Defect Chemistry in Layered LiMO2 - American Chemical Society

Sep 18, 2012 - Department of Materials Science and Engineering, Graduate School of ... University, Yoshida Nihon-matsu, Sakyo, Kyoto 606-8501, Japan...
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Defect Chemistry in Layered LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3) by First-Principles Calculations Yukinori Koyama,*,† Hajime Arai,† Isao Tanaka,‡ Yoshiharu Uchimoto,¶ and Zempachi Ogumi† †

Office of Society-Academia Collaboration for Innovation, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan Department of Materials Science and Engineering, Graduate School of Engineering, Kyoto University, Yoshida, Sakyo, Kyoto 606-8501, Japan ¶ Graduate School of Human and Environment Studies, Kyoto University, Yoshida Nihon-matsu, Sakyo, Kyoto 606-8501, Japan ‡

S Supporting Information *

ABSTRACT: The defect chemistry in a series of layered lithium transition-metal oxides, LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3), is investigated by systematic first-principles calculations. The calculations clearly show that Ni3+ ions in LiNiO2 are easily reduced, whereas Mn3+ ions in LiMnO2 are easily oxidized under ordinary high-temperature synthesis conditions. It is expected that LiCoO2 and Li(Li1/3Mn2/3)O2 with low defect concentrations are easily synthesized. These results are highly consistent with the characteristics and conductive properties of the oxides observed in experiments. The calculations also suggest that the surfaces of the oxides are reduced at a nanometer scale by immersion of the samples in organic electrolytes of lithium-ion batteries, and the tendency of the surface reduction is consistent with the defect chemistry at high temperatures. The formation of the lithium vacancy and interstitial are elementary reactions of electrode active materials in the charging and discharging processes of lithium-ion batteries, respectively. The defect formation energies in conjunction with the electrode potentials can quantitatively describe the electrode behavior. KEYWORDS: defect chemistry, first-principles calculation, lithium-ion battery, electrode active material, surface state, electrode potential

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INTRODUCTION Various lithium transition-metal compounds have been intensively investigated as electrode active materials for lithium-ion batteries. Some properties such as redox potential are ascribed to the bulk character of the compounds, whereas many other properties are associated with defects and nonstoichiometry in actual materials. For instance, LiNiO2 always has excess nickel, and the excess nickel ions exist as antisite defects at the lithium site. The amount of excess nickel should be small to obtain a large rechargeable capacity, which is an advantage of LiNiO2 over LiCoO2.1,2 LiMn2O4 has nonstoichiometry in the lithium to manganese ratio and also in the cation to anion ratio. Capacity fading by charging and discharging cycles is an issue of LiMn2O4 for practical use, and control of the nonstoichiometry can improve the cyclability.3,4 The relationship between defects and electric conduction properties has been investigated for LiFePO4, since pristine LiFePO4 is an insulator and electric conduction only occurs in defective materials.5 Transition-metal compounds often show nonstoichiometry, which necessarily leads to defects. Therefore, acquiring information on the point defects is a key to understanding the characteristics of electrode active materials and thus to improving the performance of lithium-ion batteries. © XXXX American Chemical Society

Theoretical calculations of the point defects in electrode active materials have been performed by atomistic calculations using empirical interatomic potentials6−8 and also by firstprinciples calculations based on density functional theory (DFT).9−16 Despite the systematic studies on point defects by atomistic calculations, the method has an intrinsic drawback in its difficulty to treat different valences of transition-metal species. Moreover, the formation energies and thus the equilibrium concentrations of the defects depend on chemical conditions such as temperature and oxygen partial pressure, which were not taken into account in previous studies. Recently, Hoang et al. reported a systematic study on the point defects in LiFePO4 by first-principles calculations with consideration of the chemical conditions during the synthesis.16 However, most other studies using first-principles calculations only focused on particular defects: oxygen vacancies in lithium transition-metal compounds (Li2MnO3,12 Li(Ni,Co)O2,13 V2O5,10 and lithium titanium phosphates11) and antisite ions in LiFePO4.14,15 Focusing on particular defects can be effective Received: June 12, 2012 Revised: September 18, 2012

