Modeling Polaron-Coupled Li Cation Diffusion in V2O5 Cathode

Article Cite This: J. Phys. Chem. C XXXX, XXX, XXX−XXX

pubs.acs.org/JPCC

Modeling Polaron-Coupled Li Cation Diffusion in V2O5 Cathode Material Suwit Suthirakun,† Alexander Genest,† and Notker Rösch*,†,‡,§ †

Institute of High Performance Computing, Agency for Science, Technology and Research, 1 Fusionopolis Way, No. 16-16 Connexis, Singapore 138632, Singapore ‡ TUM CREATE, 1 CREATE Way, No. 10-02 CREATE Tower, Singapore 138602, Singapore § Department Chemie and Catalysis Research Center, Technische Universität München, 85747 Garching, Germany S Supporting Information *

ABSTRACT: The transport of intercalated Li cations in oxide materials comprises two aspects, ion diffusion and migration of an associated small polaron. We examined computationally these two aspects of Li transport in vanadium pentoxide (V2O5) cathode material in a consistent fashion, using a DFT+U approach. Exploring various migration scenarios at low Li concentrations, we determined barriers of ∼0.3 eV, mostly due to polaron migration. In consequence, intercalating Li atoms, at low concentrations, migrate in the interlayer region of V2O5 as quasi-particles where Li cations remain closely associated with their valence electrons, where a small polaron structure forms around the reduced vanadium center.

ation energies between polaron and ion.16 For the materials Li2FeSiO4 21 and Na3V2(PO4)3 22 several scenarios have been examined computationally for moving a cation vacancy and its associated polaron. Studying the full dynamics of such a system may be necessary when modeling situations beyond the initial discharge stage. A previous study resorted to a kinetic Monte Carlo approach to describe the Li and polaron migration inside TiO2.20 Accordingly, it is crucial to understand the slowest process, in that particular case the Li+ diffusion, to rationalize the overall diffusion speed.20 To describe the reduction of V centers with a density functional theory (DFT) based approach, a variant of the Kohn−Sham method is required that admits proper electron localization, like the DFT+U method, by correcting, at least in part, the self-interaction error of local or semilocal (GGA) exchange−correlation approximations.23−25 A simple GGA functional, applied to Li insertion in V2O5, yields an erroneous delocalization of the electron over several (partially reduced) V centers, with associated diffusion barriers of 0.34 eV 24 or 0.39 eV,26 for Li cations. GGA+U studies24,25 on Li diffusion in bulk V2O5 reported diffusion barriers of 0.15 eV,25 0.22 eV,27 0.24 eV,25 0.31 eV,25 and 0.37 eV.24 It was also suggested that the inclusion of van der Waals interactions in the computational method notably affects the interlayer spacing and hence the barrier for Li-ion migration; calculated barriers amount to 0.22 eV 27 or 0.31 eV;25 see Table 1.

1. INTRODUCTION During the discharge process of a rechargeable Li-ion battery (LIB), Li+ ions move from the anode through an electrolyte to the cathode where they intercalate.1−5 Thus, the cathode material, usually an oxide or a phosphate, is an important aspect for improving the Li+ transport kinetics of such a battery.1−5 Recently, vanadium pentoxide (V2O5) has attracted considerable attention as cathode material due to its unique physical and chemical properties.6−10 The layered structure of V2O5 easily accommodates atoms of small radius, such as Li, leading to a high capacity for lithium insertion.8,11 During and after discharge, the cathode material vanadium pentoxide can be described by the formula LixV2O5 with 0 < x < 1.12 The electrons, formally neutralizing the Li cations, are reducing vanadium centers, V5+ → V4+.1−5,13 Thus, “small polarons” are created where the extra electron at the metal center induces small distortions of the surrounding lattice.14,15 At low Li concentrations, the Coulomb interaction requires the Li cation to remain close to a (reduced) V center. Therefore, a Li ion and its associated polaron will diffuse in a coupled fashion, as a neutral exciton-like quasi-particle.16 As the discharge progresses, the association between a Li cation and the associated polaron may break down. In a fully discharged state of α-Li0.5V2O5, the average Li−Li distance shrinks to ∼360 pm, becoming comparable to the distance between nearestneighbor V centers, ∼315 pm.12,13 This correlated movement of an inserted cation and an associated polaron has been studied previously for various materials, among them LixFePO4,16−18 Li in TiO2,19,20 Li2FeSiO4,21 and Na3V2(PO4)3.22 Support for such coupled movement comes from experiment17,18 and calculated associ© XXXX American Chemical Society

Received: October 18, 2017 Revised: November 30, 2017

A

DOI: 10.1021/acs.jpcc.7b10321 J. Phys. Chem. C XXXX, XXX, XXX−XXX

Article

The Journal of Physical Chemistry C

Table 1. Calculated Lattice Parameters, V−O Bond Lengths (Both in pm), and Lowest Diffusion Barriers Ea(Li) of Li ions (in eV) Compared to Available Experimental Valuesa DFT+Ub a b c dV−O1 dV−O2 dV−O3 Ea(Li)

DFT+Uc

expd

PBEe

PBEf

PBEg

PBEh

PBEh,i

optPBE-vdWh

PBEj

1151 356 437 158 178 188 202

1154 357 438 158 178 188 203 0.39

1164 360 442 160 180 190 204 0.28

1164 358 463 N/A N/A N/A

1157 363 468 161 181 192 203 0.15

1169 363 442 162 181 191 205 0.24

1169 363 442 162 181 191 205 0.31

0.22

0.37

a

The exchange−correlation functionals used are PBE, PBE+U, and optPBE+U-vdW. bU(V3d) = 4.0 eV. cU(V3d) = 3.1 eV. dReference 28. eReference 26. fPresent work; ratio of cell vectors fixed. gReference 24. hReference 25. iPBE energetics for a structure obtained with the optPBE-vdW functional, PBE functional with a correction to include van der Waals interactions, ref 29. jReference 27.

