results. 28

Inuence of defect formation on cation charge state
In all LiMO 2 cells with extra Ni and interlayer mixing defects, the calculated magnetic moment of 1.7 m B (S ¼ 1) for the Ni present in the Li layer along with its average Ni-O bond length 2.07Å together imply that Nickel is present as Ni 2+ . Therefore in the LiNiO 2 , LiNi 0.5 Co 0.5 O 2 and LiNi 0.5 Al 0.5 O 2 cells with the interlayer mixing defect, in order to retain charge neutrality one Ni in the NiO 2 slab is oxidised from Ni 3+ to Ni 4+ with a calculated magnetic moment 0.19 m B (S ¼ 0), as seen in the spin density contour map in Fig. 4(a), and the average Ni-O bond length of 1.89Å. In the LiNi 0.5 Mn 0.5 O 2 cell, the interlayer mixing defect does not cause any change of charge state as nickel ions are already Ni 2+ .
In cells with the extra Ni defect, since one Li + is replaced by Ni 2+ , one metal ion in the MO 2 layer must be reduced to maintain charge neutrality. In the LiNiO 2 , NaNiO 2 , LiNi 0.5 -Co 0.5 O 2 and LiNi 0.5 Al 0.5 O 2 cells, it is the Ni in the MO 2 layer that gets reduced from Ni 3+ to Ni 2+ with a calculated magnetic moment of 1.7 m B (S ¼ 0) and an average Ni-O bond length of 2.07Å. The change of preferred charge state on Ni rather than Co in LiNi 0.5 Co 0.5 O 2 is probably due to the relatively stable electronic conguration of Co 3+ (t 6 2g e 0 g ). In LiNi 0.5 Mn 0.5 O 2 , the charge state of Ni 2+ cannot be reduced further and therefore the charge compensation accompanied by the extra Ni defect takes place on manganese with Mn 4+ / Mn 3+ . Fig. 4(b) shows the case of the extra-Ni defect in LiNi 0.5 Mn 0.5 O 2 . The e g orbital character on Ni 2+ (t 6 2g e 2 g ) can be seen from the shape of spin density pointing towards oxygen ions. Similarly, the spin density on Mn 4+ (t 3 2g e 0 g ) pointing away from the oxygen represents the t 2g orbital character. The Mn ion showing the different shape of spin density is the one that is reduced from Mn 4+ to Mn 3+ .
For cells with the oxygen vacancy defect, two metal ions in the MO 2 layer next to the oxygen vacancy site are reduced to keep the charge neutrality. Fig. 4(c) clearly shows that two Co 3+ ions are reduced to Co 2+ upon the removal of one oxygen ion.

Stability of defects and the effect of cation substitution
The calculated defect formation energies in LiNiO 2 are shown in Fig. 5. The calculated formation energies of the three defects in LiNiO 2 are all small, ranging from approximately 0.3 to 1.0 eV. This is consistent with the difficulty in synthesizing stoichiometric defect-free LiNiO 2 . It is possible to rationalize these results using the idea of superexchange interactions. [29][30][31] Both Ni 2+ (t 6 2g e 2 g ) and Ni 3+ (t 6 2g e 1 g ) have fully lled t 2g states but partially lled e g states. Consequently the 180 Ni-O-Ni superexchange is much stronger than the 90 Ni-O-Ni superexchange plus direct exchange. This means there is a larger energy gain through orbital interactions when Ni-O-N is in the 180 conguration than the 90 conguration. In fact it has been shown that there is a tendency for Ni ions to locate as secondnearest neighbors (180 Ni-O-Ni conguration) in the cation sublattice of the rocksalt structure due to the energy gain from the 180 superexchange interaction. 32 Therefore the presence of Ni ions in the Li layers of LiNiO 2 can be viewed as being stabilized by the 180 Ni-O-Ni superexchange interaction, giving rise to low formation energies for both interlayer mixing and the extra Ni defects. However, the extra Ni defect is the most  The effect of Co substitution can be seen in Fig. 5(a). It is rst noted that the defect formation energies of the interlayer mixing and the extra Ni defects in LiNi 0.5 Co 0.5 O 2 with conguration A are lower than in LiNiO 2 . This is unexpected since it is known experimentally that Co substitution in LiNiO 2 suppresses the presence of Ni in the Li layer. Nevertheless the formation energies of the interlayer mixing and extra Ni defects are higher in conguration B than conguration A by about 300 meV and 360 meV respectively. The result can also be rationalized by considering superexchange interactions. As seen in Fig. 6(a) The defect formation energies in LiCoO 2 are also shown in Fig. 5(a). The defect energies of the interlayer mixing defect and the extra Co defect are considerably higher than the Ni containing compounds. This agrees with the experimentally observed perfect layering of LiCoO 2 . Given the closed-shell d 6 (t 6 2g e 0 g ) electronic conguration of Co 3+ in the CoO 2 layer, there is no interaction between Co ions that can stabilize the presence of Co in the Li layer.
