Article pubs.acs.org/JPCC
Grain Boundary Induced Conductivity in Li2O2 W. T. Geng,*,† B. L. He,‡ and T. Ohno*,†,§ †
GREEN, National Institute for Materials Science, Tsukuba 305-0047, Japan School of Materials Science & Engineering, University of Science and Technology Beijing, Beijing 100083, China § Computational Materials Science Unit, National Institute for Materials Science, Tsukuba 305-0047, Japan ‡
ABSTRACT: The dominant discharge product in Li−air batteries, lithium peroxide (Li2O2), is intrinsically a wide band gap insulator as a perfect crystal. Recent density functional theory studies have suggested both vacancy- and polaron-mediated electron transportation mechanisms. We here show computational evidence from both semilocal and hybrid density functional calculations that the Σ3(11̅00)[112̅0] tilt grain boundaries (GBs) in Li2O2 can produce spin-polarized gap states. For each type of Σ3 GBs, GB1, GB2, and GB2* which has different atomic layer as the mirror plane, we have examined stoichiometric and a number of O-rich chemistry and find that stable geometry can take both forms. We find stoichiometric GBs disturb negligibly the electronic structure of Li2O2, yet the O-rich GBs produce spin-polarized gap states in a similar manner to free surface cases. Lithium deficiency leads to compression of interfacial O−O bonds, enlarges the πp−πp* split, and pushes up the antibonding πp* to (GB2) or beyond (GB2*) the Fermi energy. As a result, GB2 becomes half-metallic and GB2* becomes semiconducting with a small band gap of 1.0 eV. In both cases, spin polarization of O ions help to stabilize the GB by leaving the up spin of its gap states shifted down below the Fermi level and the down spin states open. Since Li2O2 is always polycrystalline as a discharge product, the presence of GBs may enhance conductivity. band of Li2O2 and thus make it a band conductor.7 However, generation of a substantial amount of lithium vacancies is obviously unfavorable. On the other hand, Radin et al.’s DFT calculations demonstrated that although insulating in the bulk, oxygen rich Li2O2 surfaces could be metallic.8 This surface metallicity, if preserved well during charge and discharge, helps electron transport within the forefront surface of the Li2O2 film but cannot offer transportation path across the film. Therefore, it remains quite elusive that large Li2O2 particles with sizes of hundreds of nanometers can form during charge.9 Kang et al. investigated the self-trapping of electrons in small polarons in the presence of excess electrons in the conduction band and discovered the extremely low electron mobility.10 More recently, Ong et al. reported DFT calculations on the migration barrier of the hole polaron in Li2O2.11 A speculation prompted by the calculated low barrier is that Li2O2 may not be as insulating as previously assumed, provided that vacancy diffusion is not too slow. A larger barrier for the migration of hole polarons has been obtained by less expensive DFT+U calculations.12 As for point defects, Gerbig et al.13 investigated the electron and ion transport in Li2O2 by impedance spectroscopy and dc measurements and demonstrated that Li2O2 is an ionic conductor with discernible electronic conductivity. Firstprinciples calculations done by Radin and Siegel14 yield a
1. INTRODUCTION Lithium-ion batteries have made electronic devices increasingly portable since 1991.1 However, the highest energy storage they can carry is still not enough to meet the demand of longdistance electric vehicles.2 One hope kindled by Abraham and Jiang in rising to this challenge is to explore rechargeable Li−air (Li−O2) batteries3 which have a theoretical energy density almost 10 times higher than their Li-ion counterparts. Lithium peroxide, Li2O2, is the primary discharge product at the air cathode, usually meso- or nanoporous carbon, possibly together with little amount of LiO2 and Li2O, and even some Li2CO3 and LiOH if the cell is exposed to ambient air.4 First-principles density functional theory (DFT) calculations by Cola and de la Mora evidenced that the crystal structure of Li2O2 has a P63/ mmc hexagonal space group,5 which was later confirmed by high-energy X-ray measurement and more accurate hybrid density functional calculations.6 A recent computational work by Hummlshøj et al.7 showed that Li2O2 is an insulator with a band gap of 1.88 eV within semilocal DFT and 4.91 eV within more precise GW theory. On both oxygen reduction and evolution reactions at the cathode, transportation of electrons between the outer surface of Li2O2 and the substrate carbon sheet is needed, thus poor electronic conduction results in low rate capacity and high overpotential which is obviously very unwelcome. Design of carrier conduction paths in Li2O2 calls upon thorough understanding of the electronic properties of this material in forms other than its perfect crystalline state. It was found that lithium vacancies could induce holes in the valence © 2013 American Chemical Society
