Ultrafast Sodiation of Single-crystalline Sn Anodes - ACS Applied

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Ultrafast Sodiation of Single-crystalline Sn Anodes Yong-Seok Choi, Young Woon Byeon, Jun-Hyoung Park, Jong-Hyun Seo, Jae-Pyoung Ahn, and Jae-Chul Lee ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b14680 • Publication Date (Web): 12 Dec 2017 Downloaded from http://pubs.acs.org on December 18, 2017

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ACS Applied Materials & Interfaces

Ultrafast Sodiation of Single-crystalline Sn Anodes Yong-Seok Choi†,∥, Young-Woon Byeon†, ‡,∥, Jun-Hyoung Park†, Jong-Hyun Seo§, Jae-Pyoung Ahn‡,*, and Jae-Chul Lee†,* † ‡

Department of Materials Science and Engineering, Korea University, Seoul 02841, South Korea

Advanced Analysis Center, Korea Institute of Science and Technology, Seoul 02792, South Korea

§

Process Technology Group, Process Center, R&D Division, SK hynix, Icheon 17336, South Korea

Abstract: Sodiation was performed on crystalline Sn cylinders using in situ electron microscopy to evaluate the rate performance of the Sn anode by directly measuring the sodiation rate. We observed that the sodiation rate of the Sn anode is more than two orders of magnitude higher than the lithiation rate of the Si anode under the same conditions. This unprecedented rate displayed by the Na–Sn system is attributed to the bond characteristics and crystalline-to-amorphous transformation of the Sn crystal at the thin interface of the Na–Sn diffusion couple. Here, using atomic simulations, we explain how and why the Sn anode exhibits this high rate performance by resolving the diffusion process of Na ions in the Na–Sn interfacial region and the electron structure of the crystalline Sn. This work provides useful insight into the use of Sn as an attractive anode material for realizing ultrafast-charging batteries for electric vehicles and mobile devices. *Corresponding author: Jae-Chul Lee [E-mail: [email protected]] Jae-Pyoung Ahn [E-mail: [email protected]] ∥

These authors contributed equally to this work.

Keywords: Sodium-ion battery, Fast-charging, Sn anodes, in situ diffusion experiment, Diffusion-controlled reaction, First-principles calculations 1

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1. Introduction In addition to high energy density, long cycle life, and high stability, batteries for recent mobile devices also require excellent rate performance for fast charging. This is particularly the case for future electric vehicles. The rate capability of a battery is closely related to the transport rate, or the diffusivity, of the charge carrier in the electrodes and electrolytes 1, 2. However, the transport rate of the charge carrier is comparatively slower in the anode than in the cathode and electrolyte 3; therefore, the reaction occurring in the anode hinders the development of fast-charging batteries. The issue of improving the rate performance of batteries depends on the development of anode materials that display the high transport rates for carrier ions. Extensive studies to improve the energy capacity and rate performance of various anode materials are underway. Doping and coating of anode materials

4-9

are probably the most popular

and important techniques. The basic principle underlying these methods is the increase of the electrical conductivity of the anode. While these treatments have been effective in improving the energy capacity of an anode by promoting full penetration of carrier ions in the anodes, their effects on the rate performance of the batteries remain debated. Nanoscale materials, including nanowires (NWs), also permit the rapid transport of carrier ions by promoting surface diffusion. Previous studies commonly reported that the transport rate of carrier ions was greatly improved by the nanoscale anode materials with a large surface area 4, 9-11. Although fast charging is feasible for the batteries containing nanoscale anode materials, these anodes often require the complex/expensive synthesis routes 12. Another method to improve the energy capacity and rate performance of batteries is by changing the anode material itself. Generally, atoms in the group III-A, IV-A, and V-A, which are 2


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characterized by low redox potentials, tend to display lower bond energies as the bond length of the atomic pair increases (see Fig. S1a in Supporting Information). This suggests that, for carrier ions diffusing through anodic materials with larger bond distances, less energy is required to disconnect the atomic bonds and thus the charge carriers can migrate at higher rates. In addition, high electric conductivity can promote fast ionic transport in the anode materials. In view of the above statements, Sn, with comparatively large atomic size and good metallic conductivity, is an excellent test material to determine whether Sn anodes can promote the transport of charge carriers at high rates sufficient for ultrafast charging (For the bond distance vs. electric conductivity relation, see Fig. S1b in Supporting Information). An effective way to elucidate the structural origin of the high rate performance of the Sn anode is to compare the diffusion behavior of carrier ions in the Sn anode with another contrasting anode material. Of various anode materials, Si, owing to its comparatively small atomic size and low electric conductivity, is considered to exhibit a comparatively low rate performance (see Fig. S1 in Supporting Information). Furthermore, Si, when used with the Li cathode, undergoes anisotropic swelling and self-limiting lithiation, indicating that the diffusion of Li into the Si anode is governed by the interface-controlled reaction (ICR)

13, 14

. On the other hand, Sn, when used with the Na

cathode, does not suffer from anisotropic swelling and self-limiting diffusion behavior

