Atom-Level Understanding of the Sodiation Process in Silicon Anode

Letter pubs.acs.org/JPCL

Atom-Level Understanding of the Sodiation Process in Silicon Anode Material Sung Chul Jung,† Dae Soo Jung,‡ 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 EEWS (WCU), Korea Advanced Institute of Science and Technology, 291 Daehak-ro, Yuseong-gu, Daejon 305-701, Republic of Korea S Supporting Information *

ABSTRACT: Despite the exceptionally large capacities in Li ion batteries, Si has been considered inappropriate for applications in Na ion batteries. We report an atomiclevel study on the applicability of a Si anode in Na ion batteries using ab initio molecular dynamics simulations. While crystalline Si is not suitable for alloying with Na atoms, amorphous Si can accommodate 0.76 Na atoms per Si atom, corresponding to a specific capacity of 725 mA h g−1. Bader charge analyses reveal that the sodiation of an amorphous Si electrode continues until before the local Na-rich clusters containing neutral Na atoms are formed. The amorphous Na0.76Si phase undergoes a volume expansion of 114% and shows a Na diffusivity of 7 × 10−10 cm2 s−1 at room temperature. Overall, the amorphous Si phase turns out quite attractive in performance compared to other alloy-type anode materials. This work suggests that amorphous Si might be a competitive candidate for Na ion battery anodes. SECTION: Molecular Structure, Quantum Chemistry, and General Theory

L

inactive nature of Si still seems peculiar considering its highest capacity in Li ion batteries operating based on similar monovalent carrier ions, which led us to atomic-level theoretical investigations on any possibility of inserting Na into Si. Having noticed the inactive character of the crystalline Si, in the present study, we switched our main attention to its amorphous phase and performed an atomic-level assessment of an amorphous Si anode for Na ion batteries using ab initio molecular dynamics simulations. We report for the first time that amorphous Si can act as an active anode material for Na ion batteries as amorphous Si was found to absorb 0.76 Na atoms per Si, corresponding to a specific capacity of 725 mA h g−1. The fully sodiated Na0.76Si phase exhibits a volume expansion of 114% and a Na diffusivity of 7 × 10−10 cm2 s−1 at room temperature. The overall electrochemical performance of amorphous Si is indeed comparable to or even better than those of other well-known alloy-type anode materials, such as Ge, Sn, Sb, and Pb. Our calculations also offer a novel detailed finding on the sodiation process, such as formation of Na clusters containing zerovalent Na atoms upon full sodiation. The present work delivers an atom-level understanding for a critical but unprecedented feature of Si material.

i ion batteries have been successfully utilized as a wide range of energy storage system (ESSs).1−3 Future demand for Li ion batteries is predicted to increase continuously due to their use not only in portable electronic devices but also in larger-scale products, such as hybrid electric vehicles and ESSs. However, the geographical maldistribution of global Li reserves may bring about a rapid rise in the price of Li resources as the demand for rechargeable batteries grows exponentially.4,5 In recent years, Na ion batteries have attracted much attention because of the natural abundance of raw materials, low toxicity, and common dependence on monovalent carrier ions to Li ion batteries. With the particular advantage of a very low cost, Na ion batteries have been counted4−9 as a valid alternative to the Li ion batteries, especially targeting large-scale grid storage system. As an outcome of considerable research effort,9−23 the battery community is currently seeing remarkable progress in discovering and optimizing the electrode materials for Na ion batteries. Along these directions, the knowledge and experience accumulated during the research of Li ion batteries have made a substantial contribution. Nowadays, Si is one of the most intensively studied anode materials in Li ion batteries because of its highest specific capacity of 3579 mA h g−1 for the alloyed phase of Li3.75Si.24−32 Such exceptional specific capacity naturally raises the interest of using Si as an anode material in Na ion batteries. A prevailing view in the battery community, however, is that Si is virtually inactive when tested as an anode material for Na ion batteries.5,16,19−21 Indeed, Komaba et al.20 reported that the crystalline Si anode shows no capacity in a Na cell at all. The © 2014 American Chemical Society