Received: May 29, 2013 Revised: November 14, 2013 Published: November 20, 2013 25222
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higher electronic conductivity associated with polaron hopping and thus point to a transport mechanism through a more balanced mixture of ionic and electronic contribution. Furthermore, the calculated concentration and mobility of charge carriers and point defects in Li2O2 as a function of cell voltage also support the recent discovery that the oxygen evolution reaction occurs in two distinct stages in the charging process.15 We recall that materials in use are usually polycrystalline, which is particularly the case for Li2O2 grown at the porous carbon cathode. Grain boundaries (GBs) are well-known to alter, or, even dominate the electrical properties of the otherwise perfect crystals.16 In the advent of direct atomresolved imaging technique, determination of the atomic structure near the grain boundary of polycrystalline materials has become fairly feasible, even for oxides.17 Direct comparison between DFT predictions18 and experimental measurements has advanced greatly our understanding of the structure− property relationships for innumerable materials. Here, we aim to elucidate the influence of a Σ3(11̅00)[112̅0] tilt GBs on the electronic properties of Li2O2 using first-principles DFT computation. Previous theoretical study has established that the (0001) surface of Li2O2 has the lowest formation energy, followed by (11̅00) and (112̅0), and that O-rich configurations have lower surface energy under ambient conditions.8 It is therefore believed that (0001) is the surface which contacts the carbon cathode on one side and the gaseous O2 on the other side of the Li2O2 film; while the edge facets of the film are probably composed mainly of (11̅00) and (112̅0). In discharge, O reduction (Li oxidation) occurs simultaneously at different spots on carbon, which serves both as a holder and as reaction catalyst. Thus, neighboring nanoscale Li2O2 crystallites are very likely to get connected or merged via (11̅00) or (112̅0) surfaces as they grow larger. As an “educated guess” to the true GB structure, we chose the second most stable surface (11̅00) as the atomic plane in which a boundary between two neighboring grains having opposite atomic layer sequence along [11̅00] forms. The atomic structure of Li2O2 is displayed in Figure 1, as was determined from previous works.5 To guide the eye in an easier way, we replot the bulk structure of Li2O2 in Figure 2 (Topleft) using more convenient cell. In [110̅ 0] direction, the atomic layer sequence is P1−P2−P2−P1*−P2*−P2*−P1− with a periodicity of six. There are two inequivalent layers, namely P1 and P2, with the former containing only Li while the latter including both O and Li. It has been shown8 that the lowest energy stoichiometric (11̅00) surface is curved rather than a flat one. We indicate the curved atomic layers by purple curves. Taking P1 as the mirror plane, we can obtain type one of Σ3(11̅00)[112̅0] tilt GBs as shown in top-right of panel a, and taking P2 as the mirror plane, we can obtain GB2 and GB2* as shown in the bottom two supercells in panel a. The slabs used to simulate GBs terminate with a vacuum region of about 12 Å. To justify the slab model, we performed test calculations on the convergence of surface energy of (110̅ 0) with respect to the thickness of the slab. It turns out that a slab of three curved atomic layers is thick enough to yield a converged surface energy within an error of 0.2 meV/Å2. Therefore, the choice of stoichiometric free surfaces at both sides of the slab has no noticeable impact on the GB in between. For each type of GB, we have investigated various nonstoichiometric configurations, as displayed in panel b of Figure 2. In optimizing of GB
Figure 1. (Top left) Atomic structure of Li2O2. Note that each oxygen bonds with six lithium ions and only four of them are in this unit cell. (Top right) Schematic diagram of orbital energies of O22‑, illustrating bonding characters in Li2O2. (Bottom) The calculated density of state (DOS) of Li2O2, a comparison of semilocal PBE and HSE hybrid density functionals. The valence band maximum is set to zero.
geometry, we allowed relaxation of internal freedoms of all atoms. Since we adopted a vacuum region, the dimension in the [11̅00] direction, which is normal to the GB plane, was automatically optimized to eliminate the stress induced by GB volume expansion.
