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Cite This: Chem. Mater. 2018, 30, 3315−3322

Understanding Ionic Diffusion through SEI Components for LithiumIon and Sodium-Ion Batteries: Insights from First-Principles Calculations Fernando A. Soto,† Asma Marzouk,‡ Fedwa El-Mellouhi,*,‡ and Perla B. Balbuena*,† †

Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, PO Box 34110, Doha, Qatar

‡

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S Supporting Information *

ABSTRACT: The insufficient understanding of the physical and chemical phenomena taking place at the electrode−electrolyte interface is the main roadblock for improvement of current battery technologies and development of new ones. Of particular interest is the solid−electrolyte interphase (SEI) layer because many aspects of the battery performance depend on its quality. Recently we have shown that a stable SEI layer can be designed in specific Li- or Na-based electrolytes. In this paper, we continue exploring this concept by identifying the interactions that take place at the lithiated (or sodiated) carbon−electrolyte interface and discussing the transport mechanisms of Li and Na ions through the most commonly found SEI layer inorganic components. For the ab initio molecular dynamics (AIMD) simulations, we considered the case of the sodiated hard carbon structure. The simulations show the decomposition of ethylene carbonate on the edge of the graphite layers leading to products such as CO and other organic fragments. The decomposition of the PF6− anion is a precursor step for the formation of NaF layers. Regarding the Li- and Naion transport through the SEI, the results show that the energy to create defects is lowest when Li ions are guests at an interstitial position in NaF and lattice positions in Na2CO3. For the LiF and Li2CO3 crystals, the energy to create defects is lowest when Na ions substitute Li. This lower energy cost for Li-ion defects in Na-based components is due to the smaller size of the Li ion when compared to the Na ion. Regarding diffusion barriers, the Na ions in Li-based SEI components show a preference for the vacancy diffusion and knock-off mechanisms as the preferred pathways to migrate through the SEI while Li ions in Na-based SEI components prefer a mechanism involving the migration of the interstitial ion through the knock-off or direct hopping mechanism. This work also emphasizes the interplay between the crystallographic orientation of the SEI components and the direction dependent ion migration guiding the controlled design of efficient artificial SEI layers.

1. INTRODUCTION The insufficient understanding of the electrode−electrolyte interface is one of the major bottlenecks to developing better and safer Li-ion and Na-ion batteries (LiBs/NaBs).1,2 Degradation of the electrolyte leads to the formation of a surface film layer on top of the negative electrode, the so-called solid−electrolyte interphase (SEI) concept introduced by Peled et al.3−5 in 1979. Such a surface film layer is desired for protection, only allowing ionic transport (e.g., Li+ and Na+) while blocking electron and solvent molecule transport.6 In LiBs, the SEI is usually described as consisting of a thin inorganic compact layer close to the electrode and a thick porous (formed from oligomer and polymer products) secondary layer closer to the electrolyte. An ideal SEI layer would allow the battery to maintain its capacity during cycling. However, computational and experimental studies in recent years have shown that the SEI layer is defective leading to further electron transfer, electrolyte decomposition, unstable electrolyte decomposition products, and uncontrollable SEI growth.7−9 In LiBs these processes consume cyclable Li ion rendering the battery useless. The operation of NaBs is similar © 2018 American Chemical Society

to that of LiBs, and it commonly uses sodium hexafluorophosphate (NaPF6) dissolved in a mixture of alkyl carbonates as the electrolyte solution and two high-/low-potential operation electrodes exhibiting reversible redox reactions with Na ions.10,11 Due to the limitations posed by Na-ion intercalation into graphite (e.g., Na-ion intercalation leads to a low storage capacity of 248 mA h/g or NaC9), hard carbons are used as the intercalation material for the anode in NaBs.12−14 The reactions that take place in NaBs lead to the formation of a nonuniform SEI layer that consists of inorganic compounds, sodium carbonate (Na2CO3) and NaCO3R (R = alkyl) in ethylene-carbonate-/propylene-carbonate-based (EC-/ PC-based) electrolytes.11,15 In both LiBs and NaBs, the uncontrolled formation of an SEI layer can lead to loss of charge carriers and slower ionic transport among other factors that contribute to battery failure. Recent work has suggested that the initially formed SEI layer Received: February 10, 2018 Revised: April 21, 2018 Published: April 23, 2018 3315