Since there are no d electrons in the Al 3+ ion, there can be no superexchange interaction between Al 3+ and Ni 2+ . The effect of Al substitution on defect formation energies is therefore expected to be similar to that of Co substitution since Al substitution should also effectively screen the Ni-O-Ni superexchange interaction. Indeed by adopting the linear cation ordering in the LiNi 0.5 Al 0.5 O 2 cell ( Fig. 1(a)), as shown in Fig. 5(b) the calculated formation energies of the interlayer mixing and the extra Ni defects are very similar to those in LiNi 0.5 Co 0.5 O 2 . Defects of conguration A are also more favourable than conguration B due to the stabilisation by the exchange interaction. However, unlike in LiNi 1Àx Co x O 2 with x > 0.3, neither the interlayer mixing defect nor extra Ni defects are observed. 15 Experimentally 5% of extra-nickel ions are still found in the lithium layer in LiNi 1Àx Al x O 2 with 0.1 < x < 0.5. 19 This is because Al tends to segregate to interfaces 33 and hence a core-shell structure can be formed 34 31 Consequently, although the number of 180 Ni-O-Ni interactions is reduced due to Mn substitution, the presence of Ni 2+ can be stabilized not only by the 180 Ni-O-Ni interaction but also by the 180 Ni 2+ -O 2À -Mn 4+ interaction. Moreover, since the ionic radius of Ni 2+ is similar to Li + , these ions can exchange sites readily without signicant rearrangement of the surrounding atomic positions. No charge compensation is necessary to create the interlayer mixing defect in LiNi 0.5 Mn 0.5 O 2 . In contrast to the interlayer mixing defect, the defect formation energy for the extra Ni defect is much higher in LiNi 0.5 Mn 0.5 O 2 compared to LiNiO 2 . The probable reason for this is that the reduction of Mn 4+ to Mn 3+ , which is the charge compensation accompanying the extra-Ni defect, is considerably less favorable than the reduction of Ni 3+ to Ni 2+ due to the stable electronic conguration of Mn 4+ (t 3 2g e 0 g ). In NaNiO 2 , there is a structural constraint arising from the large ionic size of Na + . It is shown in Table 2 that the LiO 6 octahedron must undergo signicant distortion for the zigzag ordering of the Ni 3+ Jahn-Teller distortions or charge  disproportionation Ni 3+ / Ni 2+ + Ni 4+ in the NiO 2 layer to happen. However, the larger Na + ion lls up the interlayer space and so forbids the zigzag ordering of the Ni 3+ Jahn-Teller distortions or charge disproportionation Ni 3+ / Ni 2+ + Ni 4+ in the NiO 2 layer. Hence the Ni 3+ Jahn-Teller distortions in NaNiO 2 are forced to align collinearly as observed experimentally, which results in undistorted NaO 6 octahedra. This gives a good 2-D layered character and is less susceptible to defects as shown by the high defect formation energies for NaNiO 2 compared to LiNiO 2 in Fig. 7(b). Because of the dramatic difference in ionic radii between Na and rst-row transition metal ions, the size effect dominates the interactions between cations and consequently all NaMO 2 form perfect layered structures.