2. METHODOLOGY The computational technique we have employed in this work is density functional theory (DFT) based Vienna ab initio simulation package.19 The electron−ion interaction was described using projector augmented wave (PAW) method.20 The exchange correlation between electrons was treated both with generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof (PBE) form21 and with the screened Heyd−Scuseria−Ernzerhof (HSE) hybrid density functional.22,23 To make computational efforts manageable, we performed only PBE calculations for geometry optimization, and HSE treatments were started from the structure given by PBE. We used an energy cutoff of 500 eV for the plane wave basis set for all systems to ensure equal footing. The Brillouinzone integration was performed within Monkhorst-Pack scheme using k meshes of (8 × 8 × 4) for the bulk, (1 × 8 × 6) for free surfaces and (1 × 8 × 3) for GBs, respectively. The energy relaxation for each strain step is continued until the forces on all the atoms are converged to less than 3 × 10−2 eV Å−1. In HSE calculations, one-quarter of (α = 0.25) the local DFT exchange is replaced by the unscreened and nonlocal Fock exchange and we adopted a parameter of μ = 0.2 Å−1 for the separation of short-range and long-range electron−electron 25223
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Figure 2. Slab models of the atomic structure of Σ3(110̅ 0)[1120̅ ] grain boundary (GB) in Li2O2. On top left of part a is a perfect crystal viewed along[112̅0]. A stable stoichiometric (11̅00) surface is curved and terminates with atoms connected by a curved solid line, rather than straight dashed lines representing planes 1 and 2. Σ3 GB1 (top right of part a) is formed with plane 1 (Li only) being the common atomic layer of the two adjacent grains with mirror symmetry. Σ3 GB2 and GB2* are formed when plane 2 (O and Li) is the mirror atomic layer. The two free surfaces of each slab are curved stoichiometric (11̅00) which have minimal effect on the GB inside the slab. Panel b displays the local structure of a selected set of structure variations for GB1, GB2, and GB2* respectively. In labeling the GB structures, “stoichi’ denotes “stoichiometric” and “O-richi” means there are i more O than Li in this supercell.
overbinding effect in this process is therefore much less significant than in other oxides. As a result, we did not add this correction to the formation energy of GBs. As stated above, the supercells we used to model the Σ3(11̅00)[112̅0] tilt GBs are shown in Figure 2. Note that in panel (a) we show the complete supercells for three types of GBs. These are the ideal GB structures in the sense that no atoms are added or removed in construction of a GB using mirror symmetry. It has to be pointed out that these ideal GB structures are not necessarily stoichiometric, due to the fact that plane 1, but not Plane 2 [see top-left of panel a], divides evenly a curved plane. By stoichiometric, we mean the whole supercell has equal number of Li and O atoms. In labeling the GB structures, “stoichi’ denotes “stoichiometric” and “O-richi” means there are i more O than Li atoms in this supercell. It has been known from Radin et al.8 that under ambient conditions, the free (110̅ 0) surface prefers to terminate with a significantly O-rich configuration. But near the GBs, oxygen cannot be too much enriched because otherwise there would be strong repulsion between negatively charged O atoms across the boundary.