The valence space was represented by a plane wave basis set up to a cutoff energy of 400 eV. In the self-consistent field procedure, we invoked a Gaussian smearing technique39 (width of 0.05 eV); the final energies were obtained by extrapolating to zero smearing. The bulk structure of V2O5 was optimized regarding both the lattice parameters and the atomic positions using a 5 × 11 × 11 Monkhorst−Pack k-mesh40 and a kinetic-energy cutoff of 800 eV, while keeping the ratio a:b:c of the lattice parameters of the orthorhombic unit cell (space group Pmmn) as obtained in experiment: a = 11.51 Å, b = 3.56 Å, and c = 4.37 Å.28 We calculated the insertion energy Eins of a Li atom in bulk V2O5 as Eins = Etot(Li−V2O5) − Etot(V2O5) − Etot(Li), where the total energies Etot(Li−V2O5) and Etot(V2O5) were obtained from PBE+U calculations of bulk models with and without Li intercalation, respectively. The value Etot(Li) was determined as half the energy of bulk Li (2 atoms per unit cell),23,25 using a 21 × 21 × 21 Monkhorst−Pack k-grid.40 The resulting Li−Li distance in the bulk, 298 pm, agrees well with experiment, 301 pm.41 For the geometry relaxation after Li insertion, the transition state searches, and the polaron movement, we employed a 2 × 2 × 2 Monkhorst−Pack grid.40 The positions of the atomic centers were relaxed until residual forces were below 2 × 10−4 eV/pm. Transition state structures along the path of Li diffusion were located with the climbing-image nudged-elastic band method (CI-NEB).42 The structures of small polarons in related materials (LiFePO4,16 Fe2O3,43 TiO2)44 and their migration have successfully been modeled in similar fashion. The present polaron structure was obtained without adding an electron as the latter is provided by the inserted Li atom. The “path” of polaron migration was approximated as a linear interpolation of two (equivalent) equilibrium structures. We calculated the electron transfer coupling between two polaron states following Marcus theory.44−46 2.2. Model of V2O5. The primitive cell of V2O5 comprises two formula units, four V atoms and ten O atoms, in a series of layers that are oriented perpendicular to the z-axis (Figure 1a). Each layer consists of a periodic arrangement of edge-sharing and corner-sharing distorted VO5 square pyramids. In the experimental structure, there are three types of oxygen atoms; per VO5 unit one finds one terminal oxygen center O1 forming a vanadyl bond VO of 1.58 Å, one bridging oxygen center O2 that connects to two adjacent vanadium centers at V−O = 1.78 Å, and three chain-forming oxygen centers, O3, which are

Several materials undergo a phase transition during charging and discharging, limiting the overall capacity of a battery. Recent experiments and modeling efforts showed that the formation of small polarons in V2O5 acts as bottleneck for further Li insertion.27,30 The latter experimental and computational study also emphasized the formation of a small polaron in V2O5 upon insertion of Li, whose hopping barrier was calculated at 0.34 eV in the proximity of a static Li ion. Close spatial association of a Li ion was also determined to be crucial for stabilizing a polaron in V2O5.27 As V2O5 exhibits a relatively low electronic conductivity,31 electron transfer, via polaron migration, may also play an important role in the diffusion kinetics of Li “atoms”. The present computational study aims at providing a consistent treatment of Li transport through V2O5, at the beginning of discharge, by addressing in a coupled fashion both Li cation diffusion and small polaron migration, i.e., electron transfer between V centers. This entails examining how a Li ion and its associated polaron may migrate together in the preferred direction of transport from one V center to the nearest translationally equivalent V center. To the best of our knowledge, such a computational treatment is still lacking for V2O5. A restricted GGA+U description of either aspect of Li transport is available for the cathode materials olivine, LixFePO4.16,32 Previous studies of V2O5 materials addressed only one type of movement, either cation diffusion or polaron migration.24−27,30 Such a one-sided strategy would only be sufficient if it were known beforehand that one type of movement dominates the overall Li diffusion in this material. Rather, one has to examine models that address both types of movements such that a final situation arises where an associated pair of ion and polaron have been moved by one translational equivalent of the bulk. Hence, we have studied several such scenarios of such a combined transfer to understand the energetics of Li transport in V2O5.