Received: February 10, 2014 Accepted: March 21, 2014 Published: March 21, 2014 1283

dx.doi.org/10.1021/jz5002743 | J. Phys. Chem. Lett. 2014, 5, 1283−1288

The Journal of Physical Chemistry Letters

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Na0.76Si. We note that the experimentally known alloy phases are not necessarily observed during actual electrochemical reactions. For example, the Li4.4Si phase is the most Li-rich phase among the existing Li−Si alloys,34 but the electrochemical lithiation of the Si electrode experimentally reaches only up to the Li3.75Si phase30−32 upon full lithiation. Our calculations also predict the amorphous Li3.78Si phase as the most Li-rich phase. Sodiation results in a larger volume expansion than lithiation due to the larger size of Na, as shown in Figure 1c. However, the fully sodiated Na0.76Si phase shows a much smaller volume expansion of 114% than the 298% volume expansion of the fully lithiated Li3.78Si phase because of the smaller Na uptake by Si. Thus, the pulverization of the Si anode caused by volume expansions would be considerably mitigated in Na cells compared to that in Li cells. The volume expansion of 114% for Na0.76Si is also much smaller than 205% for Na1.56Ge (see the calculation results of amorphous NaxGe in the Supporting Information), 424% for Na3.75Sn,4 293% for Na3Sb,18 and 487% for Na3.75Pb,17 implying superior mechanical stability of the amorphous Si anode in Na ion batteries. In Figure 2, we locate several representative anode materials for Na ion batteries according to the specific capacity

Figure 1a shows the calculated formation energies of amorphous AxSi alloys (A = Li and Na). The energetically

Figure 1. (a) Formation energies of AxSi (A = Li and Na) defined as Ef(x) = Etot(AxSi) − xEtot(A) − Etot(Si), where Etot(AxSi) is the total energy per amorphous AxSi unit, Etot(A) is the total energy per atom of bcc A crystal, and Etot(Si) is the total energy per atom of amorphous Si. (b) Average voltages of AxSi defined as V(x) = −[Etot(Ax+ΔxSi) − Etot(AxSi)]/Δx + Etot(A). (c) Volume expansion ratios of AxSi.

most stable phase for lithiation is calculated to be Li3.78Si with a specific capacity of 3607 mA h g−1, in good agreement with the experimental observations of Li3.75Si upon full lithiation.30−32 The corresponding phase for sodiation is calculated to be Na0.76Si with a capacity of 725 mA h g−1. The obtained theoretical specific capacity for Na0.76Si is comparable to or higher than those for other Na cells, such as 576 mA h g−1 for Na1.56Ge (see the calculation results of amorphous NaxGe in the Supporting Information), 846 mA h g−1 for Na3.75Sn,4 660 mA h g−1 for Na3Sb,18 and 485 mA h g−1 for Na3.75Pb.20 The formation energies are −1.13 eV for amorphous Li3.78Si and −0.15 eV for amorphous Na0.76Si, implying that Si is more reactive toward lithiation than sodiation. It should be noted that the formation energy of amorphous Na0.76Si becomes positive (+0.18 eV) when crystalline Si is taken as the reference system. This implies that if crystalline Si electrodes are used for sodiation, their transformation into the Na0.76Si phase is energetically unlikely. This is also consistent with Komaba et al.’s20 experimental study that observed no specific capacity for the sodiation of the crystalline Si sample. Figure 1b shows the calculated average voltages during lithiation and sodiation of amorphous Si. In overall shape and magnitude, the lithiation voltages are in accordance with the experimental measurements.31 The sodiation voltages are lower than the lithiation voltages in the whole range of x, in line with the observations for many different electrode materials such as In,19 ACoO2, and AFePO4 (A = Li and Na).9 The NaSi phase is the most Na-rich one among the experimentally synthesized Na−Si alloys.33 In comparison, our calculations indicate that the fully sodiated NaxSi phase is

Figure 2. Specific capacities and volume expansions of several anode materials for Na ion batteries.