15, 16

. This

indicates that the Na-Sn system is governed by the diffusion kinetics other than ICR. Therefore, the choice of the Li-Si and Na-Sn systems would provide an ideal testbed for studying the effect of the atomic species of the cathode and anode materials on the diffusion mechanism and thus, the ionic transport rate. In this study, using direct-contact in situ diffusion experiments observed by electron 3



microscopy, comparative studies were performed on the Na–Sn and Li–Si diffusion couples to measure the diffusivity of the carrier ions in the anode materials. The experiments demonstrated that the rate performance of a Sn anode for Na-ion batteries is significantly greater than that of the Si anode counterpart used in Li-ion batteries. As a convincing evidence for this behavior, we observed from in situ diffusion experiments that the sodiation rate of the Sn anode is more than two orders of magnitude greater than the lithiation rate of the Si anode. By employing atomic simulations, we performed quantitative and comprehensive analyses to explore how and why the Sn anode exhibits such high rate performance. 2. Results and discussion

Figure 1. Direct-contact in situ sodiation experiment. (a) Schematic showing the setup installed in a focused ion beam (FIB) system used for direct-contact in situ sodiation experiments. (b) A series of frames captured from Movie S1 in Supporting Information, showing that sodiation occurs by direct contact with the Na lump and proceeds by forming amorphous NaxSn compounds. During sodiation, the sodiated and un-sodiated regions are clearly distinguished by the moving phase boundary formed at the reaction front of the Sn pillar (marked by yellow rhombi). 4


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Inspired by our success in observing the sodiation process of the Na–Sn system using in situ electron microscopy

15, 16

, we recorded the sodiation-related changes in the morphology of a Sn

pillar. This was achieved by bringing a Na lump into direct contact with the Sn pillar using a nanomanipulator installed in a focused ion beam (FIB) chamber, as shown schematically in Fig. 1a and outlined in detail in Methods. Figure 1b shows a series of frames captured from Movie S1 in Supporting Information, showing that the continuous and spontaneous insertion of Na proceeds through the 550-nm-diameter Sn pillar. The sodiation of the Sn pillar progresses in two stages, as revealed by the characteristic volume expansions associated with Na insertion and phase transition. In the first-stage sodiation, Na begins diffusing into the Sn pillar from the contact point, causing the Sn pillar to swell by ~100% (see the panel at t = 6 s). This volume expansion is caused by the 17

formation of the amorphous NaSn phase (a-NaSn)

. With time, the reaction front of the phase

boundary between the sodiated and crystalline Sn travels further along the long axis of the pillar, leaving the pre-formed a-NaSn behind. During this stage, the continuous supply of Na to the Sn pillar causes the pre-formed a-NaSn region to expand to ~280% without forming cracks on the surface of the pillar (see the panel at t = 56 s). Since the volume of a-NaxSn increases linearly with increasing values of x in NaxSn 17, this second-stage sodiation is associated with the transition of aNaSn to the amorphous Na9Sn4 phase (a-Na9Sn4) consistent with previous phase analysis results

17, 18

. The formation of a-NaSn and a-Na9Sn4 is

15, 16

. However, the issue of the phase transition is

not relevant to the present study and will not be discussed further. A careful examination of the surface contrast of the sodiated pillar in Fig. 1b showed that the Sn pillar expands evenly in the radial/lateral direction without distorting the cross-sectional shape. This indicates that the volume expansion rate of the Sn pillar is equal in all crystallographic directions, causing the Sn pillar to 5



swell in an isotropic manner.

Figure 2. Completely Na-infiltrated sodiated Sn pillar with isotropic swelling. (a) Backscattered electron image of the longitudinal cross-section of the sodiated Sn pillar, showing full penetration by Na atoms in the Sn pillar. Transverse cross-sectional morphologies of the (b) pristine Sn and (c) sodiated Sn pillars, showing isotropic swelling of the Sn pillar. The images in (a) and (b) were recorded from the two different locations of the same pillar.

Isotropic swelling of the Sn anode is important in determining the cycle life and rate performance of the battery; it is verified by the direct observation of the cross-sectional geometries of the sodiated Sn pillars. Figure 2 shows the images of the longitudinal and transverse crosssections of the sodiated Sn pillar. The interfaces between the reacted shell and unreacted core are clearly distinguished by the difference in contrast. Compared to the lithiation behavior of Si NWs, sodiation observed in the Sn pillar differs in two ways. First, it is clear from Fig. 2a that the reaction front propagates along the long axis of the Sn pillar while simultaneously proceeding toward the 6


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pillar center, permitting Na atoms to reach the interior region of the Sn pillar. The full penetration of the Sn anode by Na is feasible even for Sn pillars with large diameters of 300–1700 nm (see Fig. S2 in Supporting Information). This second-stage sodiation is achieved by the acceptance of ~2.3 Na atoms per Sn atom in the alloyed anode (a-Na9Sn4), corresponding to the volume expansion of

∼280%. This suggests that, unlike the partial infiltration occurring in Si NWs

19, 20

, the

electrochemical reaction prevails throughout the entire volume of the Sn pillar, allowing the full usage of the Sn anode for storing charge carriers. Another important feature noted from the sodiated Sn pillar is its isotropic swelling behavior. Figures 2b-c are the images of the transverse crosssections of the Sn pillar recorded before and after sodiation. Contrary to the lithiated Si NW that underwent anisotropic swelling