DOI: 10.1021/acs.chemmater.8b00635 Chem. Mater. 2018, 30, 3315−3322

Article

Chemistry of Materials

ultimately, improve the capacity retention of LiBs/NaBs technologies.

can be tuned to improve the ionic transport within the SEI layer of LiBs and NaBs.16,17 We explored this concept in a recent paper18 where we showed that a stable SEI layer can be designed by precycling the electrode in desired Li- or Na-based electrolyte and that the ionic transport can be tuned by preforming SEI layers of specific compositions. As an example, the capacity of the hard carbon electrodes can be tuned by the formation of a porous Na-based SEI.18 However, the design of such preformed layers demands a better knowledge about the mechanisms of ion migration through them. Thus, having a deeper understanding of the SEI layer stability and ionic transport through SEI components in LiBs/NaBs is a major step in achieving the stability of the SEI layer, ultimately improving the capacity retention of the batteries. Such understanding requires a detailed characterization of the kinetics of ionic transport, which is usually characterized via evaluation of mechanistic pathways and activation barriers via first-principles analyses. Density functional theory (DFT) calculations have allowed comparison of Li-ion transport through typical SEI materials.19 The study showed that the barrier to Li+ migration in Li2CO3 ranges from 0.23 to 0.49 eV, and 0.15 eV in Li2O. Meanwhile, the barrier to Li+ migration in LiF is much higher (0.73 eV). However, defect formation could also play a significant role in ionic transport across the SEI layer. Thus, analyses of defect formation energy and defect migration are usually carried out in these materials. Nudged-elastic band (NEB) calculations based also on DFT20 yielded diffusion barriers of dominant defects in LiF showing that the diffusion barrier for a negatively charged Li-vacancy ranges from 0.57 to 0.60 eV.21 Meanwhile, for the positively charged F-vacancy, the calculated diffusion barrier was 0.69 eV. Another important aspect is the characterization of open channels and/or structurally favorable/unfavorable directions where ionic diffusion may be promoted/blocked. As an example, slow diffusion across the planes of a defective Li2CO3 crystal (0.60 eV) was revealed by DFT calculations,22 while smaller migration barriers (0.28 eV) were found along the open channels in the [010] directions. Putting together the information regarding individual materials, an improved overall picture of transport through these complex interphases and the connection to the battery performance may emerge. In a combined experimental and computational work, the ratelimiting step in LiBs was shown to be the Li+ migration within the inner SEI layer (e.g., LiF, Li2O, and Li2CO3).23 Moreover, the main diffusion carriers in Li2CO3 at potentials below 0.98 V (vs Li/Li+) were found to be excess Li-ion interstitials, and above 3.98 V Li-ion vacancies become the dominant diffusion carrier type. Microscopic details were also revealed: the interstitial Li+ ion was shown to diffuse through a “knock-off” mechanism by continuously displacing the Li+ ions in neighboring sites. Other DFT work reported the Li+ migration through Li2CO3 to be 0.54 eV for the direct hopping mechanism and 0.31 eV for the knock-off mechanism.24 It is important to note that this mechanism has also been reported in the organic lithium ethylene dicarbonate Li2EDC (the outer and more porouslike region of the SEI layer).25 In this paper, we present results from DFT, ab initio molecular dynamics (AIMD), and NEB calculations that help us in attaining a deeper characterization of the SEI layer regarding electrolyte decomposition products and ionic transport of SEI components in LiBs and NaBs. We expect that these results may contribute to a better understanding of the SEI ionic conductive properties as a first step to design a stable and efficient SEI layer and,