(horizontal axis) and the volume expansion (vertical axis). The given materials can be ranked as Sn > Si > Sb > Ge > Pb in the specific capacity aspect and Si > Ge > Sb > Sn > Pb in the volume expansion aspect, indicating that amorphous Si is sufficiently competitive as an anode material for Na ion batteries. Table 1 shows the calculated diffusivities of Li and Na in Si, which are associated with the rate capability during battery operations. The self-diffusion coefficient D is given for the Li, Table 1. Diffusion Properties of Li3.7Si and Na0.75Sia phase Li3.7Si Na0.75Si

atom

ED

Li Si Na Si

0.30 0.51 0.38 0.54

D0 1.7 2.9 1.5 3.7

× × × ×

10−3 10−3 10−3 10−3

D 1.8 8.5 7.2 3.8

× × × ×

10−8 10−12 10−10 10−12

ED (eV) is the activation energy for diffusion, D0 (cm2 s−1) is the preexponential factor, and D (cm2 s−1) is the self-diffusion coefficient at T = 300 K. a

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Na, and Si atoms in Li3.7Si and Na0.75Si at T = 300 K. The diffusivities in Li3.7Si are 1.8 × 10−8 and 8.5 × 10−12 cm2 s−1 for Li and Si, respectively, indicating that the Li atoms diffuse about 3 orders of magnitude more quickly than the Si atoms. In Na0.75Si, the diffusivities are 7.2 × 10−10 and 3.8 × 10−12 cm2 s−1 for Na and Si, respectively, indicating that the Na atoms diffuse faster than the Si atoms by about 2 orders of magnitude. Although the diffusion of Na in Si is slower by about 1 order of magnitude than that of Li in Si, the diffusivity is comparable to that of Na in other active anode materials, such as Sb and Na0.66[Li0.22Ti0.78]O2. In the case of the crystalline Na3Sb18 and P2-type Na0.66[Li0.22Ti0.78]O2 layered material,12 the reported Na diffusivities are 1 × 10−10 to 8 × 10−9 cm2 s−1 and 1 × 10−10 cm2 s−1, respectively. Then, the next appropriate question would be how the amorphous Si anode can store up to 0.76 Na atoms per each Si. Our Bader charge analysis of Na in Figure 3 offers important

Figure 4. (a) Distribution histograms of the Bader populations of Na in NaxSi. (b) Two representative local structures of Na@Na3Si5 and Na@Na7Si1 for Na0.75Si and Na1.5Si, respectively. The yellow and magenta balls represent the Na and Si atoms, respectively. The charge states of central Na atoms are presented. The atomic bonds are connected when the Na−Na, Na−Si, and Si−Si distances are within 3.8, 3.4, and 2.8 Å, respectively.

