First-Principles Study of the Charge Transport Mechanisms in Lithium

Article pubs.acs.org/cm

First-Principles Study of the Charge Transport Mechanisms in Lithium Superoxide Shunning Li, Jianbo Liu,* and Baixin Liu Key Laboratory of Advanced Materials (MOE), School of Materials Science and Engineering, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: Lithium−air batteries have attracted intense interest due to their high energy density, yet their practical applications are still severely hindered by the low conductivity of lithium peroxide (Li2O2). Here, we perform first-principles calculations on the recently synthesized lithium superoxide (LiO2) which has the potential to replace its peroxide counterpart as the discharge product. Using HSE hybrid functional, we predict an electrical insulating behavior for LiO2. Excess electrons and holes will be localized on the oxygen dimer, thus forming small polarons that can diffuse by hopping between lattice sites. With the calculated concentrations and mobilities of the intrinsic charge carriers, we show that the charge transportation in LiO2 is governed by the migration of hole polarons and positively charged oxygen dimer vacancies. The electronic conductivity associated with polaron hopping (3 × 10−12 S cm−1) exceeds that of Li2O2 by 8 orders of magnitude, while a comparable value (4 × 10−12 S cm−1) is found for the ionic conductivity contributed by superoxide ions. Our calculations provide a detailed understanding of the role of small polarons in describing the charge transport properties of LiO2.

1. INTRODUCTION With the ever increasing global reliance on electrical energystorage technologies, it is only natural that we should search for advanced battery systems which could go beyond the horizon of lithium-ion batteries. One area of interest has been the lithium−air (Li−O2) system. The rechargeable Li−O2 battery is typically composed of a Li metal anode separated by an electrolyte solution from a gas electrode that utilizes oxygen in the cathode reaction. Ever since the earliest publications in the mid-1990s, the study of Li−O2 cells has evolved into a major field of contemporary research, owing to their high theoretical energy density which is several times that of the current Li-ion technologies.1−6 However, despite the great promise of the Li−O2 cells, their application remains difficult due to the large overpotentials, low rates, and early cell death, which altogether result in significantly degraded energy storage efficiency. In order to settle these issues, particular attention has been given to the theoretical analysis of the thermodynamics,7−9 charge transportation,10−17 and reaction kinetics18−21 in lithium peroxide (Li2O2, the dominant reaction product). In this context, recent first-principles studies15−17 pointed out that the electronic conduction in Li2O2, which is a wide band gap insulator in the bulk, relies mainly on the hopping of hole polarons, while the ionic conduction is presumably governed by the negatively charged lithium vacancies. Accordingly, Li2O2 is known as a mixed conductor, in which the conductivity comprises a larger fraction of the ionic contribution (9 × 10−19 S cm−1) than the electronic one (5 × 10−20 S cm−1).15 Some experimental investigations have also offered support for this notion.22,23 © 2017 American Chemical Society

These low conductivity values are expected to lead to unsatisfactory performance of Li−O2 cells,10,24,25 such as the sudden death far below the theoretical capacity. The limited ability to improve the transport property of Li2O2 inevitably necessitates novel designs that can suppress the formation of Li2O2 films on the cathode surface. Thus, the challenge is to either promote formation of Li2O2 in the electrolyte solution, as was accomplished recently by Gao et al.,26 or replace the peroxide by another discharge product that can afford higher electronic conductivity. The lithium superoxide (LiO2) captures our eyes when we choose to follow the latter route. Building a Li−O2 battery with LiO2 as the discharge product may offer the opportunity to circumvent the conductivity problem, but there is still a long way to go. Nowadays, a general consensus has been reached that the reduction of O2 to Li2O2 on discharge proceeds as follows:27−30 O2 + Li+ + e− → LiO2

(1)

2LiO2 → Li 2O2 + O2

(2)

LiO2 + Li+ + e− → Li 2O2

(3)

LiO2 is thereby known to be an intermediate in the reaction. In situ spectroscopic data have identified the existence of LiO2, but thermodynamic instability has rendered it subject to disproportionation into Li2O2 and O2.31−34 Most recently, Lu et al.35 have synthesized crystalline LiO2 in pure form by using Received: November 25, 2016 Revised: January 24, 2017 Published: February 15, 2017 2202

DOI: 10.1021/acs.chemmater.6b05022 Chem. Mater. 2017, 29, 2202−2210

Article

Chemistry of Materials

Nevertheless, some previous experimental observations suggested the marcasite structure (in Pnnm symmetry) as a major candidate for the ground-state configuration.50,51 This is further justified by several theoretical studies which took into account a number of possible polymorphs for LiO2.7,8,52 Moreover, the high-energy XRD patterns for LiO2, that are recently produced by using the Ir-graphene cathode, have revealed the characteristic peaks that showed strong correlation with the marcasite structure.35 Consequently, we adopt the marcasite structure (Figure 1a) for our calculations in the present work.