2. METHODOLOGY Simulations involving DFT, AIMD, and NEB calculations were performed using the Vienna ab initio simulation package (VASP)26−29 with the Perdew−Burke−Ernzerhof functional (GGA-PBE).30 The projector augmented wave (PAW) pseudopotentials were used31,32 for the exchange-correlation (XC) functional and pseudopotential treatment, respectively. For the case of NaF, s and p electrons were taken into consideration. The convergence criteria for optimizations were set up to 10−3 and 10−4 eV for the ionic relaxation loop and self-consistent electronic iteration, respectively. The kinetic cutoff energy of 500 eV has been employed for LiF, Li2CO3, and Na2CO3 and 400 eV for NaF. The Brillouin Zone (BZ) was sampled by a Monkhorst−Pack grid centered at the γ/γ point with a k-point mesh of 5 × 5 × 5 for NaF and LiF, 2 × 4 × 3 for Li2CO3, and 3 × 2 × 2 for Na2CO3. 2.1. AIMD Simulations. The AIMD simulations were performed in a constant temperature canonical ensemble (N = atoms, V = volume, T = temperature, NVT). The Nose− Hoover thermostat was applied to control the 400 K temperature during the AIMD run with a 1 fs time step and tritium replacing the H mass. Bader charges33 were calculated to investigate the bearing charge of the atoms in the system. The Becke−Jonson (BJ) damping method was used to account for van der Waals interactions.34 2.2. NEB Calculations. The nudged-elastic band (NEB) method developed by Jonsson and co-workers was used to verify the activation barrier for Na and Li ions through the SEI components.35 Between five and nine images of the ion migration reaction coordinates were used for the NEB calculations. For each reaction coordinate, the maximum energy difference among all images was considered as the migration barrier for ionic diffusion. All images were simultaneously optimized along the reaction path until the forces acting on the atoms in each image converged to 0.1 eV/ Å. Several crystals were studied as SEI components including LiF, NaF, Li2CO3, and Na2CO3. The calculation of the formation energies of the defects was done with a 3 × 3 × 3 supercell for NaF and LiF, and 1 × 2 × 2 for Li2CO3 and Na2CO3. Additional formation energies of defects are calculated using bigger supercells for Li2CO3 and Na2CO3 (2 × 2 × 2 supercell) to verify the possibility of defect interactions in the smaller cells. The energies are slightly different by few meV. NEB calculations for NaF and LiF were carried out with smaller supercells (2 × 2 × 2) to optimize the CPU time. We analyzed the following defects: (1) NaI, LiI, the guest ion is located in an interstitial position; (2) NaLi, LiNa, the substitutional guest ion occupies a lattice site; (3) Frenkel-pair defect NaI+VLi and LiI+VNa, the guest ion occupies an interstitial position with the presence of a lattice vacancy; (4) NaLi+LiI, LiNa+NaI, the guest ion occupies the lattice site, and the regular ion is located in an interstitial position; and (5) NaLi+VLi, LiNa+VNa, the guest ion is located in a lattice position with the presence of a lattice vacancy. 3. RESULTS We first conducted AIMD simulations to study the least known electrode−electrolyte interface in NaBs at three stages of sodiation (Na0.25C9, Na0.75C9, and NaC9). Because we want to 3316


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calculations. Figure 1a,b shows the two most favorable interstitial sites for Li2CO3. Two different interstitial positions of the Li ion in two different orientations ([010] and [110] directions) are also considered for Na2CO3 (Figure 1c,d). The formation energies of the interstitial defects in the different directions are comparable for each component (2.49 eV for Li2CO3 and 1.5 eV for Na2CO3). Comparison of the formation energies of the different defects (Table 1) leads to the conclusion that the defect preferably occupies the lattice site in the case of Na in LiF and Li2CO3 and Li in Na2CO3, while Li prefers to be localized in the interstitial position in NaF. It is interesting to highlight that the negative formation energy of the LiNa defect suggests that when Li occupies a lattice position, the defect stabilizes the Na2CO3 system. This behavior is in agreement with a previous study by Yatsenko et al.37 on the mixed carbonate (LiNaCO3) which is found to be more stable that Na2CO3 with formation energies of −2.18 and −2.09 eV, respectively.38 This could be explained by the high relative stability of the Li2CO3 (formation energy of −2.32 eV38) compared to Na2CO3. We tested the defect corresponding to NaLi+LiI and LiNa+NaI when the guest ion moves to the lattice position by pushing the lattice atom to the next interstitial position. Compared to the formation energy of the interstitial defect when the lattice atom is occupying its regular position, the (NaLi+LiI/LiNa+NaI) defect is found to be less favorable. In the case of LiF, the presence of the Na defect is found to be favorable at the substitutional position (NaLi) with formation energy of approximately 0.8 eV, followed by the (NaI+VLi) defect with comparable formation energy. The presence of an additional ion in an interstitial position (NaI, or NaLi+LiI) is found to be less favorable. Contrary to the LiF, the interstitial defect was found to be most favorable in the case of NaF with formation energy of about 1.7 eV. In the case of the (LiNa+NaI) defect, Na is unstable in the interstitial position while Li is occupying a lattice site. After a full relaxation of this defect, Na was found to reoccupy its lattice position and push the Li atom to its initial interstitial one. The formation of the NaLi+VLi (or LiNa+VNa) defect is the most costly one among all cases. 3.2. Ionic Diffusion Mechanisms. First, we note that the defect formation energies were calculated to identify the thermodynamically most stable bulk defects. However, these calculations were followed by a kinetic analysis in the presence of an electrical field (as happens during battery cycling) thus assuming that, under cycling experimental conditions, intrinsic defects could be created, supporting the hypothesis of kinetically dominated defect concentrations. Therefore, we assumed that the defect diffusion barriers identified in this