exchange interaction, assuming that at a distance of 2/μ = 10 Å, the short-range interaction becomes negligible. Our benchmark calculations on bulk Li2O2 (Figure 1) show that the optimized lattice constants yielded by PBE density functional are a = 3.16 Å, c = 7.68 Å, and the band gap is about 1.9 eV. With this parameters, and HSE hybrid density functional gives a band gap of about 4.2 eV. These results are in good agreement with previous theoretical works using the same method.7,8,10,11 In order to access the stability of GBs, we need the formation energy of (11̅00) surface. For a flat surface, it is 0.070 eV/Å2, and for a curved one it reduces to 0.035 eV/ Å2, compares well with the previous report.8 The overbinding of the O2 molecule by GGA calculations is a well-known effect,21 which is the key factor in underestimating the oxidation energy of metals.24 Here in the study of Li2O2, we argue that the correction to account for this overbinding is not very essential because upon oxidization, O2 (OO) molecules do not dissociate into O atoms (or O2‑ ions) but are stretched into (O−O)2‑ ions with a O−O bond length of 1.55 Å. Our GGA calculation shows that the energy needed to stretch an isolated O2 molecule in equilibrium (OO bond length, 1.23 Å) to an O−O separation of 1.55 Å is only 1.76 eV, much smaller than the total binding energy of an O2 molecule. The 25224
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formation of GB2 (0.056 eV/Å2) and GB2* (0.042 eV/Å2) turns out to be less costly in energy than GB1, an indication that they are energetically favorable over the free surface. By comparison, our calculations reveal both stoichiometric and Orich stable boundary structures for GB2 (“GB2-stoichi” and “GB2-O-rich1−1”) and GB2* (“GB2*-O-rich1−1” and “GB2*stoichi”). In labeling the GB structures, “stoichi’ denotes “stoichiometric” and “O-richi” means there are i more O than Li in this supercell. We now look at the electronic structure associated with GB2 and GB2*. The calculated density of states (DOS) for the supercells “GB2-stoichi”, “GB2-O-rich1−1”, “GB2*-stoichi”, and “GB2*-O-rich1−1” are plotted in Figure 3. The most salient feature is that bandgap states, antibonding πp*, appear at O-rich GBs, in sharp contrast to the prefect crystal. In fact, “GB2-O-rich1−1” is half-metallic and “GB2*-O-rich1−1” is semiconducting with a much reduced band gap, 1.0 eV. By contrast, stoichiometric GBs introduce only negligible perturbation to the electronic structure of Li2O2. Therefore, we show projected DOS (PDOS) on oxygen atoms only for “GB2-O-rich1−1” and “GB2*-O-rich1−1” to gain more insights into the GB-induced conductivity. For both boundaries, the PDOS of O4 resembles very much that of the bulk system, an indication that the effect of GB is vanishing here and thus the slabs we employed to model the GBs are thick enough to yield bulk-like environment inside the grain. Moreover, the spin-up channels are always insulating, the same as in the bulk. Nonetheless, “GB2-O-rich1−1” does differ from “GB2*-Orich1−1” strikingly in three features. First, its down spin πp* states fall on the Fermi energy and therefore becomes metallic, yet in the latter case the down spin πp* emerges at 1.0 eV over the valence band maximum. Second, “GB2-O-rich1−1” induces gap states on two pairs of O−O ions (O1 and O3), while in “GB2*-O-rich1−1” one can only find gap states at O2. And third, the spin-split of DOS is less prominent in the former structure than in the latter. Although both GBs have an identical total spin-magnetic moments of 1 μB, contribution to the total moment comes from both O1 and O3 in “GB2-Orich1−1”, but only from O2 in “GB2*-O-rich1−1”. Notice that the spin magnetic moment associated with some types of O, shown in Figure 3, is only for one atom. Near “GB2-O-rich1− 1”, and “GB2*-O-rich1−1”, there are 2 O1 and 4 O3 in the first and 4 O2 atoms in the second, respectively. To put it another way, the electron deficiency is covered by both O1 and O3 at GB2 but only O2 at GB2*. The more concentrated distribution of spin density at GB2* results in a larger spin-split, thus the unoccupied down spin πp* states are pushed above the valence band maximum and hence the semiconducting behavior. Distortion of the local atomic structure of oxygen at