a graphene cathode decorated with iridium (Ir) nanoparticles; they showed that the LiO2 formed in the Li−O2 battery is stable during repetitive charge and discharge cycles, and characteristic of a relatively low overpotential. In order to elucidate the conductivity mechanism, some studies using firstprinciples calculations and reporting on the band structure of LiO2 have been carried out.35−37 However, there exist important mismatches between different theoretical methods. The density functional theory (DFT) calculations with generalized gradient approximation (GGA) predict a metallic behavior for LiO2,35,37 while calculations using hybrid functionals observe a band gap of about 3.7 eV.36 Generally, the hybrid functionals are expected to offer a more accurate description of the electronic structure than the standard semilocal DFT functionals, which tend to overdelocalize electrons due to their intrinsic self-interaction errors.38 Several papers have been published using HSE hybrid functional to study the charge transport phenomena in Li2O2, Na2O2, and NaO2.12,13,15,17,39,40 Thus, it would be necessary that we reexamine the band structure with the HSE method. Our calculation result agrees quite well with the value of ref 36, and LiO2 is consequently considered to be an insulator. In such case, both electrons and holes would probably be self-trapped on oxygen dimers forming quasiparticles which are known as electron/hole polarons, similar to those found in Li2O2.12,13 It is therefore of practical importance as well as of fundamental interest to learn whether and how the polaron migration can effect charge transportation in LiO2. Moreover, to the best of our knowledge, there is, so far, no investigation available on the defect chemistry and the interaction between polarons and other point defects (vacancies and interstitials) in LiO2. These aspects will also be addressed in the present work. In this report, we perform a detailed first-principles analysis of the intrinsic conductivity in LiO2. The key issues relate to the role of point defects (polarons, vacancies, and interstitials) on the material’s charge transportation. This Article is organized as follows. A description of the computational implementation is first provided. In the following, we present results on the structure, energetics, and migration of intrinsic point defects. The relation between polarons and other point defects are also preliminarily discussed. Lastly, the concentrations and mobilities of the dominant charge carriers are determined, which are then used to predict the electronic and ionic conductivity in LiO2.

Figure 1. Crystal structure of LiO2 described in this study. (a) The marcasite unit cell (marked with black dashed lines). Each Li is bonded with six O atoms. (b) A 3 × 2 × 3 supercell model with unit cells outlined by green lines. A 3 × 2 × 3 supercell consisting of 108 atoms (Figure 1b) was constructed to model isolated point defects with a single k-point at Γ in the irreducible Brillouin zone. To maintain consistency with the electronic structure calculations, we have chosen to use HSE for the structural optimization of all the defects. The charged defects were calculated by adding or removing an electron to or from the supercell, with an additional homogeneous background charge to maintain charge neutrality in the system. However, slow convergence with respect to the supercell size is expected for the electrostatic energy between the introduced charge and its periodic images, which means that the calculated properties only converge to those of the aperiodic system in the limit of an infinitely large supercell.53 To compensate for this spurious energy, the first-order Makov-Payne correction53 was included in our work. A spatially averaged dielectric constant of 10, calculated with the aid of the perturbation expansion after discretization method,54 was taken to serve as input for the scheme. This yields a correction of EMP = 0.20 eV for defects with a charge of q = ±1 in the supercell. Within the supercell formalism for describing charged defects, the formation energy of a defect X in charge state q is expressed as55,56 E f [X q] = Etot[X q] − Etot[P] −

∑ niμi + q(EF + εVBM) + EMP i

2. METHODOLOGY

(4) where Etot[Xq] and Etot[P] are the total energies of the supercell with and without the defect. ni indicates the number of atoms of type i that have been added to (ni > 0) or removed from (ni < 0) the supercell when the defect is formed, and μi is the corresponding chemical potential of the atoms. EF is the Fermi level with respect to the energy of the bulk valence band maximum (VBM), εVBM, and is bounded between the VBM and the conduction band minimum (CBM), i.e., 0 < EF < Eg, where Eg is the band gap. EMP is the first-order MakovPayne correction. The atomic chemical potentials are on one hand connected by the relation μLi + 2μO = Etot[LiO2], with Etot[LiO2] being the total energy of LiO2 per unit formula, and on the other hand limited by the Li2O2 bulk phase in the Li-rich end and by the O2 molecule in the O-rich end. In this work, we only present results under the O-rich conditions, since the discharge products are usually assumed to be in equilibrium with oxygen in the atmosphere. Knowing that DFT calculations tend to overbind gas-phase O2, a correction of 0.27 eV for the ground-state energy of the O2 molecule was applied on the basis of the relation between the experimental and calculated formation enthalpies of marcasite NaO2,57 because no experimental

Our calculations were performed using the plane-wave based DFT method as implemented in the Vienna ab initio simulation package (VASP),41,42 with the projector augmented wave approach43,44 used to describe the interaction between the core and valence electrons. The geometries and the electronic structures were relaxed by both a standard GGA functional in the framework of Perdew−Burke− Ernzerhof (PBE)45 and a hybrid functional in the framework of HeydScuseria-Emzerhof (HSE).46 A cutoff energy of 460 eV for the plane wave basis set was used in each case, and the k-point sampling employed an 8 × 8 × 8 mesh within the Monkhorst−Pack scheme.47 A convergence threshold of 0.02 eV Å−1 in force was reached for all the configurations. As a common practice, many-body perturbation theory (GW)48,49 was applied to allow for the calculation of more accurate band gaps. We have also explored the possible spin configurations and found that ferromagnetic configuration is most stable having an energy difference of ∼9 meV per unit cell as compared with the configurations with antiferromagnetic order. Regarding the crystal structure for LiO2, it should be noted that no standard X-ray diffraction (XRD) pattern has yet been established. 2203