2. METHODS AND MODELS 2.1. Computational Method. We carried out DFT calculations on periodic bulk models in spin-polarized fashion, using the GGA-type functional PBE33 as implemented in the Vienna Ab Initio Simulation Package (VASP 5.2).34−36 For the PBE+U variant, we chose U3d(V) = 4.0 eV, as previously used for describing oxygen vacancies and intercalated Li in V2O5.23 We chose the projector augmented-wave (PAW) method37,38 to account for the core electrons: V 1s2s2p, O 1s, and Li 1s. B


Article


van der Waals (vdW) interactions (Table 1). The present strategy of constraining the ratios a:b:c yields lattice parameters that agree very well with experiment,28 Table 1. Note that in previous DFT+U studies,24,25 except for the vdW-DF treatment,25 the interlayer separation, determined by weak attractive interactions, is overestimated by 26−31 pm compared to the experimental value; see the lattice parameter c, Table 1. The most favorable position of the inserted Li atom is determined at the hollow site above a ring of four terminal oxygen centers, Figure S4a of the Supporting Information. The Li position is shifted by 57 pm toward the bridging oxygen between two V centers, away from the center of the ring. From the spin density one concludes that the extra electron is localized at the nearest V center. This polaron causes a local distortion of the lattice around the newly formed V4+ site, Figure S4b of the Supporting Information. The original V−O bond lengths in V2O5 are calculated at 160, 180, and 190 pm for V−O1, V−O2, and V−O3, respectively. After Li intercalation, the V−O bond distances of the polaron increase to V−O1 = 166 pm, V−O2 = 192 pm, and V−O3 = 196 pm. Thus, V−O bond distances are elongated by up to 6−12 pm. The elongation of the vanadyl bond V−O1, 6 pm, agrees with results of other computational studies (PBE+U,23 6 pm; PBE +U-vdW,25 4 pm).

3. RESULTS AND DISCUSSION 3.1. Intercalation and Diffusion of Li in a V2O5 Cathode. As mentioned above, the present work aims at modeling the migration of exciton-like quasi-particles that form in the V2O5 cathode material at discharge after intercalation of Li cations, the latter at low concentration, i.e., in the material LixV2O5, 0 < x ≪ 0.5. At low values of x, the structure of the oxide material is that of the α-V2O5 phase.13,23 Our 1 × 3 × 3 supercell model corresponds to Li0.06V2O5. We calculated the insertion energy of the Li atom at −3.11 eV which is similar to the value obtained with PBE+U (PAW), −3.24 eV.25 However, this calculated insertion energy differs from that determined in other works using various DFT methods. For example, Wang et al.26 reported a significantly reduced insertion energy of Li in V2O5 bulk, − 0.69 eV. These latter calculations were carried out with the PBE functional, known for its propensity to delocalize spuriously electrons in materials with strongly correlated electron. This inadequate choice of functional may have caused this low insertion energy. Interestingly, a reported insertion energy of −2.78 eV, also calculated PBE+U, is somewhat reduced compared to the value obtained in this work.23 In that study, an identical U value, U3d(V) = 4 eV, was used; the source of the difference to the present work remained unclear.23 One may approximate the V5+/V4+ voltage at 0 K by the calculated insertion energy as Eins/z because the contributions from entropic and volume change to the change in Gibbs free energy are negligible.23,25,49 Here, z is the number of electrons transferred which is equal to 1 for a Li+ ion. As previously discussed,23 the accuracy of the estimated voltage can be improved by taking into account the contribution due to the configuration entropy. However, as the Li−Li interaction is repulsive and the concentration of Li is low, one can accurately estimate the upper voltage limit from the insertion energy of the lowest energy configuration of Li. Therefore, our calculated upper limit voltage is 3.11 V, in good agreement with the experimental value of 3.25 V reported for a cell consisting of a

Figure 1. (a) Sketch of the crystal structure of the V2O5 unit cell. The labels a, b, and c denote the lattice vectors. Label O1 indicates a terminal oxygen center, label O2 a 2-fold coordinated oxygen center, and label O3 a 3-fold coordinated oxygen center. (b) Schematic illustration of the Li-intercalated 1 × 3 × 3 V2O5 supercell. The green arrow indicates the direction of the Li+ diffusion.

3-fold coordinated, with two bonds V−O = 1.88 Å and one bond V−O = 2.02 Å (experiment values,47 Figure 1a). For studying the intercalation and diffusion properties of a Li+ ion as well as the polaron migration in the V2O5 cathode material, we selected a bulk model with a 1 × 3 × 3 supercell V36O90 built from optimized unit cells as just described (Figure 1b). This supercell proved to be large enough for treating the polaron lattice distortion; see section S1 of the Supporting Information. For validating the PBE+U results of this work, we employed a cluster model, treated with the PBE0 hybrid DFT method48 as an alternative for dealing with the self-interaction problem. The cluster model V20O62H24 comprised two layers of the V2O5 structure where all O dangling bonds were saturated by H atoms (Figure S2). We examined the insertion of a Li atom, comparing the atomic and the electronic structure to results of the PBE+U calculations on the periodic supercell model; for details, see sections S2 and S3 of the Supporting Information. The Li ion position agrees within 7 pm, the changes in V−O bond lengths upon Li insertion match within 4 pm (Figure S3 of the Supporting Information). The calculated size of the V2O5 unit cell compares well to the experimental lattice constants and bond lengths (Table 1).28 The cell parameters and various V−O bond distances deviate less than 1.3% from the corresponding experimental values. The structure obtained here is consistent with the results of previous calculations using a variety of DFT approaches: PBE,26 PBE+U,24,25,27 and optPBE-vdW+U,25 a variant addressing also C