the GBs is the result of symmetry breaking in translation. In Table 1, we include the changes in O−O bond lengths near the GBs. Clearly, only minimal alterations take place in stoichiometric cases for all three types GBs. Near O-rich GBs, on the other hand, more significant decreases in O−O bond lengths appear. This is an immediate consequence of Li deficiency, under which condition the O−O bond is strengthened along with a reduced O−O distance. For instance, there are only seven (eight) Li bonding with O3−O3 (O1−O1) pair near “GB2-O-rich1−1”, while there are nine Li surrounding an O−O pair in the bulk. On the contrary, in “GB2-Li-rich1”, the O1−O1 bond is severely stretched to 2.42 Å, much larger than that in the bulk, 1.54 Å. This oxygen molecule has indeed been broken down. With an extra Li, the O1−O1 pair has two Li in between (three
3. RESULTS AND DISCUSSION The calculated formation energies of GBs shown in Figure 2 using PBE functional are listed in Table 1. The formation Table 1. Formation Energy Ef (eV/Å2) of the Three Types of Σ3(110̅ 0)[1120̅ ] Tilt Grain Boundaries (GBs) in Li2O2 with Selected GB Chemistry Modifications, at 300 K and O2 Pressure of 1 atm (Chemical Potential of O: −10.06 eV)a GB type
GB chemistry
Ef
Σ3(11̅00) GB1
stoichiometric-1 stoichiometric-2 O-rich2−1 O-rich2−2 O-rich2−3 stoichiometric O-rich1−1 O-rich1−2
0.089 0.069 0.094 0.071 0.087 0.056 0.056 0.058
O-rich2
0.065
Li-rich1 stoichiometric O-rich1−1 O-rich1−2 O-rich2 O-rich3
0.087 0.044 0.042 0.049 0.061 0.047
Σ3(11̅00) GB2
Σ3(11̅00) GB2*
change in O−O bond length 0.00, 0.02, 0.00, 0.00 0.02, −0.01, 0.00, 0.00 −0.18, 0.00, −0.01, 0.00 −0.06, −0.14, 0.00, −0.01 −0.18, 0.03, −0.03, −0.01 0.01, −0.01, 0.00, 0.00 −0.05, 0.01, −0.09, 0.00 −0.02, −0.09, −0.08, −0.01 −0.09, −0.08, −0.09, −0.01 0.87, −0.01, −0.02, 0.00 −0.01, −0.02, 0.00, 0.00 −0.01, −0.10, 0.00, −0.01 N/A, −0.09, −0.01, 0.00 −0.01, −0.19, 0.01, −0.01 −0.27, −0.11, −0.04, −0.01
a
The corresponding GB structures are shown in Figure 3. Also listed are the changes in O−O bond length (Å) for the four O−O near the GB, which are counted from the boundary plane.
energy of a GB, Ef(GB), is defined as the energy increase caused by this GB in reference to a perfect crystal 1⎡ 1 Eslab(GB, NLi , NO) − NLiE bulk (Li 2O2 ) ⎢ ⎣ A 2 ⎤ + (NLi − NO)μO⎥ − 2Ef (FS) ⎦ (1)
Ef (GB) =
where A is the area of the GB plane, Eslab is the free energy of the GB supercell, NLi and NO are the number of Li and O atoms in the slab, is the chemical potential of O in Li2O2, and Ef(FS) is the surface energy of stoichiometric free (11̅00) surface given by 1 Ef (FS) = [Eslab(FS, 16Li, 16O) − E bulk (16Li, 16O)] 2A (2)
Under O-rich conditions, the chemical potentials of O as a function of temperature and pressure were the same as in Radin et al.’s work.8 Similarly, we also focus on the 300 K and one atmosphere condition. The most stable GB1 structure “GB1stoichi-2” has a formation energy 0.069 eV/Å2, nearly the same as two times of the curved free surface, 0.035 eV/Å2. All the Orich GB1 we have examined are less stable than this structure. Thus, it can be inferred that the formation of O-rich GB1 is not energetically favorable against the free surface, i.e., two adjacent crystallites terminated with O-rich (11̅00) surfaces will repel each other while approaching the point where they come to a contact, or at most will not attract each other in the stoichiometric case. Therefore, we judge that chances for the GB1 structure to be present should be quite low. The 25225
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Figure 3. Total and local density of states on O atoms near the Σ3(110̅ 0)[1120̅ ] GB2 (left) and GB2* (right) in Li2O2 given by DFT-HSE calculations. For the geometry of each GB, see Figure 2. Oxygen atoms are numbered by the (O, Li) atomic layer counting from the GB plane. Spin magnetic moment of O is given in μB.
Figure 4. Calculated isosurfaces (outside yellow and inside blue) of the real space distribution of electronic states (2 × 10−4 e/Å3) near the Σ3(11̅00) [1120̅ ] grain boundary GB2*-O-rich1−1 in Li2O2 in the energy (in reference to the valence band maximum, VBM) window [VBM-0.5 eV, VBM)] (a) and [VBM +0.5, VBM +1.0 eV] (b). Electrons in both valence band maximum and impurity band are quite delocalized.