19, 21, 22

, the lateral expansion of the Sn pillar is nearly equal along

all radial directions of the pillar (Fig. 2c), indicating the isotropic swelling of the Sn anode. Considering that the isotropic swelling of an anode material inhibits the initiation of anode fracture by preventing locally inhomogeneous residual stresses

23-25

, the isotropic swelling observed in the

sodiated Sn pillar is an important characteristic required to improve the cycle life and energy capacity of batteries. In the following, we analyzed the different swelling behaviors displayed by the lithiated Si NW and sodiated Sn pillar in terms of the different rate-limiting reaction mechanisms that govern the diffusion kinetics of the crystalline Si and Sn. Anisotropic swelling observed in Si NWs strongly indicates that the lithiation of the Si anode is controlled by the reaction at the leading edge of the interface rather than the reaction at the lithiated bulk Si (i.e., LixSi). This kinetics associated with the lithiation of crystalline Si (c-Si) is clarified here using molecular dynamics (MD) simulations performed on the Li–Si diffusion couple (see Fig. S3 in Supporting Information). Calculations showed that the transport rate of Li+ is significantly lower at the leading edge of the propagating a-LixSi/Si interface than at the pre-formed 7



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a-LixSi phase trailing the interface, supporting the governing of lithiation of the Si anode by an interface-controlled reaction (ICR). Different Li+ transport rate at the interface and bulk region causes an abrupt change in the Li concentration at the interfacial region, which builds up residual stresses and prevents the full penetration of Li+ into Si anode

20, 26

and thus, the full usage of the

anode materials. Furthermore, due to the low Li concentration at the interfacial region of the lithiated Si, the initial crystal structures of c-Si is retained 27, causing anisotropic swelling. On the other hand, Na+ insertion in the Sn pillar causes uniform expansion of the pillar in all directions (Fig. 2c). This indirectly supports the governing of Na+ diffusion in the Sn pillar by the bulk diffusion of Na into the a-NaxSn phase, instead of the reaction at the a-NaxSn/Sn interface (or ICR). Without the restraining effects of ICRs, Na atoms can migrate into the Sn pillar at higher rates. For example, in evaluating the Na transport rate by tracking the moving phase boundary during the initial travel distance of 1 µm (see Movie S1 in Supporting Information), the propagation speed of the reaction front, measured from the 550-nm-diameter Sn pillar, was ~1.25 µm/s. This is more than two orders of magnitude higher than the ~11 nm/s rate measured from the Si pillar of the same diameter, and is comparable to the highest recorded rate of ~1.0 µm/s measured from the 80-nmdiameter Si NW

28

. This implies that the rapid migration of Na into the Sn pillar arises from a

characteristic diffusion mode other than ICR, which is validated in the following analysis of the migration length of Na, determined from the in situ sodiation experiments.

8


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Figure 3. Analyses of the diffusion kinetics based on in situ diffusion experiments. (a) Plots of the propagation length (L) of the reaction front measured as a function of diffusion time (t), showing that diffusion in the anode materials is controlled by different diffusion mechanisms depending on the diameter and species of the anode materials. (b) Propagation speeds of the reaction fronts in the Sn pillars measured as a function of the pillar diameter. For comparison, the propagation speeds of the reaction fronts in the Si NWs are plotted as a function of the Si NW diameter. To compare the propagation speeds of the reaction fronts in different systems, all measurements are obtained from reaction fronts traveling the initial distance of 1 µm from the start of diffusion. All samples are initially long cylinders or NWs.

In order to clarify the kinetics of diffusion that determines the transport rate of the charge carrier, we measured the propagation length (L) of the reaction front as a function of diffusion time (t) and analyzed their relationship. Figure 3a shows the L–t curves calculated from lithiated Si and sodiated Sn anodes with various diameters

10, 21, 28

. For Si anodes, L increases linearly with

9



increasing t for pillars with diameters of 216–4000 nm, thus following the L ∝ t relationship, indicating that the lithiation of the Si pillars is governed by the ICR. However, for Si pillars of diameters < 80 nm, L follows the L2 ∝ t relationship, typical of diffusion-controlled reactions (DCRs) 28. Therefore, the diffusion of Li+ in Si is no longer limited by the ICR for Si pillars of < 80 nm in diameter. On the other hand, L measured from the Na–Sn system follows the L2 ∝ t relationship for Sn pillars with diameters of 300–1700 nm (see Fig. S4 in Supporting Information), which is convincing evidence that the sodiation of Sn pillars is governed by DCR even for comparatively large-diameter pillars. The different rate performances displayed by the Na–Sn and Li–Si systems are therefore considered to arise from the characteristic diffusion kinetics at the two different interfaces. We next assessed the role played by the different diffusion kinetics on the rate performances of the anode materials by measuring the propagation speeds of the reaction fronts as a function of the pillar diameter (Fig. 3b). Both Si and Sn anodes show significant increases in the propagation speed of the reaction front for decreasing diameters of the pillars/NWs. However, the propagation speed of the reaction front is higher in the Sn pillar than that in the Si NW by more than two orders of magnitude for all samples with similar diameters. The experimental data shown in Fig. 3 suggest that the rapid migration of Na+ in the Sn anode is feasible because there is no ICRrelated restraining effect. In the following, the reaction kinetics operating at the interface of the Na– Sn diffusion couple is explored in detail by resolving the structural evolution at the leading front of the reacted region in the Na–Sn couple.