A

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Figure 1. (a) Crystal structure of layered LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3) and schematic structures of (b) lithium vacancy (VLi), (c) transition-metal vacancy (VM), (d) oxygen vacancy (VO), (e) interstitial lithium ion (Lii), (f) interstitial transition-metal ion (Mi), (g) antisite transition-metal ion (MLi), and (h) antisite lithium ion (LiM). Small green, small red, and large blue spheres denote lithium, transition-metal, and oxygen ions, respectively. Broken and solid lines in the crystal structure indicate the unit cell of the α-NaFeO2-type structure and the supercell used in the present work, respectively. The M layers in Li(Li1/3Mn2/3)O2 consist of lithium and manganese ions in a 1:2 ratio, forming a [√3 × √3]R30°superlattice. from the rhombohedral lattice to a monoclinic lattice (C2/m spacegroup symmetry) .18 Therefore, the monoclinic structure was adopted for LiNiO2 in this paper. LiMnO2 in the layered form is metastable and synthesized by ion-exchange techniques.19−21 The layered LiMnO2 phase has a monoclinic lattice (C2/m symmetry) due to the cooperative Jahn−Teller distortion. The (Li1/3Mn2/3) layers of Li(Li1/3Mn2/3)O2 exhibit a [√3 × √3]R30°-superlattice. Since the stacking sequence of the superlattice layers is not uniquely defined,22−24 the simplest model with the C2/m space-group symmetry was adopted in this paper. In these four oxides, the point defects of vacancies (VLi, VM, and VO), interstitial cations (Lii and Mi) at the tetrahedral sites in the lithium layers, and antisite cations (MLi and LiM) were examined, where M is the transition-metal species. These defects are schematically illustrated in Figure 1(b)−(h). The notation of the defects in this paper is based on Kröger−Vink notation, while the valence state is explicitly denoted. A set of defects with different valences is denoted without the valence notation. For instance, CoLi is the set of antisite cobalt ions at the lithium site regardless of the valence, including CoLi0, CoLi+, CoLi2+, and so forth. The defects were examined from the neutral state to the formal valence, which is estimated from the regular valences in the oxides. The examined defects and their valences are summarized in Table 1. Note that the defect may be a complex of a

if the defects are actually dominant. Otherwise, one may overlook the true dominant defects in the materials. We herein report an investigation of the defect chemistry in a series of layered lithium transition-metal oxides, LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3) by systematic first-principles calculations with the aim of understanding the characteristics of the oxides used as electrode active materials in lithium-ion batteries. We give the equilibrium concentrations of the point defects in the oxides at high temperatures. The defects are formed at high temperatures in solid-state synthesis processes, and part of the defects remains even after cooling to room temperature. Therefore, the defect chemistry at high temperatures often affects the characteristics of the actual materials. We also report the defect chemistry under strongly reductive conditions at room temperature to model electrode active materials in contact with organic liquid electrolyte in lithiumion batteries. In addition, we discuss the formation of the interstitial lithium ion and lithium vacancy. The formation of these defects can be considered as possible elementary reactions of electrode active materials in the charging and discharging processes of lithium-ion batteries. By understanding the defect formation energies and electrode potentials, we attempt to quantitatively describe the electrode behavior of active materials.

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Table 1. Defects and Valences in LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3) Examined in the Present Worka defect

CALCULATION METHOD

lithium vacancy (VLi) transition-metal vacancy (VM) oxygen vacancy (VO) interstitial lithium ion (Lii) interstitial transition-metal ion (Mi) antisite transition-metal ion (MLi) antisite lithium ion (LiM)

Systems. Four layered lithium transition-metal oxides, LiCoO2, LiNiO2, LiMnO2, and Li(Li1/3Mn2/3)O2 (Li2MnO3), were examined. LiCoO2 is isostructural with α-NaFeO2, and its space-group symmetry is R3̅m. The structure is schematically illustrated in Figure 1(a). LiNiO2 has also been shown to have an α-NaFeO2-type structure by X-ray diffraction (XRD) measurements. However, local (noncooperative) Jahn−Teller distortion was observed by extended X-ray absorption fine structure (EXAFS) measurement.17 DFT calculation suggested weak stabilization by cooperative Jahn−Teller distortion

a

B

valences 0, 0, 0, 0, 0, 0, 0,

−1 −1, −2, −3, (−4) +1, +2 +1 +1, +2, +3, (+4) +1, +2, (+3) −1, −2, (−3)

The valences in parentheses are examined only for Li(Li1/3Mn2/3)O2. dx.doi.org/10.1021/cm3018314 | Chem. Mater. XXXX, XXX, XXX−XXX

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Table 2. Calculated Interatomic Distances in a Unit of Å between Transition-Metal and Oxygen Ions in LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3), Transition-Metal Monoxides (MO), and MO2 with an O3-Type Layered Structurea

LiCoO2

2.06 × 6

LiNiO2

2.01 × (2.05) 2.11 × (2.18) 1.96 × 1.99 × 2.13 × (2.02)

LiMnO2 Li(Li1/3Mn2/3)O2

a

localized hole in LiMO2

localized electron in LiMO2

compound

regular ion in LiMO2

1.90 × 2, 1.91 × 4 (1.91) delocalized

4, 2.13 × 2 4, 2.32 × 2

1.94 × 4, 2.00 × 2 (1.96) delocalized

1, 1.97 × 2, 1, 2.12 × 1, 1

in MO

in MO2

1.94 × 6

2.15 × 6

1.89 × 6

1.90 × (1.98) 1.96 × (2.08) 1.93 × 1.95 × (1.94)

