Understanding Ionic Diffusion through SEI Components for Lithium-Ion

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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 Chem. Mater., Just Accepted Manuscript • DOI: 10.1021/acs.chemmater.8b00635 • Publication Date (Web): 23 Apr 2018 Downloaded from http://pubs.acs.org on April 23, 2018

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Chemistry of Materials

Understanding Ionic Diffusion through SEI Components for Lithium-Ion and Sodium-Ion Batteries: Insights from First-Principles Calculations Fernando A. Sotoa, Asma Marzoukb, Fedwa El-Mellouhib,* and Perla B. Balbuenaa,* a

Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843, United States b

Qatar Environment and Energy Research Institute, Hamad Bin Khalifa University, PO BOX 34110, Doha, Qatar *e-mails: [email protected]; [email protected]

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 Na-ion 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 1 ACS Paragon Plus Environment

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compared to the Na-ion.

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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 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 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

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low storage capacity of 248 mAh/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 non-uniform SEI layer that consists of inorganic compounds, sodium carbonate (Na2CO3) and NaCO3R (R = alkyl) in ethylene carbonate (EC)/propylene carbonate (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 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 paper

18

where we showed that a stable SEI layer can be designed by pre-cycling 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 SEI18 However, the design of such pre-formed 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 firstprinciples 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, analysis of defect formation energy and defect



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migration are usually carried out in these materials. Nudged-elastic band (NEB) calculations based also on DFT

20

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 rate-limiting 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 porous-like region of the SEI layer) 25. In this paper, we present results from DFT, AIMD and NEB calculations that help us 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


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efficient SEI layer; and ultimately, improve the capacity retention of LiBs/NaBs technologies. 2.

Methodology

Simulations involving DFT, AIMD and NEB calculations were performed using the Vienna ab-initio simulation package (VASP) (GGA-PBE)

30

26-29

with the Perdew-Burke-Ernzerhof functional

. The projector augmented wave (PAW) pseudopotentials were used

31,32

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 eV and 10-4 eV for the ionic relaxation loop and selfconsistent electronic iteration, respectively. The kinetic cutoff energy of 500 eV has been employed for LiF, Li2CO3, Na2CO3 and 400 eV for NaF. The Brillouin Zone (BZ) was sampled by a Monkhorst-Pack grid centered at the Gamma 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. 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 charges

33

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. NEB Calculations.The nudged elastic band (NEB) method developed by Jonsson and coworkers 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



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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 some meV. NEB calculations for NaF and LiF were carried out with smaller supercells (2×2×2 supercells) 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 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 co-intercalation 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 6 ACS Paragon Plus Environment

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comparative analysis about how Li-ions and Na-ions are allowed to pass through the main Na2CO3 and NaF and through the Li-analogous 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 ∆ is calculated by the following equation (1):36

∆ = − + −

(1)

Where Eb is the bulk total energy without the defect, Ed is the total energy of the bulk with the defect, Ea and Er 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 types NaLi NaI Na +V I

Na

Li +

Li

V

Li

Na +Li Li

VLi

I

Na in LiF 0.76 5.81 0.82

Defect formation energy (eV) Na in Li2CO3 Defect types 0.93 LiNa 2.49 LiI Li +V I

Na

7.36

5.64

Li +V

5.31 -

2.69 4.82

Li +Na

Na

Na

Na I

VNa

Li in NaF 3.47 1.74 3.43

Li in Na2CO3 -0.26 (a) 1.5 / 1.6 (b) -

5.40

4.74

n.c 5.61

1.65(a) /2.18(b) 3.30

n.c: Not converged: Li prefers to come back to its initial interstitial position and Na in its lattice position, (a)[110] direction, (b)[010] direction

Inequivalent interstitial sites present in Li2CO3 and Na2CO3 have been considered for the defect formation energy calculations. Figures 1-a and 1-b show 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 1-c and 1-d).



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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 conclude 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 eV 38) 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.

Figure 1. Interstitial sites present in the Li2CO3 (a and b) and Na2CO3 (c and d) 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.


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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.