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Chemistry of Materials value for LiO2 is available at this time. Prior studies within the GGAPBE framework have determined the O2 reference by the linear fit between the experimental and calculated values for different alkali metal oxides, peroxides, and superoxides.20,58,59 However, we note that the deviation from a linear trend is significant in our HSE calculations, which may be partially due to the different atomic interaction exerted by different crystal structures. Therefore, we used the energy correction based on NaO2 which shares the same structure with LiO2. In thermodynamic equilibrium, the concentration of a defect is given as a function of its formation energy55

c = Nsitesexp(− E f /kT )

molecular orbitals, for which quantum-mechanical splitting of the energy levels among bonding (σ, π) and antibonding (π*, σ*) states is clearly evident. The density of states (DOS) at the Fermi level in the minority-spin π* states produces the halfmetallic character for LiO2, which is in agreement with the literature.35,37 As opposed to the GGA-PBE calculation, the HSE calculation opens the band gap by splitting these π* states, as seen in Figure 2b. Here, a mixing parameter of α = 0.48 is selected, as first proposed by Radin and Siegel,15 from which we obtain a band gap of 3.6 eV, close to the result of 3.7 eV by Lee et al.36 The mixing parameter is by definition the percentage of the exact (Hartree-Fork) exchange added to the short-range part of the PBE exchange functionals.46 The choice of the mixing parameter α is empirical and can vary from case to case,62 similar to the choice of U in the GGA + U approach. Previous studies have shown that the calculated properties for Li2O2 would exhibit a relatively strong dependence on the mixing parameter.15,17 Hence, four values are tested here for α: 0.25, 0.35, 0.48, and 0.60, whose influence on the band gap is demonstrated in Figure 2c. Although the gross features of the electronic structure do not change in a drastic way with the value of α, the band gap does depend linearly on this parameter. Similar trends are observed by Varley et al.17 in Li2O2, and by Araujo et al.40 in Na2O2. In the Supporting Information, the calculated lattice parameters and the band edges (VBM and CBM) in marcasite LiO2 are also summarized for different α. Since no experimental data are available, it would be difficult to optimize the mixing parameter precisely and effectively. In this case, we choose to adopt the value of 0.48 and closely follow the methodology described in refs 15 and 39 so that consistent comparisons can be made between the present work on LiO2 and the previous studies. Additional details concerning the dependence of band structure and defect energetics upon α are provided in the Supporting Information. A better estimate of the band gap can be determined by the non-self-consistent GW approximation on top of the HSE06 (α = 0.25) functional, i.e., [email protected] Within this scheme, the band gap of LiO2 is calculated to be 4.02 eV, which not only manifests a wide band gap insulating feature comparable to that of Li2O215,17 but also indicates that α = 0.25 could not meet the need for the cancellation of self-interaction errors, and hence, a higher value for α is needed. Although experimental data on the conductivity of LiO2 are still elusive, recent evidence from other alkali metal superoxides, including NaO2,39,63 KO2,64,65 and RbO2,64,66 seems to justify their insulating nature and support the idea that the electronic carriers are localized on the oxygen dimers. It should be mentioned here that the traditional PBE functional produces a metallic state for NaO2, which is in contradiction to the experimental results,63 while HSE calculation yields a splitting of the oxygen p states near the Fermi level, giving rise to a band gap of ∼2 eV.39 The suppression of metallic-type conductivity is believed to be related in part to the moderate overlap between the orbitals of the oxygen dimers, which is better captured by the HSE functionals. Apparently, in our study, LiO2 has been shown not to be an exception to the insulating feature shared by other reported superoxides. 3.2. Energetics and Electronic Structures of the Defects. The migration of charged defects under the influence of the electric field may contribute to the conductivity in LiO2. Following eq 4, we calculated the formation energies of various intrinsic point defects in all possible charge states. These

(5)

Here, Nsites is the number density of sites in the lattice where the defect can be incorporated, k is Boltzmann’s constant, and T is the temperature. It follows from this equation that lower formation energy will imply higher equilibrium concentration of the corresponding defect in the bulk. Activation barriers and minimum energy pathways for the defect migration were obtained using the nudged elastic band (NEB) method60 with the HSE functional. Since the paths are relatively simple, a chain of five images was sufficient to achieve a reasonable approximation to the transition state. Assuming that the diffusion of defects utilizes a random-walk mechanism, the mobility of a defect is calculated by61

μ=

ν(Δx)2 Ze ⎛ Ea ⎞ exp⎜ − ⎟ ⎝ kT ⎠ kT

(6)

where ν is the attempt frequency for a jump, which is usually taken to be the atomic vibration frequency, i.e., a value of about 1013 Hz at room temperature. Δx is the distance between the hopping sites, Ze is the charge of the defect, and Ea is the activation barrier of the hop. The conductivity due to charged defects moving through a crystal is then given by the following formula:61 σ = cμZe

(7)

3. RESULTS AND DISCUSSION 3.1. Bulk Properties. As a benchmark test for our parametrization, we first examine the electronic structure of perfect bulk LiO2. Figure 2a provides the band structure in the GGA-PBE calculation. The electronic states in the energy range between −8 and 7 eV are attributed to the localized oxygen 2p