Article

The Journal of Physical Chemistry C Li anode and an α-LixV2O5 cathode in the limit of low Li concentration.50 We examined the migration of Li in V2O5 in the limit of one atom traveling in the 1 × 3 × 3 V2O5 supercell, using the CINEB method. We considered the migration within the interlayer spacing, between two minima in the [010] direction, Figure 1b. Other pathways including the diffusion through a V2O5 layer along the [001] direction were determined to have higher barriers by at least ∼0.3 eV.24,26 As discussed above, the extra electron due to an intercalated Li+ ion remains localized at a V center throughout the migration process, as schematically shown in Figure 2. Essentially, the considered diffusion event

barrier is consistent with a recently published value, 0.15 eV, using PBE+U (U3d(V) = 4 eV),25 but lower than a previously calculated value using the standard PBE functional, 0.39 eV.26 Such a high barrier, determined with the PBE functional, might have its origin in the erroneously delocalized electron from the inserted Li atom. The DFT+U barrier of 0.37 eV, reported by Ma et al. with the same PBE+U approach as used here,24 is similar to the value calculated with the standard PBE functional, 0.39 eV,26 but much higher than our PBE+U barrier, 0.13 eV. Note in particular that the electronic structure of reduced V2O5, as calculated by Ma et al.,24 does not show a localized gap state, different from experimental observations51,52 and properly carried out DFT+U calculations,23 including the present work; see Figure S3 of the Supporting Information. In conclusion, a computational method that does not appropriately describe the localization of extra electrons in the V2O5 lattice by a gap state seems to lead to an artificially high diffusion barrier. On the other hand, a migration event where a Li ion is traveling further away from the reduced V center (i.e., from its electron, pathways 1−2 and 1 m −2, Figure 2c), while maintaining the localization of the electron at the same V center, encounters a notably increased (second) diffusion barrier of 0.36 eV (Figure 2b). Thus, the migrating of Li+ away from its reduced center is an unlikely event. Rather, the progressive diffusion of a Li ion has to occur jointly with its electron. This suggests that the electron transport in V2O5 plays an important role and needs to be taken into account to determine systematically an adequate barrier of Li diffusion. 3.2. Small-Polaron and Associated Li-Ion Migration in the V2O5 Cathode. In the following we present approximate scenarios for describing the mechanism of a coupled migration of a Li ion and the corresponding small polaron in the V2O5 structure. To simplify the problem, we assume that the two rather different types of motion can be decoupled. In consequence, we are able to compute the barrier of polaron migration while keeping the Li ion at a fixed position and vice versa. In addition, we examine an event where a Li ion and the associated polaron transfer are moving synchronously. To estimate the migration barrier of a small polaron, we defined the migration coordinate by linearly interpolating between the crystal structures in the vicinity of a V5+ and a V4+ center and carried out single-point calculations along this path. Below, we present the most favorable migration path of a Li ion and its polaron, namely, in the [010] direction. While the polaron migration barrier in the [010] direction is about 0.3 eV, we calculated dramatically higher polaron activation energies, 1.19 and 0.99 eV, in the [001] and [100] directions, respectively. Details of these calculations can be found in the Supporting Information, section S4. We examined three scenarios for moving a Li cation in association with its polaron, from one energy minimum to the corresponding one in the neighboring V2O5 ring. The calculated energy profiles of these scenarios are shown in Figure 3; the resulting reaction energies and activation barriers are summarized in Table 2. We start with scenario “a”, Figure 3a, where the Li cation is moved first, keeping the polaron localized at the nearby V center. In this first step, the system changes from configuration 1 to configuration 2 (Figure 2), along the path 1 → 2. In the subsequent step, the polaron migrates with the position of the Li ion fixed at its final position; during this second step, 2 → 1′, the system changes from configuration 2 to configuration 1′,

Figure 2. (a) Structural and schematic illustrations of Li-intercalated V2O5 where rectangles, circles, and diamonds represent the V2O5 structure, the position of an inserted Li ion, and the reduced V center (center of a small polaron), respectively. (b) Energy profile of Li-ion diffusion in V2O5. (c) Schematic representation of Li-ion diffusion in the V2O5 lattice. Open circles indicate local energy minima for the positions of the Li ion.

comprises a Li+ ion (i) traveling in close proximity to its electron (denoted as diffusion path 1−1m, Figure 2c, and (ii) traveling further away from its polaron (denoted as diffusion pathways 1m−2 and 1−2, Figure 2c). According to our calculations, the Li+ ion has to overcome a relatively small diffusion barrier of 0.13 eV when it migrates in the vicinity of its electron, path 1−1m (Figure 2b). This calculated diffusion D


Article


Figure 3. Energy profiles and their corresponding activation energies of Li-ion diffusion (ion) and polaron migration (pol) for three scenarios: (a) first, the ion moves followed by polaron migration; (b) polaron migration occurs before ion diffusion; (c) ion and polaron diffuse synchronously, followed by ion movement. The insets schematically depict the various movements where the V2O5 structure, the Li ion, and the polaron are indicated by squares, circles, and diamonds, respectively. Origin and destination of the movements are depicted by closed and open symbols, respectively.