focus on ion transport mechanisms through NaB SEI components, details of the AIMD simulations and decomposition reactions are elaborated in the Supporting Information. The simulations showed the initial stages of electrolyte decomposition and the nucleation of the initial seeds of the main SEI products: Na2CO3 and NaF. These initial nuclei ultimately may self-assemble forming the “inner” and “outer” regions of the SEI layer, respectively. One important issue was found regarding the intercalation of solvent. The AIMD simulations showed a ternary cointercalation (EC, Na+, hard carbon) starting from the Na0.75C9 sodiation stage. We note that this cointercalation may result in a different SEI structure. However, the topic of SEI nucleation and growth deserves a complete separate analysis. Here we focus on developing a comparative analysis about how Li ions and Na ions are allowed to pass through the main Na2CO3 and NaF and through the Lianalogous LiF and Li2CO3, respectively, as discussed next. 3.1. Defect Formation in Crystal Structures of SEI Components. We start by discussing the defect formation of Li-based and Na-based SEI components to serve as a reference for discussions in later sections. For the defect formation calculation we only considered neutral defects, for which the formation energy ΔEf is calculated by eq 1:36 ΔEf = Ed − E b + Er − Ea

(1)

where Eb is the bulk total energy without the defect, Ed is the total energy of the bulk with the defect, and Ea and Er are the energies of the added and removed species, respectively. Table 1 lists the formation energies of all the defect types described above for LiF, NaF, Li2CO3, and Na2CO3. Table 1. Neutral Defects and Associated Formation Energies (in eV) Considered for LiF, NaF, Li2CO3, and Na2CO3 Defect Formation Energy (eV) defect types

Na in LiF

Na in Li2CO3

defect types

Li in NaF

NaLi NaI NaI+VLi NaLi+VLi NaLi+LiI VLi

0.76 5.81 0.82 7.36 5.31

0.93 2.49

LiNa LiI LiI+VNa LiNa+VNa LiNa+NaI VNa

3.47 1.74 3.43 5.40 n.c.c 5.61

5.64 2.69 4.82

Li in Na2CO3 −0.26 1.5a/1.6b 4.74 1.65a/2.18b 3.30

a [110] direction. b[010] direction. cn.c.: not converged; Li prefers to come back to its initial interstitial position and Na in its lattice position.

Inequivalent interstitial sites present in Li2CO3 and Na2CO3 have been considered for the defect formation energy

Figure 1. Interstitial sites present in the (a, b) Li2CO3 and (c, d) Na2CO3 crystals and their associated formation energies (Ef). The color code is as follows: yellow, green, brown, and red spheres represent Na, Li, C, and O atoms, respectively. 3317


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Figure 2. Potential energy profiles of the different studied ionic migration mechanisms for (a) LiF, (b) NaF, (c) Li2CO3, and (d) Na2CO3 crystals.