Figure 2. Electronic band structure and density of states plots of bulk LiO2 in (a) PBE and (b) HSE (α = 0.48) calculations. The Fermi level is located at energy zero. Orange and green lines represent the majority and minority spin states, respectively. (c) The relationship between the band gap of LiO2 and the mixing parameter α. (d) The energy level diagram for the superoxide O2−. The red dotted line is drawn as a guideline to indicate the separation between the occupied and unoccupied states. 2204


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millionth that of the hole polaron seems to cast doubt on such a role for Lii+ in the charge-transport properties of LiO2. Additionally, it should be noted that VLi− is likely to combine with hP+ and may possibly exist in the form of the neutral defect VLi0, which has a low formation energy on the same scale of VLi− and hP+. In the following, we will provide a detailed analysis of the electronic structures of the defects examined in the present work. 3.2.1. Small Polarons. When an electron is added to (or removed from) the LiO2 supercell, two possible configurations may arise: one corresponding to a delocalized electron (or hole) and another referred to as a self-trapped small polaron. In the case of the delocalized state, the symmetry of the lattice remains unchanged and all the oxygen dimers in the supercell share the extra charge equally. In contrast, if the symmetry of the lattice is allowed to be broken, the self-trapped electron or hole will be localized on a single oxygen dimer forming a small polaron, which is accompanied by a significant lattice distortion: the most prominent is the change of the O−O dimer bond length. For the electron polaron, the bond length of the formed O22− ion undergoes an expansion from 1.30 Å in the pristine superoxide to 1.44 Å, while for the hole polaron, the O−O bond length is decreased to 1.19 Å, identical to that of gaseous O2 in the HSEα=0.48 calculations. Analogous results were reported for NaO2.39 This behavior can be explained by the fact that the highest occupied molecular orbital of the O2− anion is an antibonding one, as illustrated in Figure 2d. An extra electron would result in a weakening of the bond strength, which will then manifest itself in the elongation of the bond length, whereas a self-trapped hole produces the opposite effects and yields a neutral O−O dimer that closely resembles the gaseous oxygen molecule. Both the self-trapped electron and hole are found to be more stable than the corresponding delocalized ones. The selftrapped energy, defined as the energy difference between the delocalized and self-trapped states, is found to be 1.37 eV (1.00 eV) for the electron (hole) polaron. This result is not surprising given the small dispersion of the O-2p bands in LiO2, which is believed to be conducive to the formation of small polarons.67 It should be emphasized that the partially filled π* states in the minority spin channel can generate the magnetic moment of 1 μB for each O2− anion, which is known as π-electron magnetism.68 When an electron polaron is formed, the π* orbital would be fully occupied and the corresponding oxygen dimer would lose its original magnetism. On the other hand, for the hole polaron case, the dimer with two unpaired electrons in the majority spin channel would readily possess a magnetic moment of 2 μB. Therefore, the charge state of the oxygen dimers can be well reflected by the magnetization density distribution (difference in electron density between spin up and spin down), as seen in Figure 4. The shape of the isosurface shows that, although substantial changes are visible in the transformation of O2− to O22− (Figure 4a) and O20 (Figure 4b), the magnetization density profiles of other oxygen dimers remain intact without any apparent interaction with the polaron. That is to say, the width of the localized charge does not extend to the neighboring oxygen dimers, which confirms our claim that the electron and hole polarons in LiO2 are small polarons. 3.2.2. Vacancies and Interstitials. The Li vacancy VLi− is created by removing a Li+ ion from the supercell, which accompanies the inward movement of the nearest-neighbor Li+ ions in the c direction toward the void. It is also found that the

defects include electron and hole polarons, hereafter designated as eP− and hP+, respectively; lithium vacancies (VLi) and interstitials (Lii); oxygen vacancies (VO); oxygen dimer vacancies (VO2). In Figure 3, the calculated formation energies

Figure 3. Calculated formation energies of intrinsic defects in LiO2 as a function of the Fermi level. The vertical dashed line indicates the position of the Fermi level where charge neutrality is maintained.

are plotted as a function of the Fermi level under the O-rich conditions. A positive value for line slope indicates a positively charged defect and vice versa. Here, only the segments representing the most stable charge states are shown. It is evident from Figure 3 that hole polarons (hP+) are more energetically favorable than other positively charged defects, while Li vacancies in the −1 charge state (VLi−) appear to be overwhelmingly dominant among the negatively charged defects. In the absence of electrically active impurities that can shift the position of the Fermi level, the concentrations of charge carriers are determined exclusively by the charge neutrality condition. That is to say, the Fermi level is fixed at the position where the oppositely charged defects with the lowest formation energies are equally populated; in this case, EF is 1.69 eV above the VBM for LiO2. Table 1 summarizes the Table 1. Formation Energies (Ef, eV) and Concentrations (c, cm−3) (T = 300 K) of the Relevant Defects in LiO2 under the Charge Neutrality Condition defect −