≥ 1. Then, the central Na atoms no longer lose electrons by Si because the neighboring Na atoms effectively screen them from Si. The neutral Na atoms in a local Na-rich region are enclosed with other Na atoms and hardly interact with Si atoms. For instance, Figure 4b shows that the central Na atom in a Na-rich local structure at x = 1.5, which is surrounded by seven Na atoms and one Si atom, has a charge state of −0.11. The partial coordination numbers of Na (CNNa−Na = 7 and CNNa−Si = 1) in the local structure considerably deviate from the average values of CNNa−Na = 5.66 and CNNa−Si = 3.58 at x = 1.5 (see Figure S2 in the Supporting Information). The evolution of such local structures after x = 0.75 leads to a gradual increase of approximately neutral Na atoms and thus results in overall weakening of the Na−Si ionic attractive interaction. Surprisingly, the slope-changing point of x = 0.75 on the Na charge state coincides with the minimum-energy point of x = 0.76 on the formation energy curve. This result indicates that the uptake of 0.76 Na atoms by Si is closely associated with the suppression of the charge transfer after x = 0.75. Our population analyses, in combination with the formation energy results, strongly suggest that the sodiation of the amorphous Si electrode continues until before the local Na-rich clusters containing neutral Na atoms are formed in the electrode. We note that a similar electrostatic analysis is applicable to the sodiations of Ge and Sn. Figure 5a shows the average Bader populations of Na in amorphous NaxSi, NaxGe, and NaxSn. The slopes of Na charge states versus x are virtually the same for Si, Ge, and Sn (−0.07 e per Na for Si, −0.07 e per Na for Ge, and −0.06 e per Na for Sn). It is worth noting that the Na charge states in Ge and Sn decrease rapidly after x = 1.5 and 4.0, respectively. As with NaxSi, these slope-changing points are in agreement with the minimum-energy points of x = 1.56 and

Figure 3. Average Bader populations of A in AxSi (A = Li and Na).

insights into this question. At a low Na concentration of x = 0.25, the Na atoms have a charge state of +0.79, indicating a charge transfer of 0.79 e from Na to Si and the resulting ionic Na−Si bonding nature. The Na−Si ionic bond is weaker than the Li−Si ionic bond as (i) the Na charge state of +0.79 (x = 0.25) is smaller than +0.85 (x = 0.25) for Li and (ii) the Na−Si bond lengths of 3.0−3.1 Å are longer than the Li−Si bond lengths of 2.6−2.7 Å (see Figure S1 in the Supporting Information). As sodiation proceeds, the charge state of Na decreases linearly along the red dashed line to alleviate a growing electrostatic repulsion between the Na cations. The slope of the Na charge state versus x is more drastic compared to the Li case (see the blue dashed line in Figure 3), indicating that the Na−Na repulsive interactions are more significant than the Li−Li ones because the repulsion between the larger-size Na cations begins at longer distances. The different ranges of repulsion are evidenced by the Li−Li distances formed at 2.7− 2.9 Å and the Na−Na distances formed at 3.3−3.5 Å (see Figure S1 in the Supporting Information). Interestingly, the Na charge state decreases rapidly after x = 0.75, as shown in a deviation from the red dashed line of Figure 3. This deviation is highly related to distinct changes with increasing x in distribution histograms of the Na charge state shown in Figure 4a. The main charge states change marginally from +0.8 to +0.7 with increasing x, and additional charge states ranging from −0.5 to +0.5 appear suddenly at x ≥ 1. The emergence of distinct charge states around zero originates from a local aggregation of Na atoms. Some of the Na atoms can be surrounded by other Na atoms at high Na concentrations of x 1285



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atom-level investigations of Na−anode alloy materials may lead to the discovery of the very anode materials for Na ion batteries.

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COMPUTATIONAL DETAILS We performed density functional theory (DFT) calculations using the Vienna ab initio simulation package (VASP).35 The Perdew−Burke−Ernzerhof (PBE) exchange and correlation functionals36 and the projector-augmented wave (PAW) method37 were employed. The electronic wave functions were expanded in a plane wave basis set of 271.6 eV for LixSi and 259.6 eV for NaxSi. We treated 1s22s1 for Li, 2p63s1 for Na, and 3s23p2 for Si as the valence electron configurations. The amorphous LixSi and NaxSi bulk structures were simulated by a periodic cubic supercell containing 40 × x Li (Na) atoms and 40 Si atoms. A 3 × 3 × 3 k-point mesh was used for Brillouin zone integrations. The calculated mass density of amorphous Si is 2.44 g cm−3, which is in agreement with the experimental value38 of 2.30 ± 0.01 g cm−3. We carried out ab initio molecular dynamics (MD) simulations in the course of generating the amorphous structures. For the MD simulations, the equations of motion were integrated with the Verlet algorithm using a time step of 1 fs, and the temperature was controlled by the velocity rescaling and canonical ensemble using a Nosé−Hoover thermostat. The amorphous structures were prepared using a liquid-quench method in which heating, equilibration, and cooling were done in series by the MD simulations. The radial distribution functions, coordination numbers, and Bader populations analyzed for the prepared amorphous Si and LixSi phases were found to be in good agreement with previous calculation results39−41 (see the Supporting Information). The procedures for determining the volume and total energy of amorphous structures were minutely described in our previous studies.42,43 During the MD simulations, a 1 × 1 × 1 k-point mesh was used to save computational time. We presented the results of atomic, electronic, and kinetic analyses for the amorphous LixSi and NaxSi structures and the calculation results of amorphous NaxGe and NaxSn structures in the Supporting Information.