Table 2. Calculated Migration Energy Barriers (Em), Activation Energiesa (Ea), Diffusion Lengths (a), and Diffusion Coefficients (D) of Considered Ionic Migration Mechanisms in LiF, Li2CO3, Na2CO3, and NaF D (cm2/s) model LiF

Li2CO3

Na2CO3

NaF

diffusion mechanism

Em (eV)

Ea (eV)

g

a (Å)

vacancy diffusion concerted exchange knock-off direct hopping vacancy diffusion concerted exchange knock-off direct hopping Na-vacancy diffusion concerted exchange knock-off knock-off direct hopping direct hopping vacancy diffusion concerted exchange knock-off direct hopping

0.81 3.32 0.52 0.38 0.28 1.6 0.2 0.9 0.71 1.54 1.00b 0.76c 0.73b 0.28d 0.24 2.61 n.a.e 0.86

8.17 4.07 6.1 5.96 5.92 2.53 2.75 3.38 4.11 1.28 2.50b 2.36c 2.23b 1.88d 5.67 6.54 n.a.e 2.76

3 3 3 3 1 1 1 1 1 1 1 1 1 1 3 3 3 3

4.00 2.93 7.70 3.44 4.50 2.83 5.50 7.50 2.80 3.61 5.06b 4.05c 8.27b 11.90d 2.80 3.30 n.a.e 4.50

300 K 1.82 2.96 2.36 1.03 1.57 4.27 3.29 1.91 7.72 2.22 4.46 6.23 3.85 5.58 3.81 2.01 n.a.e 1.57

× × × × × × × × × × × × × × × ×

10−139 10−71 10−104 10−102 10−102 10−46 10−49 10−59 10−72 10−76 10−45b 10−43c 10−40b 10−34d 10−98 10−112

× 10−49

1000 K 1.86 6.08 6.59 6.23 2.38 4.91 1.59 2.73 3.87 4.15 2.21 6.71 1.19 1.20 9.72 9.21 n.a.e 9.68

× × × × × × × × × × × × × × × ×

10−42 10−23 10−32 10−32 10−32 10−16 10−16 10−19 10−23 10−25 10−15b 10−15c 10−13b 10−11d 10−31 10−35

× 10−17

ε (V/Å) 0.20 1.13 0.07 0.11 0.09 0.57 0.04 0.12 0.25 0.43 0.20 0.19 0.09 0.02 0.09 0.79 n.a.e 0.19

a

The activation energies are calculated by adding the migration barrier to the corresponding defect formation energy shown in Table 1. b[110] direction. c[100] direction. d[010] direction. en.a.: not applicable.

study dominate the contribution to the activation energies for diffusion. As shown in Table 1, the ionic diffusion through perfect bulk materials would require energetically expensive formation of some defects. However, using an NEB analysis, we are not limited to only defects with lowest formation energy. To have a

deep investigation of the diffusion pathways that may reflect the real conditions with the natural presence of the defect, the NEB analysis covers various migration mechanisms, although the formation energies of some defects are sometimes costly. The following mechanisms have been investigated (Figure 2): (i) knock-off, (ii) direct hopping, (iii) vacancy diffusion, and (vi) 3318