Ef (eV)

c (cm−3) × × × ×

6

c (cm−3)

defect

Ef (eV) 0.57 1.07 0.73 1.56

1 8 5 2

× × × ×

1013 104 1010 10−4

eP VLi− VLi0 VLi+

0.97 0.57 0.60 0.97

2 1 3 2

10 1013 1012 106

hP+ V O− V O0 VO2−

Lii−

1.83

1 × 10−8

VO20

0.89

4 × 107

0.97

4 × 10

+

0.65

4 × 1011

0.93

2 × 10

Lii0 Lii+

6

V O2

7

concentrations for all defects considered, based on eq 5. The equilibrium concentrations of hP+ and VLi− are estimated to be 1 × 1013 cm−3, which is about 6 orders of magnitude greater than the reported value in Li2O2.15 The charged defect having the next-lowest formation energy turns out to be VO2+, with a concentration of 4 × 1011 cm−3. While the crucial contribution of alkali interstitials for conductivity in KO2, RbO2, and CsO2 is experimentally well established,64 the fact that the calculated concentration of Li interstitials is only of the order of one2205


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symmetrically on both sides of the vacancy, but adding a third hole polaron proves to be impossible due to the electrostatic repulsion between the two positively charged species (VLi+ and hP+). To assess the ability to dissociate these defect complexes, we calculate the binding energy of hP+ to VLi− by adding up the formation energies of the constituents and subtracting the energy of the complex.69 For better interpretation, the binding energy here is expressed as per polaron. That is, the binding energy of the first hole polaron is defined according to the reaction VLi− + hP+ ⇔ VLi0, while the binding energy of the second one is according to VLi0 + hP+ ⇔ VLi+. Our results (Table 2) indicate a relatively strong binding of hole polaron to Table 2. Calculated Binding Energies of Defect Complexes between Atomic Defects and Polarons in LiO2

Figure 4. Magnetization density distribution for (a) electron and (b) hole polarons. (c) Structural and magnetic properties of O−O dimers with different charge states. The isosurfaces represent the spin density at the value of 0.05 e Å−3.

defect

constituents

binding energy (eV)

defect

constituents

binding energy (eV)

VLi0 VLi+

VLi− + hP+ VLi− + 2hP+

0.53 0.21

V O0 V O2 0

VO− + hP+ VO2+ + eP−

0.91 0.73

Lii0

Lii+ + eP−

0.93

V O2 −

VO2+ + 2eP−

0.29

Lii−

magnetization density distribution of the neighboring oxygen dimers maintains itself except for some apparent rotation around the dimer axis (Figure 5). The neutral vacancy VLi0,

+

Lii +

2eP−

0.10

the negatively charged Li vacancy, which makes it difficult to release any free polarons by thermal dissociation of VLi0 at room temperature. Furthermore, it can also be anticipated that, during the hopping of the neutral VLi0, it drags with it the bound polaron (the polaron may be left behind becoming free polaron when binding energy is small), and therefore, their combined motion, as a single entity, will not cause any instant increase in charge carriers in the matrix. Thus, we believe that VLi0 may have little, if any, influence on the conductivity of LiO2. At the same time, we note that, when two hole polarons are bound to a Li vacancy forming VLi+, the energy cost to remove one of the hole polarons is only 0.21 eV. This value is modest enough to permit some fraction of the complexes to be thermally dissociated into VLi0 and hP+. Moreover, it should be recapitulated here that, as long as thermodynamic equilibrium is maintained, the concentration of free hole polarons is determined by its formation energy, and therefore, the clustering of defects will not affect the equilibrium concentration of charge carriers in LiO2. Similar scenarios could be derived from the Li interstitials and the O2 vacancies. It is shown in Figure 5 that Lii− and Lii0 are actually complexes of Lii+ and eP−, while VO2− and VO20 are indeed made up of VO2+ and eP−. The respective polaron binding energies are summarized in Table 2. We can expect that stable bound complexes with an overall neutral charge are formed when an electron polaron is trapped in the vicinity of Lii+ and VO2+. The O vacancies, however, appear to yield a different behavior. It should be noted that the remaining oxygen ion in VO− is reduced to a −2 charge state, which is also the charge state of oxygen anions in most transition-metal oxides. No magnetic moment is observed in this case since the eight-electron configuration is achieved for this oxygen atom. For the neutral vacancy VO0, the oxygen atom is in a −1 charge state and possesses a magnetic moment of 1 μB, the density distribution of which is characteristic of an O 2p orbital (see the inset in Figure 5). The shape of this density profile bears much resemblance to those of hole polarons in metal oxides.70 Thus, it is reasonable to suppose that VO0 is in fact a complex of VO−

Figure 5. Magnetization density distribution for lithium vacancies, lithium interstitials, oxygen vacancies, and oxygen dimer vacancies in LiO2. The isosurfaces are shown at the value of 0.05 e Å−3. The blue dashed ellipses highlight the oxygen dimers on which small polarons are formed.

instead, is formed when a Li atom is removed, which in fact corresponds to a Li+ ion and an electron from a nearby oxygen dimer. The structural and electronic characteristics associated with the removed Li+ ion are similar to those in the case of VLi−, while the loss of an electron in one of the dimers additionally leads to the contraction of the O−O bond and thereby the formation of a hole polaron (marked by a blue dashed ellipse in Figure 5). In this sense, VLi0 should be considered as a complex of VLi− and hP+, which indicates that, for each Li atom removed from LiO2 during delithiation, there remain one negatively charged Li vacancy and one hole polaron in its proximity. As for VLi+, one finds that two hole polarons would be arranged 2206


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Figure 6. Schematic representation and the calculated activation barriers for electron and hole polarons hopping along different directions.