4, 2.14 × 2

2.10 × 6

1.87 × 6

4, 2.33 × 2

2.15 × 6

1.95 × 6

2, 1.94 × 2, 2

The average distances are shown in parentheses. were individually introduced into the supercells. Lattice constants were fixed at those of the pristine oxides. Atomic positions were optimized until the residual forces became less than 0.02 eV/Å. The electrostatic potentials of the charged supercells were corrected by the “potential alignment” method, that is, the electrostatic potentials at the farthest ions from the defects were adjusted to those in the pristine crystals.16,25,26 The DFT calculations were performed using the plane-wave basis projected-augmented-wave (PAW) method implemented in the VASP code.27−29 The plane-wave basis set was determined with a cutoff energy of 500 eV. The integral in the reciprocal space was evaluated by the Gaussian smearing technique with a smearing parameter of 0.1 eV and a 2 × 2 × 1 mesh. The radii of the PAW potentials used were 1.38, 0.82, 1.32, 1.30, and 1.29 Å for Li, O, Mn, Co, and Ni, respectively. Li1s, O-1s, and 1s to 3p orbitals of the transition-metal species were treated as core states. Spin polarization was considered with ferromagnetic spin ordering. The exchange-correlation interaction was treated by the generalized gradient approximation30 with the Hubbard model correction31 (GGA+U). The electronic states and defect formation energies may be dependent on the U parameter. Zhou et al. reported first-principles self-consistent estimations of the U parameter for several lithium transition-metal oxides.32 The selfconsistent U parameter varies from 3.6 to 6.7 eV for Mn, Co, and Ni in the +2, +3, and +4 valence states in the lithium transition-metal oxides, depending on the transition-metal species, valence, and structure. Therefore, a U parameter of 5 eV was commonly used for all the transition-metal species and valences in the present work. To obtain formation energies in high accuracy, some correction methods have been proposed by fitting the calculated formation energies of reference materials to the experimental values.33−36 However, such correction was not adopted in the present work to avoid the experimental fitting procedure. The calculated properties of the pristine LiMO2 are summarized in the Supporting Information.

defect in a different valence and localized electron or hole defects. Hence, many possible combinations of the defects and their arrangements were first examined for each nominal valence, and then the most stable defect was employed. In Li(Li1/3Mn2/3)O2 with the C2/m space-group symmetry, there are three types of lithium sites (2b, 2c, and 4h in Wyckoff notation) and two types of oxygen sites (4i and 8j). Corresponding defects were examined for individual sites, although the sites are not explicitly denoted in this paper to avoid excessively complicated notation. Defect Formation Energies and Equilibrium Concentrations. The formation energy of defect X at site A in valence state q is defined as Δf E(XA q) = EDFT(XA q) − EDFT(bulk) −

∑ Δniμi + qεF i

DFT

(XAq)

(1)

DFT

and E (bulk) are the energies of supercells where E obtained by DFT calculations with and without defect XAq, respectively. Δni is the change in the number of atoms of species i, which has been added (Δni > 0) or removed (Δni < 0). μi is the atomic chemical potential of species i. εF is the Fermi energy. Note that the energy in eq 1 is, in principle, free energy. However, the entropy and volume terms can be disregarded for solid phases. Under thermal equilibrium, the concentration of defect XAq at temperature T can be obtained as

⎛ Δ E(XA q) ⎞ C(XA q) = C(AA ) exp⎜ − f ⎟ kBT ⎠ ⎝

(2)

where C(AA) is the concentration of site A without any defect, and kB is the Boltzmann constant. To represent a chemical condition of the LiMO2 system under thermal equilibrium, one internal parameter (Fermi energy, εF) and four external parameters, typically the temperature (T) and the atomic chemical potentials of the species (μLi, μM, and μO), exist. The Fermi energy was determined so that the system satisfied charge neutrality. The existence of the LiMO2 phase requires a constraint on the chemical condition as follows:

μ Li+μM + 2μO = E LiDFT M O2

for M = Co,

4 2 DFT μ + μ Mn + 2μO = E Li(Li 1/3Mn2/3)O2 3 Li 3

Ni,

and Mn

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RESULTS AND DISCUSSION Electron and Hole Defects. Since transition-metal d orbitals are localized in many transition-metal oxides, electronic defects (electrons and holes) may be localized as small polarons. The electronic defects in LiMO2 are examined in both the localized and delocalized states, and then the most stable state is clarified. Table 2 summarizes the calculated interatomic distances between the transition-metal and oxygen ions for the localized electron and hole defects. The table also shows the distances for the regular transition-metal ions in LiMO2, transition-metal monoxides (MO) with the rocksalt structure, and lithium-removed MO2 with an O3-type layered structure for comparison. The hole in LiCoO2 is stable in the localized state with the low-spin configuration. The Co−O distance of the localized hole (1.91 Å in the calculation) is

(3)

for M = (Li1/3Mn2/3) (4)

EDFT LiMO2

where is the energy of LiMO2 obtained by DFT calculation. The stable conditions for LiMO2 with the chemical potentials are shown in the Supporting Information. The remaining three parameters were determined to match the conditions of interest. Details of the conditions are described in the following sections. DFT Calculation. The defect energies were calculated using 144atom (Li36M36O72) supercells constructed by the expansion of the αNaFeO2-type unit cell by 2√3 × 2√3 in the ab plane. Single defects C