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characterized by the presence of a local minimum, representing the Na occupation of a lattice position [(NaLi+LiI) defect]. As for the diffusion of Li through NaF, the most favorable diffusion mechanism based on the activation energies is the direct hopping mechanism with a migration barrier of 0.86 eV, slightly less favorable than the diffusion of the Li through LiF (0.75 eV) as reported by Greeley et al.39 The knock-off mechanism, which results in the occupancy of the interstitial site by Na and the lattice site by Li, is found to be unfavorable; the Na atom cannot fit into the interstitial position due to its large size and returns to its initial lattice site. Regarding the diffusion of Na ions through Li2CO3, the Na ion is found to migrate easily as the channels are larger than in LiF or NaF. Figure 2c shows that the Na ion migrates easily from an interstitial position to a lattice site. It requires a low diffusion barrier (0.11 eV) to reach a more stable structure, corresponding to a split interstitial where the lattice and the interstitial atoms are at halfway positions (see Figure S7). Then, the ion needs more energy (0.19 eV) to push the lattice ion (Li) in a less stable adjacent interstitial position. The reverse pathway to come back to the interstitial site is favorable, however, slightly higher with a barrier of 0.23 eV. The NEB energy profile of the direct hopping mechanism, when the Na atom migrates between two nearby interstitial sites, confirms the presence of inequivalent interstitial sites which involve the migration of the ion to a more stable position. The diffusion by this mechanism could also be considered as favorable (diffusion barrier of 0.9 eV). Similar to Li2CO3, Na2CO3 also has inequivalent interstitial sites as confirmed by the presence of the local minimum (0.16 eV less stable) as shown in the energy profile of the interstitial Li-ion diffusion pathway in Figure 2d. The ionic migration through Li2CO3, Na2CO3 highlights the importance of the crystallographic direction on the ionic diffusion pathways. In fact, the migration of the interstitial defect along the [010] diffusion channel prefers to migrate by the direct hopping mechanism with a low barrier of 0.28 eV. This migration energy is found to be slightly different from the barrier needed by the Na ion to diffuse through Na2CO3 (0.6 eV)40 due to the difference in the ionic radii. As shown in Figure 2d, the diffusion along the [110] direction requires more energy to migrate to the next equivalent site along the [110] direction (0.73 eV). Figure S9 shows the path images of the Li-ion migration by direct hopping mechanism along the two considered directions. We should emphasize the possibility of the migration of the Li ion along the other directions ([100] and [110] directions) with a similarly high-energy barrier. The diffusion of the Li ion by the knock-off mechanism in Na2CO3, along [110] and [100] directions, results in high migration barriers (1.00 and 0.76 eV, respectively), as the final positions of the atoms are less favorable (Figure S8). The knock-off mechanism is illustrated in Figure S10. Also, it is important to note that the Na-vacancy diffusion reported for Na2CO3, in Table 2, only involves the migration of a host Na ion into a vacant site, and it is found to facilitate the migration of the ion (diffusion barrier of 0.7 eV). However, this migration requires the creation of a Na-vacancy and requires a high formation energy (3.24 eV), leading to the high activation energy. With the presence of this vacancy in the system, we studied the migration of a Li ion into a host vacant site in Na2CO3 found to be unfavorable, as the ion prefers to come back to its initial position in the interstitial site. As for the other studied systems, the concerted-exchange mechanism is the one

concerted exchange. For Na2CO3, we presented, in Figure 2d, only the diffusion along different directions starting from the two inequivalent interstitial sites located along the [010] and [110] directions, corresponding to the knock-off and direct hopping mechanisms, respectively. The diffusion coefficient of the defect (D), or dif f usivity, is the indicator of the rate at which the ion diffuses. It can be calculated using eq 2: ⎛ E ⎞ D (cm 2/s) = ga 2ν exp⎜ − a ⎟, ⎝ kBT ⎠ g = 1 − 3 and ν = 1.012 s−1

(2)

Here, g represents the dimensionality of the diffusion direction which is material dependent and relies on the crystallographic symmetry of the diffusion channels. For example, for LiF and NaF the diffusion occurs in all three crystallographically equivalent dimensions; however, in Li2CO3 and Na2CO3 it occurs along distinct one-dimensional diffusion channels along specific crystallographic directions, namely, the [110], [100], and [010] directions. Here, ν represents the attempt frequency, Ea is the activation energy associated with each defect, a corresponds to the distance traveled by the defect, and kB is the Boltzmann constant (8.617 330 3 × 10−5 eV/K). The diffusion coefficient estimations were performed at 300 and 1000 K. Table 2 gathers the migration energy barriers obtained from the NEB calculations (Em, in eV), the activation energies (Ea, in eV, adding the formation energy to the migration energy barrier), the defect diffusion coordinate (a, in Å), and the diffusion coefficients (D in cm2/s). Table 2 includes also the electric field (ε) whose effect is discussed later. The diffusion coefficients indicate a slow thermally activated ionic diffusion via vacancies, interstitial and lattice sites. These diffusion mechanisms require the application of an external electric field to accelerate the ionic transport on the seconds time scales. For vacancy-assisted dif f usion, the guest ion occupying a lattice position in bulk migrates to the neighboring vacant lattice site. This diffusion is controlled by the concentration of the defect, which is moving in the opposite direction from the diffusing atom. As shown in Table 2 the vacancy-assisted diffusion mechanism is characterized by a relatively low diffusion barrier for the studied SEI components. Thus, due to the high formation energy of creating a host vacancy in a perfect bulk (found to be 7.4, 5.4, 5.6, and 3.4 eV for the Li in LiF, Na in NaF, Li in Li2CO3, and Na in Na2CO3 models, respectively), the mechanism is considered as unfavorable with extremely low diffusion coefficients. Regarding the diffusion barrier, Na is found to migrate easily through the LiF component when it occupies an interstitial position. The lowest energy barrier was found by the direct hopping mechanism (0.38 eV), followed by the knock-off mechanism, with a slightly higher barrier of 0.52 eV. Nevertheless, the interstitial defect formation energy is high which leads to high activation energies and very low diffusion coefficients for both mechanisms. According to Table 2, the most favorable migration mechanism (lowest activation energy) for Na through LiF is the concerted exchange between two lattice positions, but this mechanism involves a considerable structural change which results in a very high migration barrier of about 3.32 eV. This high barrier leads to the conclusion that the diffusion of Na through LiF is unfavorable, comparing it to its diffusion through NaF (1.34 eV).39 The diffusion by the knock-off mechanism is 3319