10


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Figure 4. Diffusivity at the interface and the bulk region. (a) A series of snapshots captured from first-principles calculations, showing the structural evolution of the Na–Sn diffusion couple at the region near the Na/Sn interface during sodiation at 0, 1, 5, and 10 ps. In these figures, the disordered/amorphous sodiated Sn (a-NaxSn) region is denoted in green by dashed rectangles. (b) Changes in the diffusivity of Na (DNa) evaluated from regions A and B, plotted as a function of 1000/T.

Because it can depict atomic-scale structures and their corresponding properties, atomic simulation has become a powerful exploration technique for the structure–property relationships of a material. Of all presently available simulation techniques, first-principles calculations can provide the most accurate interatomic interactions and thus reliable structure–property information for a 11



material. In this section, we modeled a Na–Sn diffusion couple to simulate the spontaneous sodiation process near the Na/Sn interface and elucidate the mechanism of the fast diffusion behavior of Na observed experimentally (see Methods for the detailed atomic configurations of the Na–Sn diffusion couple). Figure 4a displays a series of snapshots obtained from the first-principles calculations on the Na-Sn diffusion couple at 500 K. Notably, when the two electrode materials come in contact with each other, the crystalline structure of Sn (see the panel at 0 ps in Fig. 4a) is first transformed to a thin amorphous-phase layer (the panel at 1 ps in Fig. 4a), which subsequently reacts with Na to form amorphous sodiated Sn (i.e., a-NaxSn, denoted by green dashed boxes in the panels at 5 and 10 ps in Fig. 4a). As Na atoms continue to diffuse through the Sn side, the transport rates of the Na atoms differ depending on the distance from the interface. In order to track the dependency of the transport rate of Na atoms on the distance from the interface, we first defined the bulk a-NaxSn region and the a-NaxSn/Sn interface by dividing the region corresponding to the aNaxSn reaction product into the two sub-regions. The 3-Å-thick a-NaxSn region, in direct contact with the pure Sn, is termed the a-NaxSn/Sn interface (denoted by region A), whereas the rest of the reacted a-NaxSn layer is termed the bulk a-NaxSn region (denoted by region B). In order to determine the reaction kinetics operating in the Na–Sn couple, we compared the transport rates of Na in regions A and B. For this purpose, the diffusion of Na atoms was accelerated by heating the diffusion couple to temperatures of 400, 450, and 500 K, below the melting point of β-Sn. We then extrapolate the diffusivity values of Na (DNa) evaluated at the elevated temperatures and calculated DNa at room temperature (RT) using an exponential fit, denoted by the dashed lines (see Methods for the detailed calculation procedures). Calculations show that the values of DNa at RT obtained for regions A and B are 2.3 × 10-6 and 3.0 × 10-6 cm2 s−1, respectively, indicating that Na diffusion speed at the bulk a-NaxSn region is nearly equal to that in 12


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the a-NaxSn/Sn interface. For the Li-Si system, DLi is significantly lower at the interface (3.02 × 108

cm2 s-1) than at the bulk region (5.36 × 10-5 cm2 s-1) (see Fig. S3 in Supporting Information). This

indicates that, unlike the ICR-governed lithiation of the Si anode, the diffusion of Na in the Sn anode is controlled by bulk-region reactions rather than interfacial reactions. Overall, the comparative studies of the Li–Si and Na–Sn systems suggest that the different rate performances of these systems arise from the characteristic reactions occurring at the few-Å-thick interfacial layer of the diffusion couple.

Figure 5. Structural evolution at the interfacial regions. Structural evolution of the anode materials near the interface of the (a) Li–Si and (c) Na–Sn diffusion couples. Partial radial distribution functions calculated for (b) Si and (d) Sn atoms comprising the structure of the interfacial regions denoted by red dashed boxes in (a) and greed dashed boxes in (c), respectively. Black vertical lines in (b) and (d) indicate the nearest bond lengths of the crystalline Si–Si and Sn– Sn pairs. 13