and hP+, the latter of which is localized preferentially on the remaining O atom at the defect center. However, VO+, which involves a negative binding energy, is comprised of a VO0 and a hole polaron far away from each other, leading us not to consider VO+ as a single point defect or defect complex. These findings further substantiate our inference that, by defining VLi−, Lii+, VO−, and VO2+ as the basic atomic defects, all other defects should be viewed as complexes between these basic defects and electron/hole polarons, rather than configurations of point defects in other charge states. Such a result emphasizes the fundamental role of small polarons in the defect chemistry of LiO2. 3.3. Defect Migration. It is expected that small polarons in peroxides and superoxides can be thermally or electrically activated and diffuse through the lattice via hopping from an oxygen dimer to another. In the framework of density functional theory, the polaron migration can be described by the adiabatic evolution of the distorted lattice configuration between two adjacent polaronic sites. Here, four diffusion pathways along different crystal orientations are depicted in Figure 6. The path along the c axis offers the shortest diffusion route with a distance of 3.0 Å, while diffusion along the b axis turns out to be the longest measuring 4.7 Å. The calculated migration barriers for the diffusion of electron polaron are in the range of 0.25 to 0.46 eV for different directions, while those for hole polaron hopping are between 0.32 and 0.53 eV, both reflecting the anisotropic behavior of the diffusion of polarons in LiO2. Previous studies regarding Li2O2 have claimed the potential link between such anisotropy and the preferential growth in certain crystallographic directions during discharge.15,16 Given that the experimentally synthesized crystalline LiO2 is obtained through epitaxial growth,35 our findings may provide some clues to the growth mechanism and the resulting morphology of the LiO2 discharge product. It is seen that the lowest barriers are consistently found to be for a hop along the c axis, as indicated by Path 3. Perceivably, templates that direct the growth of LiO2 along the c axis may allow faster growth of the nuclei, which would in turn produce a rod-like structure of the discharge product as compared to a more platelike pattern with other growth directions. Nevertheless, further experimental and theoretical research is still needed before any definitive conclusion is drawn. Moreover, in comparison with prior calculations involving Li2O2 that reported diffusion barriers of 0.54−0.66 and 0.42−0.71 eV for electron and hole polarons, respectively,12,15 our study clearly highlights that LiO2 will permit faster migration of small polarons and thereby help

to facilitate better performance in terms of electronic conductivity. Although the lowest barrier for migration of an electron polaron is slightly smaller than that for migration of a hole polaron, the much greater concentration of hole polarons would mean a proportionally larger contribution to the electronic conductivity as compared with the electron polarons. A detailed discussion of the calculated conductivity of small polarons will be presented in the next section. Vacancy diffusion is simulated by exchanging the defect with one of its nearest neighbors that are crystallographically equivalent. Regarding the mobility of the lithium vacancies, it is shown (Figure 7a) that VLi− has moderate diffusion barriers

Figure 7. Pathways for the diffusion of (a) VLi− and (b) VO2+ in LiO2 and the corresponding activation barriers.

with anisotropy similar to that of hole polarons. Among the three pathways considered in our work, the diffusion along the c axis (Path 2) shows a barrier of around 0.47 eV, which is 0.03 eV lower than that along the [1 1 1] direction (Path 3). The small difference implies that the mobilities of VLi− in both pathways are on the same scale. However, given that Path 3 involves a random three-dimensional diffusion process while 2207


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dislocations, surfaces, grain boundaries, and amorphous regions15,71 will further increase the conductivity, so a higher value for σ would most probably be derived from future experimental measurements. It can also be reasonably anticipated that the discharge products, in which LiO2 and Li2O2 are embedded, would probably have an overall conductivity higher than those consisting solely of Li2O2. Thus, the discharge process will be more efficient in the former. This may rationalize the recent experimental observations37,72 that an increased content of LiO2-like phase in the Li2O2 particles will generally encourage their growth into large toroids, while in the considerably smaller particles only minor amounts of LiO2 are detected. As for the ionic conductivity in LiO2, our results confirm a high mobility of superoxide ions in the solid, giving rise to conductivity superior to that of small hole polarons. The n-type conduction from negative lithium vacancies also contributes to the ionic conductivity, but it is attributable to a much lesser degree. Thus, it can be concluded that oxygen dimers are highly mobile in the interior of LiO2, while lithium ions are believed to be more or less immobile. This may cast light on the oxidation mechanism of LiO2, which probably involves the formation of the off-stoichiometric LiO2−x compounds in the reaction region before the complete decomposition of LiO2 into Li and O2. This mechanism is in contrast to the decomposition pathway of Li2O2, which undergoes delithiation to form Li2−xO2 compounds in the bulk, identical to the charging mechanism in typical Li-ion electrode materials.52 The theoretical conductivity of VO2+ in NaO2 is 3 orders of magnitude higher than that in LiO2,39 thus lending further credence to the idea that superoxide ions may intrinsically facilitate fast ion transport and can therefore exert beneficial effects on the electrochemical reactions during the charge and discharge cycles.