in bulk), but four Li (three in bulk) on top of each of them. The additional electron contributed from the 10th Li prompts transition of (O−O)2‑ to (O−O)3‑, and then (O2‑-O2‑)+, and hence the breaking of O−O bond. By comparison, the compression of the interfacial O−O bonds near the O-rich GB2 or GB2* turns O22‑ to O21‑ and amplifies the split of πp−πp*, pushing the spin-down antibonding πp* up and beyond the valence band maximum. A localized hole state is thus formed. Spin polarization of antibonding states help to
stabilize the grain boundary structure by leaving spin-up state fully occupied and the spin-down state empty. Spin-polarization also split the bonding πp states and a localized spin-down state appears at the πp−πp* gap around −3.5 eV below the valence band maximum. To better perceive the localization of the above-mentioned new states, we plot in Figure 4 the distribution of electronic states at O-rich GB2* in those particular energy (in reference to the valence band maximum, VBM) windows, i.e., [VBM−0.5 25226
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in Figure 4, this gap state is quite delocalized along [0001], the growth direction of the oxide film. Unlike Li vacancy in the bulk, GB2* is an extensive defect, excited holes and electrons in these antibonding states can be essentially connected to their equivalent neighbors in the GB2* plane. More importantly, “GB2-O-rich1−1” even shows metallic behavior. Although it is 0.014 eV/ Å2 less stable than GB2*, “GB2-O-rich1−1” still have good chances to be present in discharge.
eV, VBM)] (panel a) and [VBM+0.5, VBM+1.0 eV] (panel b). The electron density of the isosurfaces is 2 × 10−4 eV/Å3. We can see charges around GB2* are fairly delocalized suggesting that excited holes and electrons near GB2* could open up a conduction channels in polycrystalline Li2O2. It has to be pointed out that in the case of charge injection, the extra electron might prefer to split (O−O)2‑ into (O2‑−O2‑)+, and compensate for the missing electron on the hole polaron state, rather than filling the empty gap state, down spin πp*. To elucidate this issue, we added an extra electron into the “GB2*O-rich1−1” system and reinvestigate the atomic and electronic properties. Interestingly, we find that unlike in the bulk system, the presence of an excess electron near this GB imposes only a marginal perturbation to the atomic structure and will not break up any O−O bonds. By contrast, it helps to recover the O2− O2 bond length from 1.45 to 1.50 Å, toward the bulk value, 1.55 Å. This is an indication that the added electron compensate to some extent for the lacking electron around the Li atom at the GB which is bonded to four O2 atoms, and hence partially transform the hole polaron state from superoxide-like to peroxide-like. The calculated local DOS on oxygen is shown in Figure 5. That for the neutral system is also
4. CONCLUDING REMARKS To summarize, we have employed first-principles density functional theory calculations to study the structural, electronic, and magnetic properties of the Σ3(11̅00)[112̅0] tilt grain boundaries in Li 2O 2 . We have determined the stable stoichiometric and O-rich grain boundary structures. Interestingly, it is found that some of these stable grain boundaries change the electronic properties of the material by opening up a conduction channel, without the need of point defects such as vacancies. Therefore, the lithium peroxide formed on the carbon cathode in a Li−air battery is probably not as insulating as was generally inferred from the properties of its perfect crystals. Similar to the bulk case, the hybrid density functional predicts a significantly higher gap states than does the semilocal density functional, an indication that the former description is more appropriate for defective Li2O2. The conduction channels supplied by grain boundaries could be responsible for the observed large size of Li2O2 particles.9,25
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AUTHOR INFORMATION
Corresponding Authors
*E-mail:
[email protected]. Telephone: +81-29-8513354, ext 6386. *E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are grateful to the support of MEXT Program for Development of Environment Technology using Nanotechnology.
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Figure 5. The local density of states on O atoms near the Σ3(11̅00) [112̅0] GB2*-O-rich1−1 in Li2O2 given by DFT-HSE calculations, with (blue) and without (red) an extra electron.
REFERENCES
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plotted for easy comparison. The two pronounced features shown here is that (i) the GB2* induced band gap down spin πp* is now closer to the VBM and becomes partially occupied by the injected electron and (ii) as a consequence, the Fermi level is shifted up. Therefore, a notable amount of carriers could be expected via thermal excitation across the reduced band gap between VBM and the down spin πp*, leading the GB an efficient charge conduction channel. Kang et al.10 and Ong et al.11 considered respectively the introduction of electron and hole into the bulk Li2O2 system. The electron introduction results in the formation of a small polaron, which is 2.3 eV more stable than the delocalized electron in the conduction band of perfect Li2O2. But localization makes the polaron hopping difficult which leads to low electronic conductivity. The migration of hole polaron, on the other hand, is limited by availability of Li vacancies which have a rather high formation energy, 3.8 eV. As we show 25227
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The Journal of Physical Chemistry C
Article
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