In order to understand why ionic transport in the Li–Si and Na–Sn systems is governed by different diffusion mechanisms, the atomic structures of these two systems were resolved by observing the local structures near the interfaces and their subsequent evolution. Figure 5a displays a series of snapshots depicting the simulated interfacial region of the Li–Si diffusion couple, showing the sequence of structural evolution of the interfacial region during lithiation at 500 K. Although the Li and Si atoms spontaneously diffuse into each other because of the chemical potential gradients, a careful examination of the electrochemical reactions at the diffusion couple interface in Fig. 5a demonstrates that the diffusion of Li in the Si anode occurs in two stages. Firststage Li diffusion always occurs through interstitial sites in the Si lattice without disrupting the initial crystallinity of Si and thereby forms a thin layer of lithiated crystalline Si (referred to as cLixSi). The changes in the local structure near the interface of the Li–Si diffusion couples are further analyzed using the partial radial distribution functions (RDFs, g(r)). The interatomic distance of the Si atom pairs in the c-LixSi phase near the interface is determined from the first peak of the RDF (Fig. 5b) as ~2.3 Å; this value measured from a few atomic layers of c-LixSi at the interfacial region remains constant throughout lithiation. In addition, the sharpness of the first peak obtained from the interfacial region remains constant during lithiation, further indicating that the lithiated phase at the interface retains the initial crystalline structure of c-Si. This explains why the transport rate of Li+ differs depending on the crystallographic orientation of the interfacial region, which acts as the origin of anisotropic swelling (the detailed mechanism responsible for anisotropic expansion was reported by the authors in Ref. [27]). Subsequently, Li+ continues to diffuse across the Si side, leaving the lithiated layer behind (see the panel with t = 20 ps in Fig. 5a). During this stage, a continuous supply of Li+ breaks the Si–Si bonds of the pre-existing c-LixSi, causing the c-LixSi 14


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layer to evolve into disordered/amorphous lithiated Si (a-LixSi). This two-stage lithiation of c-Si observed from first-principles calculations is also observed in the MD simulation performed on a comparatively large-scale Li–Si diffusion couple for a prolonged period (see Fig. S3 in Supporting Information). Unlike the structural evolution observed in the interfacial region of the Li–Si diffusion couple, the spontaneous insertion of Na into Sn is observed to proceed by beginning with the disruption of the crystalline structure of c-Sn, causing c-Sn to evolve to amorphous Sn (a-Sn; see the panel with t = 1 ps in Fig. 5c). The subsequent migration of Na+ across a-Sn causes the formation of the a-NaxSn phase near the interface (see the panels for t = 5 and 10 ps in Fig. 5c). This amorphization of c-Sn during sodiation is also evidenced by the diffuse-halo pattern observed in the RDFs (Fig. 5d). Furthermore, based on the first peak of the RDFs, the interatomic distance of the nearest Sn–Sn pairs at the Sn-side interfacial region of the Na–Sn diffusion couple tends to increase gradually from ~3.1 to ~3.2 Å as the diffusion time increases from 0 to 10 ps. This increase in the bond length of the Sn–Sn pairs confirms the crystalline-to-amorphous transformation that occurs in c-Sn. Considering that amorphous phases and materials are characterized by comparatively loose atomic packing and locally open space (also termed the free volume), the amorphization behavior observed at the interface of the Na–Sn diffusion couple is likely to widen the Na+ diffusion passages. This crystalline-to-amorphous phase transformation of the Sn side interface causes the Na–Sn system to display a high diffusivity and thus high rate performance. Furthermore, the amorphization of c-Sn at the Sn side interface nullifies the crystallographic orientation effects on the ionic transport rate, promoting isotropic swelling of the Sn pillar.

15



Figure 6. Potential energy curve and valence electron charge density. Potential energy curves of the (a) Si–Si and Sn–Sn pairs and (b) Li–Si and Na–Sn pairs plotted as a function of the bond distance. Distribution of the electron charge density in the unit cell of (c) c-Si (diamond cubic) and (d) c-Sn (body-centered tetragonal). In these images, the regions enclosed by the level surface (denoted in sky blue) correspond to those with charge densities higher than the median value. (e) Variations in the charge densities evaluated along the lines A–B and C–D connecting the atomic bonds of Si–Si and Sn–Sn, respectively, as denoted in the insets. The images in the insets correspond to cross-sectional views of (c) and (d), showing the charge density distributions on the (110) plane of c-Si and the (001) plane of c-Sn, respectively. The charge density measured along the Sn–Sn bond less than half that of the Si–Si bond.

Another parameter affecting the diffusivity of the charge carrier is the anode material itself, because the bond energy of the material depends on the atomic species in the material. For the Li– Si and Na–Sn systems, the diffusion of the carrier ions occurs by breaking the bonds made by the constituent atoms of the anodes. Therefore, the transport rate of the carrier ions is thought to be 16