with a rather low activation barrier of 0.19 eV. The ion diffusion of scenario “a” exhibits a higher barrier than that of the polaron migration, indicating that the charge-separating first step, the Li ion diffusion, is rate-limiting. Next, in scenario “b”, the two steps occur in reverse order (Figure 3b). The polaron migrates first, while the Li ion remains at its initial position. The system changes from configuration 1 to configuration 3, 1 → 3. In the corresponding second step, the Li cation diffuses to the energy minima in the nearest V2O5 ring, 3 → 1t. As expected, the polaron migration

the latter being extremely close to the translational image 1t of configuration 1. The difference between configurations 1′ and 1t is the missing final relaxation of the Li+ position due to the polaron being now in close proximity; a full relaxation is associated with a change in energy of −0.03 eV. In this scenario “a”, the Li cation first travels away from its electron. Hence the step 1 → 2 is endothermic by 0.09 eV, featuring an activation energy of 0.36 eV, Figure 3a and Table 2. The following polaron migration step 2 → 1′, where the electron moves toward the Li cation, is an exothermic process by −0.06 eV, E


Article

The Journal of Physical Chemistry C Table 2. Reaction Energies Er and Activation Barriers Ea of Li Ion Diffusion and Polaron Migration, As Described in Figure 3a scenario

stepb

migrating species

Er, eV

Ea, eV

a

1→2 2 → 1′ 1→3 3 → 1t 1 → 1m 1m → 1t

ion polaron polaron ion ion-polaron coupled ion

0.09 −0.06 0.11 −0.11 0.00 0.00

0.36 0.19 0.28 0.13 0.31 0.13

b c

0.15 to 0.31 eV (Table 1).25 This result may in part be due to a decrease of distance between the V2O5 layers;25 the effect of the vdW functional on the barrier of polaron migration remains unclear. Note that the lattice vector c, describing the interlayer distance, as calculated in the present work, essentially agrees with the reduced interlayer distance of the PBE-vdW calculation.25 A theoretical study on polaron migration in the LiFePO4 cathode also found that Li ions and polarons in that material exhibit a strong association energy of −0.37 eV, i.e., the energy released when bringing together a Li ion and a polaron from a large separation within the crystal.16 This energy value suggests that Li+ ions and polarons may also migrate together as exciton-like quasi-particles through the crystal.16 Indeed a recent combined experimental and computational study27 determined a close proximity between polarons and Li ions in V2O5, assigning this as a crucial effect on the Li+ diffusion. The calculated barriers of that work for polaron migration, analogous to step 1 → 3, are 0.34 eV and for the Li+ diffusion 0.22 eV (1 → 2).27 Finally, we note an experimental work54 that showed that Li intercalation and the diffusion kinetics in a carbon-coated LiFePO4 porous electrode are limited by electron transfer (at an interface) rather than by the cation transfer by itself.

a

All atomic positions were allowed to relax, with a threshold of 0.02 eV Å−1 for the residual forces. bConfiguration 1′ designates a structure very close to configuration 1t, the latter being a configuration translated by one lattice parameter from configuration 1.

away from the Li ion is calculated to be endothermic, by 0.11 eV, with a higher activation energy of 0.28 eV. The associated diffusion of the Li cation toward its electron is exothermic, by −0.11 eV, with a low diffusion barrier of only 0.13 eV, Figure 3b and Table 2. As a result, the rate-determining step of this scenario again is the first, charge-separating step, namely, the polaron migration. Finally, we examined a third scenario “c”, where in the first step, the Li ion and its associated polaron are moving in synchronous fashion, from a lowest-energy minimum to the nearest such energy minimum in the same V2O5 ring. Both the Li cation and the polaron shift simultaneously in [010] direction, from one side of the V2O5 ring to the other side of the same ring. Inspection of Figure 3c reveals that the corresponding energy profile is symmetric; the step 1 → 1m represents an isothermal process between configuration 1 and its mirror configuration 1m. The corresponding energy barrier is determined by the energy, 0.31 eV, at the midpoint of the reaction coordinate, Figure 3c and Table 2. Subsequently, to reconstitute the system configuration 1t, a diffusion of the Li ion to the following V2O5 ring takes place, associated with an activation energy of 0.13 eV, Figure 3c and Table 2; see also Figure 2 and the discussion in the preceding section. These results suggest that in scenario “c” the first step, the Li cation coupled electron transfer, is also rate-limiting. The crucial energy barrier of scenario “b” is calculated lowest, at 0.28 eV, among the three scenarios considered. Note that all three scenarios exhibit comparable energy barriers, ∼0.3 eV, in their first step, be it Li ion diffusion, polaron migration, or a synchronous transition. Overall, our study confirmed that the polaron migration plays an essential role in determining the effective barrier of Li ion transport in the V2O5 cathode. We estimated the electronic coupling constant VAB between reactant and product states that characterizes the electron transfer at the barrier of the polaron migration step 1 → 1m, invoking the simplified fragment charge difference method;53 for details, see section S5 of the Supporting Information. The resulting value is very small indeed, VAB = 0.001 eV, because the distance between two neighboring V centers in the [010] direction is quite large, 360 pm, and the involved V(3d) orbitals are not oriented in the transfer direction, leading to a small overlap between the initial and final localized states, Figure S5c of the Supporting Information. In view of the very small value of VAB, the electron transfer is nonadiabatic. Interestingly, with the inclusion of van der Waals interaction, via the combined PBE and optimized vdW functional, a barrier twice as large was calculated for the Li diffusion, increased from

