Sodium Ion Diffusion in Al2O3: A Distinct Perspective Compared with

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Sodium Ion Diffusion in Al2O3: A Distinct Perspective Compared with Lithium Ion Diffusion Sung Chul Jung, Hyung-Jin Kim, Jang Wook Choi, and Young-Kyu Han Nano Lett., Just Accepted Manuscript • DOI: 10.1021/nl503169v • Publication Date (Web): 06 Oct 2014 Downloaded from http://pubs.acs.org on October 9, 2014

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Sodium Ion Diffusion in Al2O3: A Distinct Perspective Compared with Lithium Ion Diffusion Sung Chul Jung,† Hyung-Jin Kim,† Jang Wook Choi,‡ and Young-Kyu Han*† †

Department of Energy and Materials Engineering and Advanced Energy and Electronic

Materials Research Center, Dongguk University-Seoul, Seoul 100-715, Republic of Korea ‡

Graduate School of Energy, Environment, Water, and Sustainability (EEWS) and Center for

Nature-inspired Technology (CNiT), KAIST Institute NanoCentury, Korea Advanced Institute of Science and Technology (KAIST), 291 Daehakro, Yuseong-gu, Daejeon 305-701, Republic of Korea

ACS Paragon Plus Environment

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ABSTRACT

Surface coating of active materials has been one of the most effective strategies to mitigate undesirable side reactions and thereby improve the overall battery performance. In this direction, aluminum oxide (Al2O3) is one of the most widely adopted coating materials due to its easy synthesis and low material cost. Nevertheless, the effect of Al2O3 coating on carrier ion diffusion has been investigated mainly for Li ion batteries, and the corresponding understanding for emerging Na ion batteries is currently missing. Using ab initio molecular dynamics calculations, herein, we first find that, unlike lithiation, sodiation of Al2O3 is thermodynamically unfavorable. Nonetheless, there can still exist a threshold in the Na ion content in Al2O3 before further diffusion into the adjacent active material, delivering a new insight that both thermodynamics and kinetics should be taken into account to describe ionic diffusion in any material media. Furthermore, Na ion diffusivity in NaxAl2O3 turns out to be much higher than Li ion diffusivity in LixAl2O3, a result opposite to the conventional stereotype based on the atomic radius consideration. While hopping between the O-rich trapping sites via an Na–O bond breaking/making process is identified as the main Na ion diffusion mechanism, the weaker Na–O bond strength than the Li–O counterpart turns out to be the origin of the superior diffusivity of Na ions.

KEYWORDS: Na ion batteries, Al2O3, ion conductivity, molecular dynamics, density functional calculations


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The electrode–electrolyte interface is a critical component in terms of determining overall performance in a variety of electrochemical energy devices such as fuel cells,1 capacitors,2 and batteries.3 Effective protection of the interface against undesirable side reactions is very important to avoid rapid degradation of the device performance during repeated electrochemical cycles. Particularly in rechargeable batteries,4–8 to this end, a conformal ultrathin coating by atomic layer deposition (ALD) has been widely employed among various available surface modifications. An ALD coating produces an artificial surface layer serving as an alternative to a solid electrolyte interphase (SEI) film9–11 and can thus be a useful tool to tune critical interfacial properties. The artificial coating layers can protect the electrode surface from further electrolyte decomposition, resulting in long-term durability and high rate capability of the given electrode materials.6–8 Despite this critical role of coating layers, reports on electrochemical reactions and ionic transport in the coating layers are relatively scarce. Moreover, atom-level studies on the effects of thin surface coatings have been oriented only to existing Li ion batteries (LIBs), but the corresponding theoretical efforts have been missing in emerging sodium ion batteries (SIBs). The binary compound aluminum oxide (Al2O3) is one of the most effective coating materials for LIBs and has been extensively utilized for various positive and negative electrodes.6–8,12–20 The pioneering work by Liu et al.21 monitored the morphological changes of Al nanowires surrounded by Al2O3 surface layers during lithiation–delithiation cycles using in situ transmission electron microscopy (TEM) technique. The authors observed that the lithiation first takes place in the Al2O3 layer by forming a stable Li–Al–O glass tube, and once the volume expansion of LixAl2O3 reaches a certain level, subsequent lithiation into the inner Al core is followed. Jung et al.22 showed, via first-principles calculations, that the observed Li–Al–O tube contains 3.4 Li atoms per each Al2O3. They suggested that the lithiation of the Al2O3 layer