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higher in the anode material that requires less energy to break its interatomic bonds. With reference to the RDF curves in Fig. 5, the interatomic distance of the nearest atomic pair is greater for c-Sn than for c-Si. Considering that atomic pairs with longer interatomic distances tend to display lower bond energies, this RDF result suggests that the Sn–Sn bonds are weaker than the Si–Si bonds. In evaluating the bond energies of these two bonds by the potential energy curve, the 2.5-eV bond energy of the Sn–Sn pair is ~30% lower than the 3.4-eV energy of the Si–Si pair (Fig. 6a). This indicates that the Sn–Sn bonds are more readily disconnected to allow the fast migration of Na in the Sn anode. Furthermore, in evaluating the bond energies between the charge carriers and the anode materials, the Na–Sn bond energy of 1.2 eV is only ~66% of the Li–Si bond energy of 1.8 eV (Fig. 6b). This result again suggests that Na ions are capable of rapid migration through the surrounding Sn atoms because of the easy breakage of Na–Sn bonds. The present analysis based on the bond energy leads us to conclude that, in addition to the crystalline-to-amorphous phase transformation of c-Si at the interface, the low bond energies of the constituent atoms also contribute to the high rate performance of the Na–Sn system; thus, a comprehensive understanding of why the Na–Sn system exhibits such a low bond energy is of great importance. In order to explore the origin of the bond energy displayed by the atomic pairs comprising the Li–Si and Na–Sn systems, we calculated the distribution of the electron charge density of c-Si and c-Sn. Figures 6c-d display the charge density distributions of c-Si and c-Sn, showing the regions with charge densities higher than the median values of 0.30 and 0.17 e Å-3 for c-Si and c-Sn, respectively. The calculation shows that the majority of the electrons are localized to form Si–Si and Sn–Sn bonds by sharing electrons between nearest atomic pairs. However, compared to those in Si– Si bonds, the electrons comprising Sn–Sn bonds are distributed over relatively broader regions. Therefore, the charge density of Sn–Sn bonds is lower than that of Si–Si bonds, which in turn 17



correlates to the lower bond energy of the Sn–Sn pairs. In order to confirm this behavior, we evaluated the distributions of the charge densities comprising the Si–Si and Sn–Sn bonds. Figure 6e shows the changes in charge density evaluated along the Si–Si and Sn–Sn atomic bonds, denoted as lines A–B and C–D in the insets, respectively. The results indicate that the charge density of the Sn– Sn bond less than half that of the Si–Si bond. Furthermore, in comparing the charge density distributions of c-Si and c-Sn, the Sn–Sn bonds display more dispersed charge distribution than the Si–Si bonds (see the inset images in Fig. 6e). The broad distribution and low value of the charge density measured in the Sn–Sn bonds cause the Sn–Sn pairs to display lower bond energies that are easily broken by the penetration of c-Sn by Na, which explains the high rate performance of Na–Sn batteries. 3. Conclusions In this study, we performed comparative investigations of the Na–Sn and Li–Si diffusion couples to explain the high rate performance displayed by Na–Sn batteries. We found that the transport rate of the carrier ions depends strongly on the size/diameter and species of the anode materials. While the transport rate of the carrier ions in Si and Sn anodes was higher for smallersize anodes, it was more than two orders of magnitude higher in Sn than in Si anodes of the same size. Atomic simulations of the Na–Sn and Li–Si diffusion couples showed that the rate performance of the anode material was closely related to the interfacial reaction characteristics and the bond energy of the anode material; unlike the Li–Si system, the spontaneous insertion of Na+ into c-Sn causes the crystalline-to-amorphous transformation of c-Sn at the leading front of the interface, which broadens the diffusion passage for Na+, causing the Na-Sn system to display high diffusivity. In addition, of the two anode materials considered in this study, the comparatively lower 18


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bond energy of c-Sn enables easier disconnection of Sn–Sn bonds, permitting fast diffusion of Na into the Sn anode. 4. Methods 4.1. Fabrication of single-crystalline Sn pillars. Pristine β-Sn pillars with diameters and lengths of 300–1700 nm and ~12 µm, respectively, were prepared from a bulk Sn foil (>99%) using a dualbeam focused ion beam (FIB, Quanta 3D FEG, FEI) in a scanning electron microscope (SEM). All Sn pillars had the longitudinal orientation of , because they were sampled from a single grain with the normal direction of . During FIB milling, the beam current was reduced gradually from 300 to 10 pA to prepare pillars with smooth surfaces and taper angles of < 2°. Potential Ga contamination associated with FIB milling was minimized by further milling at a lower beam voltage (3.0 kV and 50 pA) for 2 min, followed by O2 plasma cleaning for another 2 min. The crystallinity and microstructure of the fabricated pillar were confirmed by electron diffraction based on transmission electron microscopy (TEM, Tecnai F20 G2, FEI), while the composition of the pillar was analyzed using energy-dispersive spectroscopy (EDS) in TEM; all samples were single crystals with surfaces covered by 4-nm-thick amorphous layers, and all were free of Ga contamination. For comparison, Si pillars with the longitudinal orientation of were also prepared from Si wafers using procedures similar to those used for preparing the Sn pillars. All pillars machined from the bulk material were then transferred to a Mo FIB lift-out grid (#460223, Ted Pella) and fixed using Pt deposition for the direct-contact in situ diffusion experiments.