Path 2 only contributes to one-dimensional diffusion, the collective effect would presumably lead to an anisotropic diffusion behavior with a preferred c-axis direction. The direction-dependent behavior is also observed in the diffusion of an oxygen dimer vacancy (Figure 7b). From the NEB images, we notice that the oxygen dimer exchanging with the vacancy undergoes a rotation (∼53° in Path 1, ∼90° in Path 2, and ∼85° in Path 3) during the translational motion, similar to the case in NaO2.39 At the same time, the trajectory of the oxygen dimer is shown to be without any breaking of the O−O bond. Intriguingly, the diffusion along Path 2 turns out to exhibit a barrier as low as 0.23 eV. The facile migration of oxygen dimers in LiO2 coincides with the theoretical and experimental findings that have demonstrated the high mobility of superoxide ions in other alkali metal superoxides.39,64 Considering that the O−O bond length of superoxide ions are substantially smaller than that of peroxide ions, the energy cost in the diffusion process due to overlapping electron clouds between the dimer and the nearby atoms will be considerably reduced. Thus, we may assume that such a high mobility is most likely a general characteristic of the superoxide ions. 3.4. Electronic and Ionic Conductivity. The calculated mobility and conductivity of the main charge carriers in LiO2 are summarized in Table 3. The electronic transportation in Table 3. Calculated Mobility (μ, cm2 V−1 s−1) and Conductivity (σ, S cm−1) of the Relevant Charge Carriers in LiO2 at Room Temperature charge carrier eP− hP+ VLi− VO2+

μ (cm2 V−1 s−1) 2 2 4 6

× × × ×

10−5 10−6 10−9 10−5

σ (S cm−1) 8 3 7 4

× × × ×

10−18 10−12 10−15 10−12

LiO2 is primarily dictated by the hole polarons with a conductivity of 3 × 10−12 S cm−1, which is around 8 orders of magnitude higher than that in Li2O2 (∼10−20 S cm−1).15 This difference appears to be distinct from the case of NaO2 and Na2O2, both of which have a nearly identical electronic conductivity contributed by small polarons.39 When the particle size of the discharge product exceeds a threshold value for electron tunneling (on the scale of 5−10 nm),10 bulk charge transport via hopping of polarons would probably be the limiting factor for the cell reaction. In this context, even a modest enhancement of the electronic conductivity would have promoted relatively faster growth of the discharge product in the electrode. More importantly, a high intrinsic electronic conductivity would help produce a fairly small overpotential needed for activating charge transport, thus reducing the voltage losses in the cell and resulting in better battery performance. Lu et al. reported the low charge overpotential for crystalline LiO2 in a cell and suggested that this feature is mainly originated from the half-metal character of LiO2 as well as the efficient catalytic performance of the iridium nanoparticles.35 However, in our work, LiO2 is predicted to be an insulator within the HSE framework. We therefore feel the metallic conduction mechanism proposed in ref 35 cannot be correct. Instead, we propose that the electronic conductivity in LiO2 is predominantly governed by the hopping of small hole polarons which, in the adiabatic limit, exhibit marked improvements of concentration and mobility over those in Li2O2. Moreover, one can expect that extended defects such as

4. CONCLUSIONS We have carried out DFT studies of the bulk properties and intrinsic defects in LiO2 using the HSE hybrid functionals. Our calculations reveal that bulk LiO2 is an insulator rather than half-metal. The excess electrons and holes are predicted to localize on the oxygen dimer in the form of small polarons. These polarons can propagate through LiO2 with directional dependence favoring the diffusion along the c-axis, which exhibits barriers of 0.25 and 0.32 eV for the self-trapped electrons and holes, respectively. It is also found that small polarons can form complexes with vacancies and interstitials, which exhibit high binding energies that prevent the polarons from breaking loose. By calculating the concentrations and mobilities of intrinsic charge carriers, we find that the electronic conductivity is mainly contributed by hole polarons, while the ionic conductivity is dominated by VO2+. The electronic conductivity is around 8 orders of magnitude higher than that in Li2O2, which may help rationalize the experimentally observed low overpotential of the LiO2 cells. Irrespective of the fact that the obtained conductivity values tend to vary with different exact exchange fractions, our study unequivocally highlights the fundamental role of small polarons in the charge transport in LiO2 and may stimulate further research to form a deeper understanding of the electrochemical mechanisms taking place in a Li−O2 battery. 2208