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(3)

achieved by growing these components along crystallographic directions parallel to the ionic diffusion channels. Qi44 and co-workers reported electron tunneling probability values and critical thickness of SEI crystals such as LiF and Li2CO3. Based on their work function and band gap calculations, a 2 nm LiF can completely block electron tunneling while Li2CO3 requires a thickness of approximately 3 nm. The authors made a connection between irreversible capacity loss and DFT-calculated electron tunneling barrier, and they concluded that the initial capacity loss is due to the self-limiting electron tunneling property of the SEI. More broadly, they suggest that other electron transport mechanisms (e.g., polarons, defects) need to be considered to explain the leakage through SEI films with increased thickness (e.g., beyond 10 nm). Here we note two aspects that make previous calculations and ours somehow “idealized”. First, we analyze bulk crystal structures. These structures most likely do not exist during battery cycling where amorphous structures are more possible. Moreover, formation energy of defects calculated in pristine crystals are also “ideal”. Amorphous films may have natural defects that may enhance/block both ionic and electronic transport. Thus, interfacial ionic/electronic transport in thin films in contact with the electrode surfaces should be investigated. With respect to electronic transport, the same comment can be made. The analysis by Qi et al. assumes electronic transport in perfect crystals. Thin films behave differently, as recently shown.45 In current work we are addressing these issues by analyzing electron transfer through SEI nuclei in their initial stages of nucleation. This study will be reported elsewhere.

To provide a prediction of the expected diffusion pathways that may be activated at the same time when applying a given value of an electric field we use the following procedure: We considered the longest distance traveled by the ion (Table 2) for each SEI component (7.7, 4.5, 7.5, and 11.88 Å for LiF, NaF, Li2CO3, and Na2CO3, respectively) requiring enough potential energy to overcome barriers of 0.77, 0.45, 0.75, and 1.19 eV, respectively. At ε = 0.1 V/Å, ions could overcome the diffusion barriers for the knock-off mechanism in LiF and vacancy-assisted diffusion in NaF. Importantly, the direction of the applied electric field is determinant in the case of Li2CO3 and Na2CO3. In some cases, two diffusion mechanisms are found to be activated at the same time. For Li2CO3, both the diffusion by vacancy-assisted and knock-off mechanisms would be activated simultaneously as they require similar diffusion barrier (0.28 and 0.2 eV, respectively). Therefore, to overcome these diffusion barriers, the application of an electric field along [001] direction is required. For Na2CO3, in terms of diffusion barrier, both direct hopping mechanisms along the [010] and [110] diffusion channels seem to be the activated upon the application of 0.1 V/Å electric field, suggesting that if the electric field is oriented along either [010] or [110] direction, the Li diffusion is possible. The activation of these onedimensional ionic diffusion channels in Li2CO3 and Na2CO3 depends strongly on the direction of the applied electric field [56]. In summary, NaF and LiF favor the 3-dimensional ionic diffusion pathways suggesting that the growth of these components along different crystallographic direction would not affect their ionic transport. On the other hand, the ionic diffusion in Li2CO3 and Na2CO3 occurs along one-dimensional channels suggesting that an efficient ionic transport could be