4.2. In situ diffusion experiments. The rate performance of an anode material has typically been evaluated indirectly using the electrochemical tests of a full- or half-cell battery 19


29-31

. Despite the


Page 20 of 36

simplicity of this approach, this technique is unable to resolve/extract accurately the ionic transport rate of the anode from the overall rate that arises from the collaborative effects of various primary reactions in the entire cell. This causes the measured diffusivity to scatter by six orders of magnitude

4, 32-34

. One way to reduce the uncertainty of evaluating the diffusivity in the anode

material is through directly measuring the transport rate of Na in the Sn anode. However, the direct observation of diffusion behaviors is challenging because of the experimental difficulties and delicacy encountered with the high oxygen affinity of Na and Sn. In this study, the diffusivity of Na to c-Sn was measured using direct-contact diffusion experiments based on in situ electron microscopy. The β-Sn pillars and lumps of pure Na (>99%) were used as the materials for the in situ sodiation experiment. To promote the sodiation of Sn while preventing the oxidation of Na and Sn, the target materials were handled inside an O2-free chamber filled with high-purity Ar (>99.999%). They were transferred into the FIB chamber using cryotransfer (ALTO 2500, Gatan Inc.). The lump of Na was cut again inside the FIB chamber to prepare an oxide-free surface and then moved toward the β-Sn pillars for the sodiation experiment using a nanomanipulator (MM3A-EM, Kleindiek Nanotechnik). To avoid artifacts, all experiments were performed with neither external electrical potentials nor liquid electrolytes. The electron beam intensity (5 keV, 42 pA) was minimized during the in situ diffusion experiments.

4.3. First-principles calculations. Car–Parrinello simulations

35

under a canonical ensemble were

performed to describe the spontaneous diffusion process of Na in β-Sn and to evaluate the diffusivity of Na atoms (DNa) during the sodiation of the Sn anode. We prepared the 20


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computationally generated Na–Sn diffusion couples by attaching a (5 × 5 × 3) Na supercell to a (3 × 3 × 2) β-Sn supercell oriented parallel to , such that the (211) plane of the Sn crystal made contact with the Na crystal. The dimensions of the Na–Sn diffusion couple were 47.7 × 20.5 × 20.5 Å. An additional 15-Å-thick vacuum layer was added on the free surface of the Na slab to provide space for volume expansion during sodiation. Periodic boundary conditions were enforced along the x-, y-, and z- directions (Fig. 4a) of the diffusion couple. The diffusion couple was fully relaxed using the conjugate gradient method until the residual forces were smaller than 10-3 eV/Å eV/Å. A cut-off energy of 30 Ry was set for the plane-wave expansion and only the gamma point was sampled. 4.4. Molecular dynamic simulations. Classical MD simulations were performed to study the diffusion behaviors of Li ions on comparatively large-scale crystalline Si, which cannot feasibly be obtained via first-principles calculations. For this purpose, the Li-Si diffusion couple was generated by attaching an amorphous Li slab to crystalline Si slab whose respective orientations were aligned along the . The dimensions of the Li-Si diffusion couple was 3.9 × 12.4 × 2.7 nm. Three types of boundary conditions were applied to the surfaces of the diffusion couples. Periodic boundary conditions were first imposed on the diffusion couples along the transverse directions (the x- and zaxes in Figure S2) of the diffusion couples to account for the effect of the orientation of crystalline Si while eliminating the surface effects on the Li diffusion. The reflective boundary condition was applied to the free-surface side (the y-axis in Figure S2) of the amorphous Li slab to keep the Li atoms from exiting the simulation box. The two layers of Si atoms on the free surface of the crystalline Si slab were kept fixed, whereas the rest of the system was allowed to equilibrate. The simulations for Li diffusion into crystalline Si were performed in the micro-canonical ensemble with a time step of 1 fs using the reactive force field potential 21


36

implemented in the LAMMPS


Page 22 of 36

package 37. Within the NVT ensemble, the Li/Si diffusion couples were equilibrated using a Nosé– Hoover thermostat at a temperature of 300 K.

4.5. Diffusivity calculation. DNa was obtained by calculating the mean square displacement () of the Na atoms. However, the diffusion of Na atoms was too slow to determine DNa using the measured values of . To reduce computational effort and speed the diffusion of Na atoms, we heated the couple to elevated temperatures and calculated the corresponding DNa values. All calculations were performed at temperatures (i.e., 400, 450, and 500 K) below the melting point of β-Sn. Each diffusion couple was annealed for 18 ps with a time step of 0.12 fs to promote the sodiation of the Sn anode. The positions of the ith Na atom ( ) at time t were tracked during sodiation, and the corresponding mean square displacements () of the Na atoms were calculated. To obtain the statistically meaningful result under a small number of atoms, the values were 38, 39

calculated using the time-averaged mean square displacement

. This value was obtained by

averaging the mean square displacement over the all choices of particles and time origins, which is given by =

×

∑ ∑ + −

(1)

where to is the time origins, nt the total number of to, N the total number of atoms. and

+ are the positions of the ith Na atom at the time origin to and time (to + t), respectively. The DNa values at elevated temperatures were evaluated using the Einstein relation:

= .

(2)

22


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The three diffusivity values measured at 400, 450, and 500 K were plotted in an Arrhenius plot of ln(DNa) versus 1000/T based on DNa = Do exp(-Q/kT),

(3)

where Do is the pre-exponential factor, Q the activation energy for diffusion, and k the Boltzmann constant. The values of Do, Q, and DNa at room temperature were obtained by extrapolating the DNa values calculated at 400, 450, and 500 K. All simulations were performed using norm-conserving pseudopotentials with Perdew–Burke–Ernzerhof (PBE) the Quantum Espresso package

41

40

exchange-correlation as implemented in

and an NVT ensemble with temperatures controlled by a Nosé–

Hoover thermostat 42. The cut-off energy of 30 Ry was set for the plane-wave expansion and only the gamma point was sampled. The energy convergence was achieved down to 0.2 Ry/unit cell. The Verlet algorithm was used to solve the classical equations of motion.