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continues until it reaches the thermodynamically stable phase (Li3.4Al2O3) and extra Li ions then overflow into the adjacent active electrode. SIBs have recently attracted a great deal of attention as an alternative to LIBs on the basis of their unique advantages beneficial for grid-scale energy storage systems, including natural abundance and the low toxicity of Na resources.23–36 An elegant in situ TEM study by Han et al.23 demonstrated that the Al2O3 coating on the tin nanoparticles improves cycling performance via dynamic mechanical protection in which the sodiated Al2O3 layer deforms coherently with the tin core. Besides such benefits in the mechanical stability, as a good number of LIB electrodes have witnessed improved interfacial properties from Al2O3 coating, it is naturally expected that Al2O3 coating will lend similar advantageous effects for SIB electrodes. However, a thorough atomic-level understanding is not available to interpret the aforementioned morphological changes of the Na–Al–O layer as well as to develop any strategies for implementation of Al2O3 coating layers to other similar electrode cases. In this study, we investigate the sodiation process of Al2O3 using ab initio molecular dynamics (AIMD) simulations. The amounts of Na ions present in the Al2O3 coating layer are evaluated to be 1.4 and 0.8 per each Al2O3 for the expanded and contracted Na–Al–O layers, respectively, during the first sodiation process. Although the sodiation of Al2O3 is found to be energetically unfavorable, Na ions are still kinetically trapped in the Al2O3 coating layer during the sodiation process. We suggest that the Na ions start to escape from the Al2O3 coating layer when the Na ion diffusivity reaches a threshold of ~10–10 cm2/s. Furthermore, Na ion diffusivity in Al2O3 is much higher than that of Li ions, in spite of the larger radius of Na ions. The bulk modulus of NaxAl2O3 turns out to be lower than that of Al2O3, indicating an elastic softening of Al2O3 during


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sodiation. Also, the Na ion transport mechanism in the Al2O3 coating layer is Na ion hopping between O-rich trapping sites via a Na–O bond breaking/making process. We calculated the formation energies of amorphous NaxAl2O3 (x ≤ 3.0) alloys, as shown in Figure 1a. The formation energy increases with increasing x, all in the positive value range, indicating that the sodiation process in Al2O3 is energetically unfavorable. According to a TEM investigation,23 in the first sodiation, the Al2O3 coating layer expands first during its sodiation but contracts upon the subsequent sodiation into the tin core. The positive values in our formation energy curve may explain the observed contraction behavior of the Al2O3 coating layer during the first sodiation process. Contrary to the sodiation, the lithiation is known to be energetically favorable for x values up to 3.4.22 This explains the experimental observation21 that the thickness of a Li–Al–O glass tube formed during the lithiation remains virtually unchanged even after the subsequent delithiation. The volume of sodiated Al2O3 increases almost linearly with the Na content (see Figure 1b). This linear relationship allows one to estimate the Na ion content in the Na–Al–O layer from the volume of NaxAl2O3. From the reported thicknesses of the Al2O3 shell and the diameters of the tin core,23 the calculated volume change ratios of the expanded and contracted Al2O3 layers during the first sodiation process are V/V0 = 1.90 and 1.55, respectively. By the same logic, it was estimated that the expanded and contracted Na–Al–O layers in the TEM study23 contain 1.4 and 0.8 Na ions per each Al2O3 unit, respectively (see Figure 1b). Hence, the amount of Na participating in the formation of the Na–Al–O layer is much smaller than the amount of Li in the Li–Al–O layer.22 This is attributed to the opposite polarity of the formation energies between both carrier ion cases.