4. CONCLUSIONS We studied from first-principles the intercalation and diffusion behavior of Li in V2O5 cathode material for use in Li ion batteries. Our computational results showed that intercalated Li species are fully ionized, where, at low Li loading, the reducing electron is localized at a nearby V center of the V2O5 lattice. Once again, a DFT+U approach turned out to yield an adequate description of the electronic structure. The present results support the suggestion that Li diffusion events occur in a fashion coupled with polaron migration. As evidence we examined three scenarios for coupled Li-ion-polaron diffusion in the V2O5 lattice. Scenario “b” suggests that an initial polaron migration may be the driving force of ionic diffusion, where the Li+ ion follows. However, for all three scenarios considered, the calculated apparent activation energies are rather comparable, ∼0.3 eV. Note that in the present more elaborate modeling the crucial barrier of all scenarios was the first one, which may validate results from approaches where the second part of a coupled ion and polaron transfer was not inspected.

■

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcc.7b10321. (i) Details of the V2O5 supercell model, (ii) cluster model calculations, (iii) comparison between the DFT +U approach used and a PBE0 cluster calculation, (iv) Li-ion diffusion in V2O5 in [100] and [001] directions, and (v) estimate of the coupling constant for electron transfer between neighboring vanadium centers (PDF)

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Suwit Suthirakun: 0000-0002-6590-6343 Notker Rösch: 0000-0002-4769-4332 F


Article

The Journal of Physical Chemistry C Notes

(19) Kerisit, S.; Rosso, K. M.; Yang, Z.; Liu, J. Dynamics of Coupled Lithium/Electron Diffusion in TiO2 Polymorphs. J. Phys. Chem. C 2009, 113, 20998−21007. (20) Yu, J.; Sushko, M. L.; Kerisit, S.; Rosso, K. M.; Liu, J. Kinetic Monte Carlo Study of Ambipolar Lithium Ion and Electron−Polaron Diffusion into Nanostructured TiO2. J. Phys. Chem. Lett. 2012, 3, 2076−2081. (21) Bui, K. M.; Dinh, V. A.; Ohno, T. Diffusion Mechanism of Polaron−Li Vacancy Complex in Cathode Material Li2FeSiO4. Appl. Phys. Express 2012, 5, 125802. (22) Bui, K. M.; Dinh, V. A.; Okada, S.; Ohno, T. Hybrid Functional Study of the Nasicon-Type Na3V2(PO4)3: Crystal and Electronic Structures, and Polaron-Na Vacancy Complex Diffusion. Phys. Chem. Chem. Phys. 2015, 17, 30433−30439. (23) Scanlon, D. O.; Walsh, A.; Morgan, B. J.; Watson, G. W. An Ab Initio Study of Reduction of V2O5 through the Formation of Oxygen Vacancies and Li Intercalation. J. Phys. Chem. C 2008, 112, 9903− 9911. (24) Ma, W. Y.; Zhou, B.; Wang, J. F.; Zhang, X. D.; Jiang, Z. Y. Effect of Oxygen Vacancy on Li-Ion Diffusion in a V2O5 Cathode: A First-Principles Study. J. Phys. D: Appl. Phys. 2013, 46, 105306. (25) Carrasco, J. Role of Van Der Waals Forces in Thermodynamics and Kinetics of Layered Transition Metal Oxide Electrodes: Alkali and Alkaline-Earth Ion Insertion into V2O5. J. Phys. Chem. C 2014, 118, 19599−19607. (26) Wang, Z.; Su, Q.; Deng, H. Single-Layered V2O5 a Promising Cathode Material for Rechargeable Li and Mg Ion Batteries: An Ab Initio Study. Phys. Chem. Chem. Phys. 2013, 15, 8705−8709. (27) De Jesus, L. R.; Horrocks, G. A.; Liang, Y.; Parija, A.; Jaye, C.; Wangoh, L.; Wang, J.; Fischer, D. A.; Piper, L. F. J.; Prendergast, D.; Banerjee, S. Mapping Polaronic States and Lithiation Gradients in Individual V2O5 Nanowires. Nat. Commun. 2016, 7, 12022. (28) Enjalbert, R.; Galy, J. A Refinement of the Structure of V2O5. Acta Crystallogr., Sect. C: Cryst. Struct. Commun. 1986, 42, 1467−1469. (29) Tkatchenko, A.; Scheffler, M. Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and FreeAtom Reference Data. Phys. Rev. Lett. 2009, 102, 073005. (30) Parija, A.; Liang, Y.; Andrews, J. L.; De Jesus, L. R.; Prendergast, D.; Banerjee, S. Topochemically De-Intercalated Phases of V2O5 as Cathode Materials for Multivalent Intercalation Batteries: A FirstPrinciples Evaluation. Chem. Mater. 2016, 28, 5611−5620. (31) Kang, M.; Jung, J.; Lee, S.-Y.; Ryu, J.-W.; Kim, S. W. Conductivity, Carrier Density, Mobility, Seebeck Coefficient, and Power Factor in V2O5. Thermochim. Acta 2014, 576, 71−74. (32) Dathar, G. K. P.; Sheppard, D.; Stevenson, K.; Henkelman, G. Calculations of Li-Ion Diffusion in Olivine Phosphates. Chem. Mater. 2011, 23, 4032−4037. (33) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized Gradient Approximation Made Simple. Phys. Rev. Lett. 1996, 77, 3865−3868. (34) Kresse, G.; Hafner, J. Ab-Initio Molecular-Dynamics for Liquid Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1993, 47, 558−561. (35) Kresse, G.; Furthmüller, J. Efficient Iterative Schemes for Ab Initio Total-Energy Calculations Using a Plane-Wave Basis Set. Phys. Rev. B: Condens. Matter Mater. Phys. 1996, 54, 11169−11186. (36) Kresse, G.; Furthmüller, J. Efficiency of Ab-Initio Total Energy Calculations for Metals and Semiconductors Using a Plane-Wave Basis Set. Comput. Mater. Sci. 1996, 6, 15−50. (37) Blöchl, P. E. Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 50, 17953−17979. (38) Kresse, G.; Joubert, D. From Ultrasoft Pseudopotentials to the Projector Augmented-Wave Method. Phys. Rev. B: Condens. Matter Mater. Phys. 1999, 59, 1758−1775. (39) Kresse, G.; Hafner, J. Ab Initio Molecular-Dynamics Simulation of the Liquid-Metal−Amorphous-Semiconductor Transition in Germanium. Phys. Rev. B: Condens. Matter Mater. Phys. 1994, 49, 14251−14269. (40) Monkhorst, H. J.; Pack, J. D. Special Points for Brillouin-Zone Integrations. Phys. Rev. B 1976, 13, 5188−5192.