4. CONCLUSIONS We report a first-principles investigation of the decomposition products of EC + salt when in contact with various degrees of sodiated carbon layers and the effect of the SEI components on the ionic transport in LiBs and NaBs. AIMD simulations show that the main decomposition of EC on sodiated hard carbon structures takes place at the edge of the carbon layers leading to decomposition products that can be considered as precursor structures for the formation of Na2CO3 and others that can be precursor steps for the formation of NaF blocks. These two types of salts, Li and Na carbonates, and Li and Na fluorides were used as model SEI products in the diffusion analyses. For the migration of ions through SEI blocks, different neutral defects in the SEI compounds were investigated along various ionic diffusion channels. Several pathways such as vacancy diffusion, direct hopping, knock-off, and concerted-exchange mechanisms were characterized, although the high formation energies of some defects would not allow ionic migration. The calculation of the defect formation and migration energies leads to the conclusion that some defects could be easy to form, but migrate very slowly and vice versa. Considering that under experimental conditions intrinsic defects may be created during cycling, it could be assumed that the defect diffusion barriers identified in this study dominate the contributions to the migration activation energies and to the diffusion coefficients. As a general trend, we observe that in Li-based SEI components Na ions migrate using the concerted-exchange mechanism, due to the larger ionic size of Na compared to its host Li. On the other hand, Li ions in Na-based SEI components migrate through an interstitial mechanism due to the smaller ionic size of Li compared to its host Na. This work

that requires a high migration barrier (1.54 eV), but this mechanism remains the most stable for the Na2CO3 case with the lowest activation energy of 1.23 eV. In the case of Li-ion diffusion, it is important to note how these diffusion coefficients differ from calculated Li-ion diffusion values in graphite (1.12 × 10−10 to 6.51 × 10−11 cm2/s at room temperature for a neutral state of charge) and EC solvent.41,42 This difference in diffusion coefficients may cause interesting phenomena to take place at the various interfaces. Indeed, in a recent paper, Zhang et al. reported a synergetic effect of LiF and Li2CO3 interfaces caused by a space charge accumulation and higher ionic carrier concentration which not only facilitates Li-ion migration across boundaries but also prevents undesired electrolyte decomposition.43 It is expected that higher temperature yields a high ionic diffusivity and thus a fast cycling behavior. However, in the case of bulk material, the formation energies of the defects are high, giving rise to high values of activation energies and very low diffusivity of the ions even at 1000 K (as shown in Table 2). According to these observations, it is noteworthy that the application of an external electric field (ε) is essential to promote the ionic migration through the bulk materials and activate specific diffusion pathways. Based on the calculated energy barriers obtained for each component, we calculated the corresponding electric field threshold required to activate each diffusion pathway, as shown in Table 2, by the following eq 3: ε (V/Å) =

Em (eV) ; q (e) a (Å)

where q = 1e

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shows that there is a difference in ionic diffusion coefficients among various SEI components that is strongly dependent on the dimensionality of the ionic diffusion channel and the crystallographic orientation of the material that should be taken into account when designing an artificial SEI layer. Thus, strategies that encourage or prohibit the formation of certain SEI components and certain defects are envisioned as a way to improve the stability and life of LiBs and NaBs. This paper presents key results toward achieving that goal.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.chemmater.8b00635. Additional figures including AIMD results, Li2CO3 structure during knock-off mechanism, LiNa+NaI defect in Na2CO3, and pathway images for Li-ion migration (PDF)

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. ORCID

Fedwa El-Mellouhi: 0000-0003-4338-9290 Perla B. Balbuena: 0000-0002-2358-3910 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are thankful for the NPRP grant 7-162-2-077 from the Qatar National Research Fund (a member of Qatar Foundation). F.A.S. and P.B.B. also acknowledge partial support from the Assistant Secretary for Energy Efficiency and Renewable Energy, Office of Vehicle Technologies of the U.S. Department of Energy under Contract DE-EE0007766 under the Advanced Battery Materials Research (BMR) Program. The findings achieved herein are solely the responsibility of the authors. Computational resources are provided by research computing at Texas A&M, University at Qatar, and the KAUST Supercomputing Laboratory. Authors acknowledge fruitful discussions with Prof. Jorge Seminario.

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REFERENCES

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