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(14) Radin, M. D.; Rodriguez, J. F.; Tian, F.; Siegel, D. J. Lithium Peroxide Surfaces Are Metallic, While Lithium Oxide Surfaces Are Not. J. Am. Chem. Soc. 2012, 134, 1093−1103. (15) Radin, M. D.; Siegel, D. J. Charge Transport in Lithium Peroxide: Relevance for Rechargeable Metal−Air Batteries. Energy Environ. Sci. 2013, 6, 2370. (16) Garcia-Lastra, J. M.; Myrdal, J. S. G.; Christensen, R.; Thygesen, K. S.; Vegge, T. DFT+U Study of Polaronic Conduction in Li2O2and Li2CO3: Implications for Li−Air Batteries. J. Phys. Chem. C 2013, 117, 5568−5577. (17) Varley, J. B.; Viswanathan, V.; Nørskov, J. K.; Luntz, A. C. Lithium and Oxygen Vacancies and Their Role in Li2O2 Charge Transport in Li−O2 Batteries. Energy Environ. Sci. 2014, 7, 720−727. (18) Hummelshoj, J. S.; Blomqvist, J.; Datta, S.; Vegge, T.; Rossmeisl, J.; Thygesen, K. S.; Luntz, A. C.; Jacobsen, K. W.; Norskov, J. K. Communications: Elementary Oxygen Electrode Reactions in the Aprotic Li-Air Battery. J. Chem. Phys. 2010, 132, 071101. (19) Mo, Y.; Ong, S. P.; Ceder, G. First-Principles Study of the Oxygen Evolution Reaction of Lithium Peroxide in the Lithium-Air Battery. Phys. Rev. B: Condens. Matter Mater. Phys. 2011, 84, 205446. (20) Hummelshoj, J. S.; Luntz, A. C.; Norskov, J. K. Theoretical Evidence for Low Kinetic Overpotentials in Li-O2 Electrochemistry. J. Chem. Phys. 2013, 138, 034703. (21) Zhu, J.; Ren, X.; Liu, J.; Zhang, W.; Wen, Z. Unraveling the Catalytic Mechanism of Co3O4 for the Oxygen Evolution Reaction in a Li−O2Battery. ACS Catal. 2015, 5, 73−81. (22) Gerbig, O.; Merkle, R.; Maier, J. Electron and Ion Transport in Li2O2. Adv. Mater. 2013, 25, 3129−33. (23) Dunst, A.; Epp, V.; Hanzu, I.; Freunberger, S. A.; Wilkening, M. Short-Range Li Diffusion vs. Long-Range Ionic Conduction in Nanocrystalline Lithium Peroxide Li2O2  the Discharge Product in Lithium-Air Batteries. Energy Environ. Sci. 2014, 7, 2739. (24) Luntz, A. C.; Viswanathan, V.; Voss, J.; Varley, J. B.; Nørskov, J. K.; Scheffler, R.; Speidel, A. Tunneling and Polaron Charge Transport through Li2O2 in Li−O2 Batteries. J. Phys. Chem. Lett. 2013, 4, 3494− 3499. (25) Radin, M. D.; Monroe, C. W.; Siegel, D. J. Impact of SpaceCharge Layers on Sudden Death in Li/O2 Batteries. J. Phys. Chem. Lett. 2015, 6, 3017−22. (26) Gao, X.; Chen, Y.; Johnson, L.; Bruce, P. G. Promoting Solution Phase Discharge in Li-O2 Batteries Containing Weakly Solvating Electrolyte Solutions. Nat. Mater. 2016, 15, 882−888. (27) Laoire, C. O.; Mukerjee, S.; Abraham, K. M.; Plichta, E. J.; Hendrickson, M. A. Elucidating the Mechanism of Oxygen Reduction for Lithium-Air Battery Applications. J. Phys. Chem. C 2009, 113, 20127−20134. (28) Black, R.; Oh, S. H.; Lee, J.-H.; Yim, T.; Adams, B.; Nazar, L. F. Screening for Superoxide Reactivity in Li-O2 Batteries: Effect on Li2O2/LiOH Crystallization. J. Am. Chem. Soc. 2012, 134, 2902−2905. (29) Johnson, L.; Li, C.; Liu, Z.; Chen, Y.; Freunberger, S. A.; Ashok, P. C.; Praveen, B. B.; Dholakia, K.; Tarascon, J.-M.; Bruce, P. G. The Role of LiO2 Solubility in O2 Reduction in Aprotic Solvents and its Consequences for Li−O2 Batteries. Nat. Chem. 2014, 6, 1091−1099. (30) Aetukuri, N. B.; McCloskey, B. D.; García, J. M.; Krupp, L. E.; Viswanathan, V.; Luntz, A. C. Solvating Additives Drive SolutionMediated Electrochemistry and Enhance Toroid Growth in Nonaqueous Li−O2 Batteries. Nat. Chem. 2015, 7, 50−56. (31) Peng, Z.; Freunberger, S. A.; Hardwick, L. J.; Chen, Y.; Giordani, V.; Bardé, F.; Novák, P.; Graham, D.; Tarascon, J.-M.; Bruce, P. G. Oxygen Reactions in a Non-Aqueous Li+ Electrolyte. Angew. Chem. 2011, 123, 6475−6479. (32) Yang, J.; Zhai, D.; Wang, H.-H.; Lau, K. C.; Schlueter, J. A.; Du, P.; Myers, D. J.; Sun, Y.-K.; Curtiss, L. A.; Amine, K. Evidence for Lithium Superoxide-Like Species in the Discharge Product of a Li-O2 Battery. Phys. Chem. Chem. Phys. 2013, 15, 3764−3771. (33) Xia, C.; Waletzko, M.; Chen, L.; Peppler, K.; Klar, P. J.; Janek, J. Evolution of Li2O2 Growth and Its Effect on Kinetics of Li−O2 Batteries. ACS Appl. Mater. Interfaces 2014, 6, 12083−12092.

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.6b05022. Additional discussion of the influence of exchangecorrelation functional on lattice parameters, band structure, defect concentrations, and defect migration barriers in LiO2 (PDF)

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AUTHOR INFORMATION

Corresponding Author

*Tel: +86-10-62772619. Fax: +86-10-62771160. E-mail: jbliu@ mail.tsinghua.edu.cn. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The authors are grateful for the financial support from the National Natural Science Foundation of China (51571129, 51631005), Science Challenge Project (JCKY2016212A504), and the Administration of Tsinghua University.

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REFERENCES

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First-Principles Study of the Charge Transport Mechanisms in Lithium

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