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conditions, a single variable remains. In this investigation, the atomic chemical potential of lithium was set to be under equilibrium with Li2O. This corresponds to setting the most lithium-rich condition during the synthesis to minimize the lithium deficiency in the samples. The defect formation energies in LiMO2 are shown as a function of the Fermi energy in the Supporting Information. Figure 2 illustrates the equilibrium concentrations of the point defects in layered LiMO2 as a function of temperature. The defect concentrations in the figure are the totals for each type of defect summed over all possible valences. The dominant defect in LiCoO2 is the antisite cobalt ion at the lithium site (CoLi) as shown in Figure 2(a). The dominant valence in the

shorter than the regular Co−O distance in pristine LiCoO2 (1.94 Å) but longer than the Co−O distance in CoO2 (1.89 Å). The electron defect in LiCoO2 is stable in the localized state with the high-spin configuration, although the regular cobalt ion in LiCoO2 is in the low-spin configuration. The Co−O distance of the localized electron (2.06 Å) is longer than the regular Co−O distance in LiCoO2 but shorter than that in CoO (2.15 Å). The electron and hole defects have longer and shorter Co−O distances than the regular Co ions in LiCoO2 but shorter and longer Co−O distances than those in divalent and tetravalent cobalt ions, respectively. This is ascribed to the constraint on the lattice of LiCoO2. LiMnO2 also preferentially forms localized states of the electron and hole defects. LiNiO2 and Li(Li1/3Mn2/3)O2 preferentially have localized electron defects. The localized electrons exhibited longer M−O distances than the regular ions but shorter distances than the ions in NiO and LiMnO2, similarly to in LiCoO2. In contrast, the holes in LiNiO2 and Li(Li1/3Mn2/3)O2 exhibit delocalized states. Small polaron of the hole (localized Ni4+) is suggested in LiNi0.8Co0.2O2 by electrical conductivity measurements and thermoelectronic power measurements.37 The state of the hole would be dependent on the magnitude of the localization of the Ni-3d orbital, and thus on the U parameter in the GGA+U framework. However, the predominant defect in LiNiO2 is the antisite nickel ion at the lithium site (NiLi) as will be mentioned later, and the state of the hole only insignificantly affects the defect chemistry discussed in the present work. The delocalized holes in Li(Li1/3Mn2/3)O2 are qualitatively consistent with the electronic states after the removal of lithium ions, in which the charge of the removed lithium ions is compensated by the holes at the oxygen ions instead of the manganese.12,23 Although the holes can be delocalized in these oxides, their concentrations were estimated using eq 2 from the number of transition-metal ions. Defect Chemistry at High Temperatures. The electrode active materials of lithium-ion batteries are often synthesized by solid-state reaction processes,38 and defects can be formed at high temperatures in these processes. Some of the defects may vanish during cooling to room temperature, but other defects may remain in the samples owing to their slow diffusion at low temperatures. The residual defects are the origin of the characteristics and properties of the materials. Knowledge of the defect chemistry at high temperatures is essential to optimize the synthesis conditions. Therefore, the concentrations of point defects under equilibrium at high temperatures are examined in this section. Temperature was used as a variable in the investigation. The atomic chemical potential of oxygen at temperature T and partial pressure PO2 is given as 1 μO= GO2 2 ⎛ PO2 ⎞⎞ 1⎛ 0 0 = ⎜EODFT + ( G ( T ) − G (0 K)) + k T ln ⎜ 0 ⎟⎟ O O B 2 2 2⎝ 2 ⎝ P ⎠⎠ (5)

where EDFT O2 is the energy of an O2 molecule obtained by DFT calculation, which corresponds to the Gibbs free energy at 0 K without the zero-point energy. G0O2 is the Gibbs free energy of the gaseous O2 phase under the standard pressure P0 as a function of temperature, which is estimated by assuming it to be an ideal gas on the basis of experimental results.39 The oxygen partial pressure was fixed at 0.2 atm. With these two

Figure 2. Equilibrium defect concentrations at high temperatures in (a) LiCoO2, (b) LiNiO2, (c) LiMnO2, and (d) Li(Li1/3Mn2/3)O2. The chemical conditions are under equilibrium with 0.2 atm oxygen gas and solid Li2O phases. The concentrations are given both per formulaunit (in f.u.−1) and per volume (in cm−3). D

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small polaron, namely a (CoLi+ + h+) complex. The oxygen vacancy (VO) is a minor defect in LiCoO2 at very high temperatures as shown in Figure 2(a). The oxygen vacancy leads to 5-fold-coordinated cobalt ions (see Figure 1(d)). The PDOS of nearest-neighboring 5-fold-coordinated cobalt ions and the average PDOS of the other cobalt ions in the supercell for the VO2+ defect are illustrated in Figure 3(c). The 5-foldcoordinated cobalt ions are in the trivalent state with an intermediate-spin configuration, in which four electrons occupy the majority spin state and two electrons occupy the minority state. This intermediate-spin configuration was proposed by Levasseur et al. for a defect complex of the oxygen vacancy (VO) and an antisite lithium ion (LiCo) in lithium-overstoichiometric LixCoO2 (x > 1).40 Our calculations suggest that the intermediate-spin configuration is also stable for the oxygen vacancy even without the associated antisite lithium ion. LiCoO2 is generally synthesized at 800−900 °C.38 The equilibrium concentration of the CoLi defect is calculated to be as low as 1% at 1200 K, suggesting that LiCoO2 with low defect concentrations can be easily obtained. The antisite nickel ion at the lithium site (NiLi) is dominant in LiNiO2 (Figure 2(b)), as similarly to in LiCoO2. The dominant valence of the antisite defect is NiLi0. It is, more specifically, a complex consisting of a NiLi+ antisite defect and a nearest-neighbor electron small polaron (Ni2+ at the regular nickel site), namely a (NiLi+ + e−) complex. By removing an electron from the NiLi0 defect complex, the nearest-neighbor Ni2+ ion is oxidized to the trivalent state. Upon the removal of another electron, a hole is introduced into regular nickel ions, while the antisite nickel ion still remains in the divalent state. Figure 4(a) and (b) illustrates the PDOS of the nickel ions in pristine LiNiO2 and that of the antisite nickel ion and the average of the other nickel ions in the supercell for the NiLi+ defect, respectively. The antisite nickel ion makes a smaller