Figure 5. (a) Average Bader populations of Na in NaxM (M = Si, Ge, and Sn). (b) Two representative local structures of Na@Na7Ge1 and Na@Na7Sn1 for Na4.25Sn and Na2Ge, respectively. The yellow, blue, and green balls represent the Na, Ge, and Sn atoms, respectively. The atomic bonds are connected when the Na−Na, Na−Ge, and Na−Sn distances are within 3.8, 3.5, and 3.6 Å, respectively.

3.89 on the formation energy curves of NaxGe and NaxSn, respectively (see the calculation results of amorphous NaxGe and NaxSn in the Supporting Information). Such rapid decreases of the Na charge states are due to the formation of Na-rich clusters, including neutral Na atoms in NaxGe and NaxSn, as shown in Figure 5b. The central Na atoms, surrounded by seven Na atoms and one Ge (Sn) atom, have charge states of −0.07 and −0.15 e in the sodiated Ge and Sn phases, respectively. It is worth mentioning that the amorphous alloy, unlike the crystalline one, can contain peculiar local structures such as the Na clusters containing zerovalent Na atoms found in our study. In the nuclear magnetic resonance studies of Grey’s group,28,29 the formation of isolated Si atoms and smaller Si−Si clusters embedded in a Li matrix was reported during the lithiation of amorphous Si. Such local structures and their evolutions in the amorphous phase cannot only be linked to electrochemical performance but also be one of the major issues in the physical chemistry community. In summary, we performed an atomic-level assessment of an amorphous Si anode for Na ion batteries using ab initio molecular dynamics simulations. Amorphous Si has the specific capacity of 725 mA h g−1, volume expansion of 114%, and Na diffusivity of 7.2 × 10−10 cm2 s−1, which are comparable to or better than those reported for other alloy-type anode materials such as Ge, Sn, Sb, and Pb. In particular, the relatively smaller volume expansion of amorphous Si during sodiation would provide superior mechanical stability, which is critical for good cycle durability during repeated sodiation/desodiation. Our population analyses reveal that the specific capacity of amorphous Si is decided at the sodiation stage before emergence of the local Na-rich clusters containing neutral Na atoms. The current work suggests that amorphous Si can be a competitive anode candidate for Na ion batteries. Continued

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ASSOCIATED CONTENT

S Supporting Information *

Radial distribution functions, coordination numbers, Bader populations, and mean square displacements of the amorphous LixSi and NaxSi structures and formation energies and volume expansion ratios of the amorphous NaxGe and NaxSn structures. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Prof. Kyu Tae Lee (UNIST) for proofreading this manuscript. The authors acknowledge the financial support by the National Research Foundation of Korea Grant funded by the Korean Government (MEST, NRF-2010-C1AAA0010029018). This work was also supported by the Energy Efficiency & Resources Core Technology Program of the 1286



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KETEP granted financial resource from the Ministry of Trade, Industry & Energy (No. 20132020000260 and 20132020000340). This work was partly supported by the IT R&D program (10041856) and the Industrial Strategic Technology Development Program (10041589) of MOTIE.

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