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Then, how can Na ions be trapped in the Al2O3 coating layer during the energetically unfavorable sodiation process? To answer this question, we now focus on the kinetic aspects of the inserted Na ions in Al2O3. Table 1 presents the calculated Na ion diffusivities in NaxAl2O3 at different x values and T = 300 K. Notably, the Na ion diffusivity has a strong dependence on the Na concentration of Al2O3. As x increases, the Na ion diffusivity increases dramatically from 9.2 × 10–12 cm2/s at x = 0.2 to 5.9 × 10–8 cm2/s at x = 3.0 (see Figure 2). The faster Na diffusion at a higher Na concentration is related to both the decreased number of attractive O ions and the increased number of repulsive Na ions along the Na ion pathways. This trend is also reflected in the coordination numbers of Na (see Figure S1 in the Supporting Information). Remarkably, the diffusivity of Na ions surpasses that of Li ions by at least two orders of magnitude at each x value in the whole range of x ≤ 3.0, indicating that the Na ion diffusion in the Al2O3 coating layer is far more efficient and Na ions reach the adjacent active electrode more quickly for all of the x values. Also, in Figure 2, the experimentally observed contents of carrier ions (xNa = 0.8– 1.4 in NaxAl2O3 and xLi = 2.8–3.5 in LixAl2O3) are positioned in the same diffusivity range of 10– 10

~ 10–9 cm2/s (marked in yellow). The distinct diffusivities can thus be interpreted in a way that

the critical carrier ion content where continuous diffusion into the adjacent active material begins is much smaller for the Na ion case. As a result, it is expected that the Na ion diffusion through Al2O3 exerts less mechanical stress in this coating layer during battery operations because of the smaller volume expansion. Despite the energetically unfavorable sodiation, the Na ions can be kinetically trapped in the Al2O3 layer, namely, there exist local activation barriers for the diffusing Na ions in Al2O3. In this context, the trapping of a certain portion of Na ions in the Al2O3 layer during desodiation, experimentally observed in Ref. 23, can be also rationalized by the kinetic aspect.


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The current investigation in conjunction with the experimental observations has led us to revise our previous view on the carrier ion diffusion in the Al2O3 layer. The previous study on the Li case has taken consideration mainly of thermodynamic viewpoint, and the threshold content of Li ions was correlated with the most thermodynamically stable phase (Li3.4Al2O3).22 In other words, further Li diffusion into the adjacent active phase does not occur until the lithiated Al2O3 reaches the most stable phase, and even after this point, this phase remains all the time during repeated charge-discharge cycles. By contrast, the current study based on the Na ion case implies that the thermodynamically unfavorable situation could still have a threshold content for its ionic diffusion, and the kinetic perspective should be added to explain this threshold behavior and understand the ionic diffusion. In the same line, in the case of LixAl2O3, an x range of 2.8~3.5, rather than a fixed value of 3.4, would be a more reasonable threshold for further diffusion into the adjacent active phase, and the accurate value will be determined in each case by various kinetic parameters. The bulk modulus of sodiated Al2O3 is important in relation to the structural deformation of the Na–Al–O layer during sodiation. The calculated bulk modulus of NaxAl2O3 decreases sharply as x increases up to x = 1 and decreases gradually with a further increase of x (see Figure 3). It is noticeable that the bulk modulus of NaAl2O3 at x = 1 is 62% lower than that of pristine Al2O3, indicating a markedly increased elastic softening of Al2O3, or its increased deformation capability, after sodiation. This property originates from a relatively weaker Na–Al–O network, and also indicates that the sodiation allows the Al2O3 coating layer to better accommodate the volume expansion of the active material. In fact, repeated swelling and shrinking behavior of an


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Al2O3 coating layer was experimentally verified for a tin nanoparticle anode undergoing large volume change.23 It is crucial to understand the Na ion diffusion mechanism in the Al2O3 coating layer at the atomic scale. To this end, we first analyzed the trajectories of Na ions in NaAl2O3 during AIMD simulations. These analyses were carried out at a high temperature of T = 1200 K because the AIMD simulations of an NaAl2O3 system at room temperature require substantial computation time (approximately 107 time steps) to monitor meaningful diffusion events. Indeed, AIMD runs at higher temperatures to accelerate the reaction kinetics have been reported previously.37–39 The trajectories of Na ions displayed in Figure 4a show their active vibrational and translational motions. A representative trajectory of a Na ion enclosed within the ellipse in Figure 4a is illustrated in Figure 4b. The Na ion in an equilibrium state (A) vibrates around its stable position surrounded by five O atoms and then migrates to another equilibrium state (C) by passing through an intermediate state (B) in which three of the five Na–O bonds are broken. The Na residence time in the intermediate state B is 0.1 ps, which is much shorter than the residence times (2.2 and 2.5 ps) in the equilibrium states A and C, respectively. We present direct Na hopping between the trapping sites surrounded by O atoms, accompanied by an intermediate Na– O bond breaking/making process, as the main microscopic mechanism of Na ion transport in the Al2O3 coating layer. Now we address why Na ions in Al2O3 diffuse much faster than the Li counterpart. As shown in Figure 4a, while Li ions exhibit mainly vibrational motions, Na ions exhibit both vibrational and translational motions, explaining the faster Na ion transport in Al2O3. This difference in the ionic motion originates from an appreciable difference between the Li–O and Na–O bond strengths. From density functional theory (DFT) calculations for the dissociation of the molecule A2O into