Oxygen vacancy Fig. 8 shows the calculated defect formation energies of the oxygen vacancy plotted against the oxygen charge calculated using the Bader analysis. 35,36 The formal charge on oxygen is À2 in highly ionic compounds. However, in transition metal oxides, there is a considerable overlap between the oxygen 2p and metal 3d orbitals, particularly for late transition metals or metals with high charge states. This is reected in the calculated oxygen charge as shown in Fig. 8, from le to right (LiAlO 2 / LiNiO 2 and LiCoO 2 / Li 0.5 CoO 2 ) the decrease of calculated oxygen charge is a consequence of the increase in overlap between oxygen 2p and metal ion 3d orbitals or equivalently greater metal-oxygen covalency. A correlation can be clearly seen between the formation energy of the oxygen vacancy defect and the calculated oxygen charge. Also, as shown in Fig. 5 and 7, in LiNi 0.5 Co 0.5 O 2 , LiNi 0.5 Al 0.5 O 2 and LiNi 0.5 Mn 0.5 O 2 , the defect formation energy for removing the oxygen bonded to two Ni (conguration A) is lower than the oxygen bonded to one Ni (conguration B). The oxygen bonded to two Ni has a lower charge. The smaller the oxygen charge is, the easier it seems to be to remove the oxygen. It has previously been suggested that the strength of the metal-oxygen bond depends on the effective charge on oxygen. 37 In addition when the charge on oxygen ions is low, there would be a tendency for them to form peroxide at the surface as suggested by Goodenough et al. 38 and then dissociate through the following reaction: This is consistent with experimental results that the temperature for oxygen evolution on heating (i.e. the thermal stability) decreases as x decreases in layered Li x MO 2 . 39-41 It seems that low oxygen charge/high metal-oxygen covalency causes the chemical instability of an oxide compound against oxygen loss. A recent study has also proposed that a greater metal-oxygen covalency promotes the surface oxygen evolution reaction which involves the creation of surface oxygen vacancies. 42 On comparing LiNiO 2 with LiCoO 2 there is no noticeable difference in the oxygen charge, but the defect formation energy   of the oxygen vacancy in LiCoO 2 is signicantly higher than in LiNiO 2 (by $1.2 eV). This is probably due to the relatively stable electronic conguration of low-spin Co 3+ t 6 2g e 0 g . Therefore by creating an oxygen vacancy, it costs more energy to reduce Co 3+ to Co 2+ than to reduce Ni 3+ to Ni 2+ in LiNiO 2 . Although the defect formation energy of an oxygen vacancy in LiCoO 2 is markedly higher than in LiNiO 2 , it drops drastically by $1.5 eV in Li 0.5 CoO 2 upon the removal of half the lithium ions. This can again be explained by the decrease of oxygen charge that is associated with the creation of Co 4+ ions.
Given this correlation between oxygen charge and the defect formation energy of the oxygen vacancy, doping with a more electro-positive cation should mitigate the oxygen loss in layered Li x MO 2 compounds and result in better thermal stability. Indeed doping with Mn 4+ decreases the oxygen loss 43 and so does Al or Mg doping, 18,44,45

Conclusions
All the calculated formation energies for the various LiMO 2 compounds are consistent with experimental results. It is demonstrated that the defect formation energies in LiNiO 2 are low, in agreement with the experimental difficulty of synthesizing stoichiometric defect-free LiNiO 2 . The presence of Ni in the Li layer can be rationalized in terms of the 180 Ni-O-Ni superexchange interaction. Substituting Ni with Co in the MO 2 layer screens the 180 Ni-O-Ni congurations and thus effectively reduces the concentration of Ni in Li layers. A correlation between the defect formation energy of the oxygen vacancy and oxygen charge (as measured from a Bader analysis) is reported. It appears that the smaller the oxygen charge/higher metaloxygen covalency, the lower the oxygen vacancy formation energy. This can explain the thermal instability of Li x CoO 2 and Li x NiO 2 at low x, as well as the improved electrochemical behavior in Al, Mg or early transition metal doped LiMO 2 . In the quest for designing better cathode materials, the use of high electropositive cations is highly desirable.