temperature range shown in Figure 2(a) is CoLi+, and the antisite cobalt ion is in the divalent state with the high-spin configuration. The excess charge is compensated by an electron small polaron (Co2+ at the regular cobalt site). The large space at the lithium site (2.11 Å for the regular Li−O distance in the calculation) can be ascribed to the lower valence and high-spin configuration of the antisite cobalt ion. The calculations indicate that the CoLi+ defect is more difficult to oxidize than the regular cobalt ions. Figure 3(a) and (b) illustrates the

Figure 3. Projected density of states (PDOS) of cobalt ions in LiCoO2 for (a) pristine LiCoO2, (b) (red) antisite cobalt ion (CoLi+) and (blue) average of the other regular cobalt ions, and (c) (red) nearestneighboring cobalt ions of the oxygen vacancy (VO2+) and (blue) average of the other cobalt ions. Schematic local structures of the defects are illustrated as insets. The Fermi energy is set at zero.

projected density of states (PDOS) of the cobalt ions in pristine LiCoO2 and that of the antisite cobalt ion and the average of the other cobalt ions at the regular sites in the supercell for the antisite CoLi+ defect, respectively. The regular cobalt ions for the antisite CoLi+ defect have a similar PDOS to the cobalt ions in pristine LiCoO2. The electronic states just below the Fermi energy (0 eV) are dominated by the regular cobalt ions. On the other hand, the occupied 3d states of the antisite cobalt ion have a rather deep energy level. Consequently, the more oxidized defect, CoLi2+, is actually not a single antisite defect of a Co3+ ion at the lithium site but a pair consisting of a CoLi+ defect and a nearest-neighboring hole

Figure 4. Projected density of states (PDOS) of nickel ions in LiNiO2 for (a) pristine LiNiO2 and (b) (red) antisite nickel ion (NiLi+) and (blue) average of the other regular nickel ions. Schematic local structure of the defect is illustrated as an inset. The Fermi energy is set at zero. E

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defects are of importance only when the temperature is very high. This suggests that Li(Li1/3Mn2/3)O2 with a low defect concentration is easily synthesized. Large formation energy of the electron and hole pair of 1.71 eV (see the Supporting Information) and the low defect concentration suggest low conductivity, which is consistent with the insulator behavior observed by experiments.47 In the structure of Li(Li1/3Mn2/3)O2 with the C2/m space-group symmetry, there are two oxygen sites, 4i and 8j in Wyckoff notation. The oxygen vacancy is more stable at the 8j site than at the 4i site by 0.3 eV. Okamoto also reported the stability of the oxygen vacancy at the 8j site on the basis of similar DFT calculations on oxygen-defective Li2MnO3.12 In this way, the defect concentrations under thermal equilibrium at high temperatures were estimated for the layered lithium transition-metal oxides based on first-principles calculations. The calculations indicate low defect concentrations in LiCoO2 and Li(Li1/3Mn2/3)O2, suggesting that they are insulators. In LiNiO2, the antisite nickel is dominant and unavoidable, and Ni3+ ions are easily reduced to Ni2+. In contrast, Mn3+ ions are easily oxidized to Mn4+ in LiMnO2 under ordinary high-temperature synthesis conditions. These results are highly consistent with the characteristics and conductive properties of the oxides observed in experiments.1,2,37,45−47 The differences in the defect concentrations and the formation energy of the electron and hole pair between LiCoO2 and LiNiO2 can explain well that the insulator−metal transition upon the lithium removal is observed in LiCoO2 and it is not in LiNiO2 and its derivatives.37,45,46 Unfortunately, the defect concentrations are very difficult to measure accurately in such lithium transition-metal oxides. The defect chemistry based on first-principles calculations can provide more quantitative information on the characteristics of electrode active materials than conventional experimental techniques. Defect Chemistry under Reductive Conditions. The defect chemistry at high temperatures is consistent with the characteristics of electrode active materials. However, chemical conditions in lithium-ion batteries are different from those in air. As organic liquid electrolytes are used in lithium-ion batteries, the conditions are strongly reductive. In this section, we report the defect chemistry under equilibrium with strongly reductive conditions at room temperature to discuss the surface states of electrode active materials in contact with organic electrolytes. At room temperature, the diffusion of transitionmetal and oxygen ions is very slow. The approximate diffusion length, x, can be estimated as x ∼ (Dt)1/2, where D is the diffusivity and t is the diffusion time. Assuming a diffusivity of 10−20 cm2/s and a time of 10 days, the diffusion length is about 1 nm. [Diffusivity is estimated assuming hopping of noninteractive particles as D = (1/2d)a2ν0 exp(−EA/kBT), where d is the diffusion dimension, a is the hopping length, ν0 is the attempt frequency, EA is the activation potential barrier for the hopping, kB is the Boltzmann constant, and T is the temperature. Assuming d = 2, a = 2.8 Å, ν0 = 1013 s−1, EA = 1 eV, and T = 300 K, one obtains D = 3 × 10−20 cm2/s. Since experimental values are unknown for ν0 and EA, the diffusivity is just a rough estimate.] Hence, the defects of the transitionmetal and oxygen in the bulk are likely to be frozen even in organic electrolytes. From another viewpoint, nanometer-scale surfaces of the samples can be affected by the chemical conditions in the electrolytes even at room temperature. Therefore, possible defects on the nanometer-scale surfaces are