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AO + A (A = Li and Na), we reveal that the Na–O bond breaking energy (2.30 eV) amounts to only 60% of the Li–O bond energy (3.84 eV) (see Figure S3 in the Supporting Information). The much smaller Na–O bond breaking energy allows Na ions to more easily overcome the energy barrier required for hopping between the O-rich trapping sites. Our diffusivity calculations reveal that the room-temperature activation energy for Na diffusion in NaAl2O3 is 0.37 eV (see Table 1), which is much lower than the activation energy (0.67 eV) for Li diffusion in LiAl2O3 (see Table S1 in the Supporting Information). Note that the Li–Al(III) and Na–Al(III) repulsive interactions do not explain the large diffusivity differences between Li and Na ions. The calculated energy curves for the A–Al bond formation between the AF and AlF3 molecules (A = Li and Na) show that the difference between the Li–Al(III) and Na–Al(III) repulsive strengths is negligible (see Figure S3 in the Supporting Information). We also anticipate that the large difference between the Li–O and Na–O bond strengths is the basis of the opposite polarity of the formation energies in both cases. In conclusion, our study provides an in-depth atomic level understanding of Na ion diffusion in an Al2O3 coating layer. Our calculations reveal that the experimentally observed expanded and contracted Na–Al–O layers, respectively, contain 1.4 and 0.8 Na ions per each Al2O3 unit. Despite the thermodynamically unfavorable nature of sodiation in Al2O3, it still shows a threshold behavior in the Na content before further diffusion into the neighboring active phase, which is ascribed to a kinetic effect. This leads to a new viewpoint that ionic diffusion in any given medium should be understood by taking both thermodynamic and kinetic perspectives into consideration. Remarkably, despite the larger radius of Na ions, the Na ion diffusivity in Al2O3 is found to be much higher than that of Li ions, due to the weaker Na–O bond strength that accelerates Na hopping between O-rich trapping sites. The current study conveys a vision that, in


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emerging SIBs, coating layers could behave differently and even benefit electrochemical properties more than in their LIB counterparts, due to the distinct bonding characteristics between Na ions and the host anions. This work also provides new insight that the use of coating materials that are thermodynamically unfavorable in reacting with carrier ions could be a viable approach to minimize carrier ion trapping and therefore improve the charge-discharge efficiency.

Computational Details The DFT calculations were carried out using the Vienna ab initio simulation package (VASP).40 We used the Perdew-Burke-Ernzerhof (PBE) exchange and correlation functionals41 and the projector augmented wave (PAW) method.42 The electronic wave functions were expanded on a plane wave basis set of 400 eV. In terms of valence electron configurations, we treated 1s22s1 for Li, 2p63s1 for Na, 3s23p1 for Al, and 2s22p4 for O. The amorphous AxAl2O3 bulk structures were simulated by a periodic cubic supercell that inlcuded 20 × x A atoms, 40 Al atoms, and 60 O atoms (A = Li and Na). The 2 × 2 × 2 k-point meshes were used for Brillouin zone integrations. We performed AIMD simulations to generate the amorphous structures. The equations of motion were integrated with the Verlet algorithm using a time step of 1 fs, and the temperature was controlled by velocity rescaling and canonical ensemble using a Nosé-Hoover thermostat. A 1 × 1 × 1 k-point mesh was used to reduce the computation time during the AIMD simulations. Detailed procedures for constructing the amorphous structures are described in the Supporting Information and also can be found in our previous studies.22,43,44 The DFT calculations for A–O bond breaking in the A2O molecule and A–Al bond formation between the AF and AlF3


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molecules (A = Li and Na) were performed by using the Gaussian 09 program package.45 The PBE functional and standard 6-311+G* basis sets were used. ASSOCIATED CONTENT Supporting Information DFT calculations, AIMD simulations, coordination numbers, bulk moduli, molecular calculations, radial distribution functions, Bader populations, diffusivities, and atomic structures. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] Author Contributions All authors contributed to writing the manuscript and have approved its final version. Notes The authors declare no competing financial interest.