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank Prof. Ulrich Stimming for a stimulating discussion. We gratefully acknowledge generous computing resources provided by the A*STAR Computational Resource Centre.

■

REFERENCES

(1) Goodenough, J. B.; Kim, Y. Challenges for Rechargeable Li Batteries. Chem. Mater. 2010, 22, 587−603. (2) Ceder, G. Opportunities and Challenges for First-Principles Materials Design and Applications to Li Battery Materials. MRS Bull. 2010, 35, 693−701. (3) Park, M.; Zhang, X.; Chung, M.; Less, G.; Sastry, A. A Review of Conduction Phenomena in Li-Ion Batteries. J. Power Sources 2010, 195, 7904−7929. (4) Goodenough, J. B.; Park, K.-S. The Li-Ion Rechargeable Battery: A Perspective. J. Am. Chem. Soc. 2013, 135, 1167−1176. (5) Islam, M. S.; Fisher, C. A. J. Lithium and Sodium Battery Cathode Materials: Computational Insights into Voltage, Diffusion and Nanostructural Properties. Chem. Soc. Rev. 2014, 43, 185−204. (6) Giorgetti, M.; Passerini, S.; Smyrl, W. H.; Mukerjee, S.; Yang, X. Q.; McBreen, J. In Situ X-Ray Absorption Spectroscopy Characterization of V2O5 Xerogel Cathodes Upon Lithium Intercalation. J. Electrochem. Soc. 1999, 146, 2387−2392. (7) Jin, A. P.; Chen, W.; Zhu, Q. Y.; Yang, Y.; Volkov, V. L.; Zakharova, G. S. Structural and Electrochromic Properties of Molybdenum Doped Vanadium Pentoxide Thin Films by Sol-Gel and Hydrothermal Synthesis. Thin Solid Films 2009, 517, 2023−2028. (8) Lee, J.-W.; Park, S.-M.; Kim, H.-J. Enhanced Cycleability of LiCoO2 Coated with Vanadium Oxides. J. Power Sources 2009, 188, 583−587. (9) Zhou, X. W.; Wu, G. M.; Gao, G. H.; Cui, C. J.; Yang, H. Y.; Shen, J.; Zhou, B.; Zhang, Z. H. The Synthesis, Characterization and Electrochemical Properties of Multi-Wall Carbon Nanotube-Induced Vanadium Oxide Nanosheet Composite as a Novel Cathode Material for Lithium Ion Batteries. Electrochim. Acta 2012, 74, 32−38. (10) Rui, X.; Lu, Z.; Yu, H.; Yang, D.; Hng, H. H.; Lim, T. M.; Yan, Q. Ultrathin V2O5 Nanosheet Cathodes: Realizing Ultrafast Reversible Lithium Storage. Nanoscale 2013, 5, 556−560. (11) Braithwaite, J. S.; Catlow, R. A.; Gale, J. D.; Harding, J. H. Lithium Intercalation into Vanadium Pentoxide: A Theoretical Study. Chem. Mater. 1999, 11, 1990−1998. (12) Cocciantelli, J. M.; Ménétrier, M.; Delmas, C.; Doumerc, J. P.; Pouchard, M.; Broussely, M.; Labat, J. On the σ → γ Irreversible Transformation in Li//V2O5 Secondary Batteries. Solid State Ionics 1995, 78, 143−150. (13) Rocquefelte, X.; Boucher, F.; Gressier, P.; Ouvrard, G. FirstPrinciple Study of the Intercalation Process in the LixV2O5 System. Chem. Mater. 2003, 15, 1812−1819. (14) Landau, L. Ü ber die Bewegung der Elektronen im Kristallgitter. Phys. Z. Sowjetunion 1933, 3, 644−645. (15) Pekar, S. I. Research in Electron Theory of Crystals; U.S. Atomic Energy Commission, Division of Technical Information: Oak Ridge, TN, 1963. (16) Maxisch, T.; Zhou, F.; Ceder, G. Ab Initio Study of the Migration of Small Polarons in Olivine LixFePO4 and Their Association with Lithium Ions and Vacancies. Phys. Rev. B: Condens. Matter Mater. Phys. 2006, 73, 104301. (17) Ellis, B.; Perry, L. K.; Ryan, D. H.; Nazar, L. F. Small Polaron Hopping in LixFePO4 Solid Solutions: Coupled Lithium-Ion and Electron Mobility. J. Am. Chem. Soc. 2006, 128, 11416−11422. (18) Tracy, S. J.; Mauger, L.; Tan, H. J.; Muñoz, J. A.; Xiao, Y.; Fultz, B. Polaron-Ion Correlations in LixFePO4 Studied by X-Ray Nuclear Resonant Forward Scattering at Elevated Pressure and Temperature. Phys. Rev. B: Condens. Matter Mater. Phys. 2014, 90, 094303. G