contribution to the electronic states just below and above the Fermi energy than the regular nickel ions, and the antisite nickel ion is more stable in the divalent state. The antisite transition-metal ion at the lithium site preferentially exists in the divalent state for both LiCoO2 and LiNiO2. However, the antisite defect is more easily formed in LiNiO2, and the concentration of such defects rapidly increases as the temperature increases. The concentration was calculated to be more than 10% at 800 K. The high concentration of the antisite NiLi defect suggests formation of a wide range of solid solution between LiNiO2 and NiO. The existence of the antisite nickel ions is well-known by experiments, and more than 10% of the antisite nickel ion (x > 0.1 in Li1‑xNi1+xO2) has been reported.1,2 Therefore, development of the synthesis process to reduce the antisite ions has been an issue of LiNiO2. LiNiO2 is usually synthesized at lower temperatures (600−750 °C) than LiCoO2 under pure oxygen gas.38 The calculations suggest that the antisite defect and thus the excess nickel are unavoidable in LiNiO2, and such oxidative conditions are necessary to synthesize LiNiO2 with fewer defects. It should be noted that the defect calculation technique used in the present work assumes noninteractive defects. When the interaction between the defects is not negligible, systematic error may be made under high defect concentration. Other approaches, for instance, the cluster expansion technique, should be employed for quantitative estimation of the high defect concentrations.41−44 LiCoO2 exhibits the insulator−metal transition, where significant change in the conductivity and activation energy occurs upon the lithium removal.45,46 On the other hand, LiNi0.8Co0.2O2 shows much smaller changes upon the lithium removal.37 The different behavior of the conductive properties is consistent with the calculation results. The defect concentrations in LiCoO2 is expected to be low, as already mentioned. In addition, the calculated formation energy of the electron and hole pair is 1.36 eV (see the Supporting Information), resulting in low concentration of either electron or hole. The lithium removal generates a hole simultaneously with a lithium vacancy, resulting in a drastic increase in the hole concentration. In contrast, LiNiO2 contains high concentration of the antisite nickel ion, and the formation energy of the electron and hole pair is as low as 0.38 eV. This leads to high concentrations of the electron and hole in LiNiO2, and the lithium removal causes a gradual change of the hole concentration. Therefore, the insulator−metal transition is clearly observed in LiCoO2, while it is not in LiNiO2 and its derivatives. In contrast to LiCoO2 and LiNiO2, the antisite lithium ion at the manganese site (LiMn) is dominant in LiMnO2, as shown in Figure 2(c). The antisite defect is coupled with one or two hole small polarons, namely LiMn− (LiMn2‑ + h+) or LiMn0 (LiMn2‑ + 2 h+) complexes. The concentration of antisite defects was calculated to be 10% or more at temperatures below 800 K. The dominance of the antisite lithium ion associated with the holes (Mn4+) suggests that the layered LiMnO2 phase can exist as a solid-solution system between LiMnO2 and Li(Li1/3Mn2/3)O2 (Li2MnO3). This is reasonable since Li(Li1/3Mn2/3)O2 is one of the stable phases of the lithium manganese oxides synthesized in air, and these two layered oxides can be merged into each other from the structural viewpoint. As shown in Figure 2(d), the interstitial lithium ion (Lii) is dominant below 1000 K and the oxygen vacancy (VO) is dominant above 1100 K in Li(Li1/3Mn2/3)O2. However, the concentrations of these F

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discussed on the basis of the results of first-principles calculations for the bulk. As little thermodynamic data are available for electrolytes, the chemical conditions, particularly the oxygen chemical potential, in organic liquid electrolytes are unclear. The Gibbs free energy change of the full oxidation reaction of ethylene carbonate (EC) in the solid phase to H2O and CO2, namely 2 EC (solid) + 5 O2 (gas) → 6 CO2 (gas) + 4 H2O (liquid), is reported to be −2,400 kJ/mol (−25 eV) at room temperature.48 This means that EC can be thermodynamically oxidized unless the atomic oxygen chemical potential is lower than −2.5 eV, which corresponds to 10−85 atm partial pressure of O2 gas at room temperature. In reality, organic electrolytes are likely to be oxidized through intermediate products, for instance, alkyl carbonates, and thus the oxygen chemical potential depends on the reaction path. As organic electrolytes are often mixtures of several components, consideration of the mixing effect on the activity of each component is necessary for precise estimation of the oxygen chemical potential. To discuss the defect chemistry under strongly reductive conditions, the oxygen chemical potential was treated as a variable in this investigation. The temperature was set at 300 K. The lithium chemical potential was assumed to be under equilibrium between the surface and bulk, and the bulk was assumed to have been under equilibrium with 0.2 atm O2 gas and Li2O before the sample was immersed in the electrolyte. The lithium chemical potential in this condition can be described as μ Li(surface) = μ Li(bulk) 1 1 = E LiDFT GO (300 K, 0.2 atm) O − 2 2 4 2