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ACKNOWLEDGMENT Y.K.H. acknowledges the financial support by the Energy Efficiency & Resources Core Technology Program of the KETEP granted financial resource from the Ministry of Trade, Industry & Energy (No. 20132020000260). J.W.C. acknowledges the financial support by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (NRF-2012-R1A2A1A01011970). This work was partly supported by the National Research Foundation of Korea (NRF) grant funded by the Ministry of Science, ICT and Future Planning of Korea (2010-C1AAA001-0029018).


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Figure 1. (a) Formation energies of AxAl2O3 (A = Li and Na), defined as Ef(x) = Etot(AxAl2O3) – xEtot(A) – Etot(Al2O3), where Etot(AxAl2O3) is the total energy per AxAl2O3 unit, Etot(A) is the total energy per atom of bcc A bulk, and Etot(Al2O3) is the total energy per Al2O3 unit. (b) Volume change ratios of AxAl2O3. V0 and V represent the volumes of pristine Al2O3 and AxAl2O3, respectively. In (a) and (b), the data for LixAl2O3 were taken from our previous study (Ref. 22).


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Figure 2. Diffusivities of Li and Na in AxAl2O3 (A = Li and Na) at T = 300 K. The yellow diffusivity window corresponds to x = 2.8–3.5 in LixAl2O3 and x = 0.8–1.4 in NaxAl2O3.

Figure 3. Bulk moduli of NaxAl2O3, defined as B = V0(∂2Etot/∂V2), where Etot is the total energy of unit cell, V0 is the equilibrium volume of unit cell, and V is the volume of unit cell. Total energies of NaxAl2O3 as a function of the volume of unit cell are displayed in Figure S2 in the Supporting Information.


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Figure 4. (a) Trajectories of the Li and Na ions in the MD simulations of AAl2O3 (A = Li and Na) for 5 ps at T = 1200 K. Different colors are used to distinguish the individual ions. (b) The Na ion trajectory inside the ellipse in (a) and three representative local structures in the two equilibrium states A and C as well as an intermediate state B. The number in parentheses represents the residence time of Na in each state. Yellow, white, and red balls represent the Na, Al, and O atoms, respectively. The atomic bonds are connected when the Na–Na, Na–Al, Na–O, Al–Al, Al–O, and O–O bonds are within 3.8, 3.6, 3.0, 2.8, 2.4, and 2.8 Å, respectively.


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Table 1. Diffusion Properties of NaxAl2O3a x

atom

ED (eV)

D0 (cm2/s)

D (cm2/s)

0.2

Na

0.42

9.3 × 10–5

9.2 × 10–12

Al

0.55

2.3 × 10–4

1.3 × 10–13

O

0.55

2.0 × 10–4

9.8 × 10–14

Na

0.37

6.3 × 10–4

3.2 × 10–10

Al

0.63

4.6 × 10–4

1.4 × 10–14

O

0.63

4.5 × 10–4

1.4 × 10–14

Na

0.33

8.5 × 10–4

2.4 × 10–9

Al

0.64

9.0 × 10–4

1.5 × 10–14

O

0.55

4.8 × 10–4

2.7 × 10–13

Na

0.24

6.1 × 10–4

5.9 × 10–8

Al

0.55

8.4 × 10–4

4.9 × 10–13

O

0.50

5.6 × 10–4

2.3 × 10–12

1.0

2.0

3.0

a

ED is the activation energy for diffusion, D0 is the pre-exponential factor, and D is the self-

diffusion coefficient at T = 300 K.


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Table of Contents Graphics


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Sodium Ion Diffusion in Al2O3: A Distinct Perspective Compared with

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