Article

The Journal of Physical Chemistry C (41) Anderson, M. S.; Swenson, C. A. Experimental Equations of State for Cesium and Lithium Metals to 20 kbar and the High-Pressure Behavior of the Alkali Metals. Phys. Rev. B: Condens. Matter Mater. Phys. 1985, 31, 668−680. (42) Henkelman, G.; Uberuaga, B. P.; Jonsson, H. A Climbing Image Nudged Elastic Band Method for Finding Saddle Points and Minimum Energy Paths. J. Chem. Phys. 2000, 113, 9901−9904. (43) Rosso, K. M.; Smith, D. M. A.; Dupuis, M. An Ab Initio Model of Electron Transport in Hematite (α-Fe2O3) Basal Planes. J. Chem. Phys. 2003, 118, 6455−6466. (44) Deskins, N.; Dupuis, M. Electron Transport Via Polaron Hopping in Bulk TiO2: A Density Functional Theory Characterization. Phys. Rev. B: Condens. Matter Mater. Phys. 2007, 75, 195212. (45) Marcus, R. A.; Sutin, N. Electron Transfers in Chemistry and Biology. Biochim. Biophys. Acta, Rev. Bioenerg. 1985, 811, 265−322. (46) Marcus, R. A. Electron Transfer Reactions in Chemistry. Theory and Experiment. Rev. Mod. Phys. 1993, 65, 599−610. (47) Shklover, V.; Haibach, T.; Ried, F.; Nesper, R.; Novak, P. Crystal Structure of the Product of Mg2+ Insertion into V2O5 Single Crystals. J. Solid State Chem. 1996, 123, 317−323. (48) Adamo, C.; Barone, V. Toward Reliable Density Functional Methods without Adjustable Parameters: The PBE0 Model. J. Chem. Phys. 1999, 110, 6158−6170. (49) Aydinol, M. K.; Kohan, A. F.; Ceder, G.; Cho, K.; Joannopoulos, J. Ab Initio Study of Lithium Intercalation in Metal Oxides and Metal Dichalcogenides. Phys. Rev. B: Condens. Matter Mater. Phys. 1997, 56, 1354−1365. (50) Moss, P. L.; Fu, R.; Au, G.; Plichta, E. J.; Xin, Y.; Zheng, J. P. Investigation of Cycle Life of Li−LixV2O5 Rechargeable Batteries. J. Power Sources 2003, 124, 261−265. (51) Hermann, K.; Witko, M.; Druzinic, R.; Chakrabarti, A.; Tepper, B.; Elsner, M.; Gorschlüter, A.; Kuhlenbeck, H.; Freund, H. J. Properties and Identification of Oxygen Sites at the V2O5(010) Surface: Theoretical Cluster Studies and Photoemission Experiments. J. Electron Spectrosc. Relat. Phenom. 1999, 98, 245−256. (52) Wu, Q. H.; Thissen, A.; Jaegermann, W.; Liu, M. L. Photoelectron Spectroscopy Study of Oxygen Vacancy on Vanadium Oxides Surface. Appl. Surf. Sci. 2004, 236, 473−478. (53) Voityuk, A. A.; Rösch, N. Fragment Charge Difference Method for Estimating Donor−Acceptor Electronic Coupling: Application to DNA π-Stacks. J. Chem. Phys. 2002, 117, 5607−5616. (54) Bai, P.; Bazant, M. Z. Charge Transfer Kinetics at the SolidSolid Interface in Porous Electrodes. Nat. Commun. 2014, 5, 3585-1-7.

H


Modeling Polaron-Coupled Li Cation Diffusion in V2O5 Cathode

Recommend Documents