(6)

where EDFT Li2O is the energy of Li2O obtained by the DFT calculation. The Gibbs energy of oxygen gas, GO2, was estimated by eq 5. See also the Supporting Information for the chemical potentials of oxygen and lithium in this study. Equilibrium defect concentrations were examined under these chemical conditions for LiCoO2, LiNiO2, and Li(Li1/3Mn2/3)O2. As the concentration of the antisite lithium ions in LiMnO2 is too high in the standard state, LiMnO2 was excluded from this discussion. Figure 5 illustrates the equilibrium defect concentrations in LiCoO2, LiNiO2, and Li(Li1/3Mn2/3)O2 as a function of the atomic oxygen chemical potential. In the standard state, the defect concentrations are very low in these three oxides. As the oxygen chemical potential decreases, the concentrations of antisite transition-metal ions, MLi (M = Co, Ni, and Mn), increase. Finally, the concentrations of the antisite defects become close to unity at low oxygen chemical potentials. Under such conditions, the defect concentrations are too high, and these oxides are no longer regarded as the LiMO2 phases. The instability of the LiMO2 phases at the low oxygen chemical potentials is also suggested by the stable regions in the chemical-potential diagrams (see the Supporting Information). Among the three oxides, it is particularly easy for LiNiO2 to form the antisite defect. NiO-like surface components have been reported for LiNiO2-based materials after charging and discharging cycles on the basis of transmission electron microscopy (TEM),49 X-ray absorption spectroscopy (XAS) measurements,49 and hard X-ray photoemission spectroscopy (HX-PES).50 The tendency to form the antisite defect at a low oxygen chemical potential is greater for LiNiO2 than for

Figure 5. Equilibrium defect concentrations at 300 K under given atomic oxygen chemical potentials in (a) LiCoO2, (b) LiNiO2, and (c) Li(Li1/3Mn2/3)O2. The atomic oxygen chemical potential in the standard state at 300 K is set at zero. See the text for details of the chemical conditions. The concentrations are given both per formula unit (in f.u.−1) and per volume (in cm−3).

LiCoO2 and Li(Li1/3Mn1/3)O2, which is consistent with the defect chemistry at high temperatures (Figure 2). Although LiCoO2 and Li(Li1/3Mn2/3)O2 are more stable against reduction than LiNiO2, the surfaces of these oxides are in somewhat reduced states under the strongly reductive conditions of organic electrolytes. Recently, our co-workers have found that the cobalt ions at the surface of LiCoO2 are reduced after immersion in organic electrolytes as a result of performing HX-PES on composite electrodes,51 surfacesensitive XAS techniques on thin-film model electrodes,52,53 and solid-state nuclear magnetic resonance (NMR) measurements.54 Surface reduction appears to be a feature of electrode active materials in lithium-ion batteries and responsible for the deterioration of the active materials. Formation Energies of Li Vacancy/Interstitial and Electrode Potentials. The charging and discharging processes in lithium-ion batteries respectively correspond to the removal and insertion of lithium ions from/into the electrode active materials. Therefore, the formation of the lithium vacancy (VLi) and the interstitial lithium ion (Lii) can be considered as the first elementary reactions in the charging and discharging processes, respectively. The defect formation energies and electrode potentials are herein compared. Table 3 summarizes G

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insertion into LiCoO2 is as low as 1.18 V. Considering the low formation energy of the interstitial lithium ion and the possible large hysteresis in the voltage profile, a very low potential should be needed to insert lithium into LiCoO2. Comparing LiMnO2 and Li(Li1/3Mn2/3)O2, the electrode potential of LiMnO2 for the lithium insertion reaction is slightly higher, but the formation energy of the interstitial lithium ion is lower. This implies that lithium insertion into LiMnO2 is difficult owing to the large hysteresis in the voltage profile. In contrast, lithium insertion is possible for Li(Li1/3Mn2/3)O2. By understanding both the defect formation energies and electrode potentials, it is possible to quantitatively describe the electrode behavior of the active materials.

Table 3. Defect Formation Energies and Average Electrode Potentials for LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3)a defect formation energy (eV)

a

average electrode potential (V)

compound

Li vacancy

Li interstitial

Li removal

Li insertion

LiCoO2 LiNiO2 LiMnO2 Li(Li1/3Mn2/3)O2

3.97 3.88 3.60 4.58

−0.54 −1.26 −0.84 −1.02

3.88 3.74 3.48 4.62

1.18 2.51 1.83 1.73

The lithium chemical potential is set at that of lithium metal.