3.3

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 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) concerted 9 ACS Paragon Plus Environment


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exchange. For Na2CO3, we presented, in Figure 2(d), 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.

Figure 2. Potential energy profiles of the different studied ionic migration mechanisms for (a) LiF, (b) NaF, (c) Li2CO3 and (d) Na2CO3 crystals. The diffusion coefficient of the defect (D), or diffusivity, is the indicator of the rate at which the ion diffuses. It can be calculated using equation (2): . = exp −

! "

# , = 1 − 3 '( = 1.0

(2)

Here, 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 10 ACS Paragon Plus Environment

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specific crystallographic directions namely the [110], [100], [010] directions. Here, represents the attempt frequency, is the activation energy associated with each defect, corresponds to the distance traveled by the defect and *+ is the Boltzmann constant (8.6173303 × 10-5 eV·K-1). 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 angstroms) and the diffusion coefficients (D in cm2.s-1). Table 2 includes also the electric field (ε) whose effect is discussed later. Table 2. Calculated migration energy barriers (Em), activation energies (Ea), diffusion lengths (a) and diffusion coefficients (D) of considered ionic migration mechanisms in LiF, Li2CO3, Na2CO3, and NaF. The activation energies are calculated by adding the migration barrier to the corresponding defect formation energy shown in Table 1. Models

LiF

Li2CO3

Diffusion Mechanisms Vacancy Diffusion Concerted exchange Knock-Off Direct Hopping Vacancy Diffusion Concerted exchange Knock-Off Direct Hopping Na-Vacancy Diffusion Concerted exchange

Ea (eV)

g

a ( Å)

0.81 3.32 0.52 0.38 0.28 1.6 0.2 0.9

8.17 4.07 6.1 5.96 5.92 2.53 2.75 3.38

4.00 2.93 7.70 3.44 4.50 2.83 5.50 7.50

300K 1.82E-139 2.96E-71 2.36E-104 1.03E-102 1.57E-102 4.27E-46 3.29E-49 1.91E-59

1000K 1.86E-42 6.08E-23 6.59E-32 6.23E-32 2.38E-32 4.91E-16 1.59E-16 2.73E-19

0.71

4.11

3 3 3 3 1 1 1 1 1

2.80

7.72E-72

3.87E-23

1.54

1.28

1

3.61

2.22E-76

4.15E-25

(a)

Na2CO3

NaF

Knock-Off

D(cm2.s-1)

Em (eV)

1.00 0.76(b)

(a)

2.50 2.36(b)

(a)

1

5.06 4.05(b)

Direct Hopping

0.73 (a) 0.28(c)

2.23(a) 1.88(c)

1

8.27 (a) 11.90(c)

Vacancy Diffusion Concerted exchange Knock-Off Direct Hopping

0.24 2.61 n.a 0.86

5.67 6.54 n.a 2.76

3 3 3 3

2.80 3.30 n.a 4.50

(a)

(a)

4.46E-45 6.23E-43 (b)

2.21E-15 6.71E-15 (b)

3.85E-40 (a) 5.58E-34 (c)

1.19E-13 (a) 1.20E-11 (c)

3.81E-98 2.01E-112 n.a 1.57E-49

9.72E-31 9.21E-35 n.a 9.68E-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 0.19

(a)

[110] direction, (b)[100] direction, (c)[010] direction

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 timescales. For vacancy-assisted 11 ACS Paragon Plus Environment


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diffusion, 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 conclude 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 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


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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 6-c 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 6-d. 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 Na-ion to diffuse through Na2CO3 (0.6 eV)40 due to the difference in the ionic radii. As shown in Figure 6-d, 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



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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 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 (1.12E-10 to 6.51E-11 cm . 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 facilitates not only 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


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high giving rise to high values of activation energies and very low diffusivity of the ions even at 1000K (as shown in Table 2). According to these observations, it is noteworthy that the application of an external electric field (0) 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 equation (3): 0 1 ⁄Å =

3 45

6 4 7Å8

; :ℎ = 1

Understanding Ionic Diffusion through SEI Components for Lithium-Ion

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