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the defect formation energy of the neutral lithium vacancy (VLi0) and that of the neutral lithium interstitial (Lii0). The lithium chemical potential is set at that of lithium metal. Table 3 also shows the average electrode potentials of the lithium removal reaction (LiMO2 → MO2 + Li) and those of the lithium insertion reaction (LiMO2 + Li → Li2MO2). The average electrode potentials EAVE were estimated as EAVE = −

CONCLUSIONS Defect chemistry in the series of layered lithium transitionmetal oxides LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3) was investigated by systematic first-principles calculations. The electron defects are localized as small polarons in these four oxides. The hole defects are localized in LiCoO2 and LiMnO2, whereas they are delocalized in LiNiO2 and Li(Li1/3Mn2/3)O2. The calculations indicate that LiCoO2 and Li(Li1/3Mn2/3)O2 with low defect concentrations are easily synthesized unless the synthesis temperature is very high. In LiNiO2, the antisite nickel ion is the dominant defect and unavoidable, and Ni3+ ions are easily reduced to Ni2+. In contrast, Mn3+ ions are easily oxidized to Mn4+ in LiMnO2 with the antisite lithium ion under ordinary high-temperature synthesis conditions. The differences in the defect concentrations and the formation energy of the electron and hole pair between LiCoO2 and LiNiO2 suggest that the insulator−metal transition upon the lithium removal is observed in LiCoO2 and it is not in LiNiO2 and its derivatives. These results are highly consistent with the characteristics and conductive properties of the oxides observed in experiments. Such knowledge of the defect chemistry at high temperatures is essential to optimize the synthesis conditions. The first-principles calculations also suggest that the surfaces of the oxides are reduced at a nanometer scale by immersion of the samples in the organic electrolyte of lithium-ion batteries. The stability to the surface reduction is consistent with the defect chemistry at high temperatures. The surface reduction appears to indicate the nature of electrode active materials of lithium-ion batteries and is considered responsible for the deterioration of the active materials. The formation of the lithium vacancy and interstitial lithium ion correspond to the charging and discharging processes of electrode active materials, respectively. The defect formation energies in conjunction with the electrode potentials can quantitatively describe the electrode behavior of the active materials. The defect chemistry based on the first-principles calculations can provide more quantitative information on the electrode active materials than conventional experimental techniques. The surface states in contact with the organic liquid electrolyte can also be revealed, which are difficult to investigate by conventional experiments.

DFT E LiDFT − E LiDFT M O2 − ΔnE Li 1 +ΔnM O2

Δne

(7)

where e is the elementary charge, and Δn is the change in the number of lithium ions (Δn = −1 for the lithium removal reaction and Δn = +1 for the lithium insertion reaction). O3 and T1-type stacking sequences were employed for the structures of MO2 and Li2MO2, respectively. Note that the electrode potential for the lithium removal reaction corresponds to the positive formation energy of the lithium vacancy, whereas the electrode potential for the lithium insertion reaction corresponds to the negative formation energy of the interstitial lithium ion by definition. The defect formation energies of the lithium vacancies in these oxides are comparable to the electrode potentials of the lithium removal reaction. This suggests that the formation of the lithium vacancy is indeed the elementary reaction of the charging process. The inconsistency of the quantities can be ascribed to differences in the amount of removed lithium ions: a single ion is removed in vacancy formation, whereas cooperative full removal occurs in the charging. In contrast to the removal of lithium, a considerable difference is found between the defect formation energies of the interstitial lithium ions and the electrode potentials of the lithium insertion reaction. The lithium insertion reaction for LiNiO2 has been observed experimentally to occur at 1.9 V, and the corresponding lithium removal reaction occurs at 2.5 V with a large hysteresis in the voltage profile.55 The calculated potential for lithium insertion into LiNiO2 was consistent with the average of the experimental potentials. In the formation of the lithium interstitial, the structure of LiNiO2 is maintained, and the interstitial lithium ion shares its faces with the neighboring lithium and nickel ions. On the other hand, a cooperative structural change occurs during the lithium insertion reaction, and the stacking sequence is changed from the O3-type to the T1-type. The lithium ions share only their edges in T1-type Li2NiO2. This structural change is the cause of the large underestimation of the potential by considering the defect formation energy of the interstitial lithium ion. The structural change dissipates the energies of lithium insertion and reremoval, and thus, a large hysteresis can be expected in the voltage profile. Lithium insertion into LiCoO2 has not been observed even at 1 V. The calculated potential for lithium

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ASSOCIATED CONTENT

* Supporting Information S

DFT calculation for pristine LiMO2, chemical potentials for LiMO2, and defect formation energies in LiMO2 (M = Co, Ni, Mn, and Li1/3Mn2/3). This material is available free of charge via the Internet at http://pubs.acs.org. H

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by the Research and Development Initiative for Scientific Innovation of New Generation Battery (RISING) project from New Energy and Industrial Technology Development Organization (NEDO), Japan. The authors thank Dr. Daiko Takamatsu and Dr. Yuki Orikasa at Kyoto University in Japan for fruitful discussions on surface states of the electrode active materials.

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