ASSOCIATED CONTENT Supporting Information Additional information and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

AUTHOR INFORMATION Corresponding Authors *Corresponding author: Jae-Chul Lee

[E-mail: [email protected]] 23



Jae-Pyoung Ahn

[E-mail: [email protected]]

Author Contributions ∥

These authors contributed equally to this work.

Notes The authors declare no competing financial interests. ACKNOWLEDGMENT This work was supported by Samsung Research Funding Center of Samsung Electronics under Project Number SRFC-MA1602-04. REFERENCES (1) Zhang, H.; Yu, X.; Braun, P. V., Three-Dimensional Bicontinuous Ultrafast-Charge andDischarge Bulk Battery Electrodes. Nat. Nanotechnol. 2011, 6, 277-281. (2) Kang, B.; Ceder, G., Battery Materials for Ultrafast Charging and Discharging. Nature 2009, 458, 190-193. (3) Park, M.; Zhang, X.; Chung, M.; Less, G. B.; Sastry, A. M., A Review of Conduction Phenomena in Li-Ion Batteries. J. Power Sources 2010, 195, 7904-7929. (4) Liu, X. H.; Zhang, L. Q.; Zhong, L.; Liu, Y.; Zheng, H.; Wang, J. W.; Cho, J.-H.; Dayeh, S. A.; Picraux, S. T.; Sullivan, J. P., Ultrafast Electrochemical Lithiation of Individual Si Nanowire Anodes. Nano Lett. 2011, 11, 2251-2258. (5) Ishihara, T.; Nakasu, M.; Yoshio, M.; Nishiguchi, H.; Takita, Y., Carbon Nanotube Coating Silicon Doped with Cr as a High Capacity Anode. J. Power Sources 2005, 146, 161-165.

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(6) Kong, M.-h.; Noh, J.-h.; Byun, D.-j.; Lee, J.-k., Electrochemical Characteristics of Phosphorus Doped Silicon and Graphite Composite for the Anode Materials of Lithium Secondary Batteries. J. electroceram. 2009, 23, 376. (7) Zhou, S.; Liu, X.; Wang, D., Si/Tisi2 Heteronanostructures as High-Capacity Anode Material for Li Ion Batteries. Nano Lett. 2010, 10, 860-863. (8) Usui, H.; Yoshioka, S.; Wasada, K.; Shimizu, M.; Sakaguchi, H., Nb-Doped Rutile Tio2: A Potential Anode Material for Na-Ion Battery. ACS Appl. Mater. Interfaces 2015, 7, 6567-6573. (9) Balogun, M.-S.; Luo, Y.; Qiu, W.; Liu, P.; Tong, Y., A Review of Carbon Materials and Their Composites with Alloy Metals for Sodium Ion Battery Anodes. Carbon 2016, 98, 162-178. (10) Wang, J. W.; He, Y.; Fan, F.; Liu, X. H.; Xia, S.; Liu, Y.; Harris, C. T.; Li, H.; Huang, J. Y.; Mao, S. X., Two-Phase Electrochemical Lithiation in Amorphous Silicon. Nano Lett. 2013, 13, 709-715. (11) Goriparti, S.; Miele, E.; De Angelis, F.; Di Fabrizio, E.; Zaccaria, R. P.; Capiglia, C., Review on Recent Progress of Nanostructured Anode Materials for Li-Ion Batteries. J. Power Sources 2014, 257, 421-443. (12) Ellingsen, L. A.-W.; Hung, C.; Majeau-Bettez, G.; Singh, B.; Chen, Z.; Whittingham, M. S.; Strømman, A. H., Nanotechnology for Environmentally Sustainable Electromobility. 2016. (13) McDowell, M. T.; Lee, S. W.; Wang, C.; Nix, W. D.; Cui, Y., Studying the Kinetics of Crystalline Silicon Nanoparticle Lithiation with in Situ Transmission Electron Microscopy. Adv. Mater. (Weinheim, Ger.) 2012, 24, 6034-6041. (14) Zhao, K.; Pharr, M.; Wan, Q.; Wang, W. L.; Kaxiras, E.; Vlassak, J. J.; Suo, Z., Concurrent Reaction and Plasticity During Initial Lithiation of Crystalline Silicon in Lithium-Ion Batteries. J. Electrochem. Soc. 2012, 159, A238-A243. 25



(15) Byeon, Y.-W.; Choi, Y.-S.; Ahn, J.-P.; Lee, J.-C., Origin of High Coulombic Loss During Sodiation in Na-Sn Battery. J. Power Sources 2017, 343, 513-519. (16) Choi, Y.-S.; Byeon, Y.-W.; Ahn, J.-P.; Lee, J.-C., Formation of Zintl Ions and Their Configurational Change During Sodiation in Na–Sn Battery. Nano Lett. 2017. (17) Chevrier, V.; Ceder, G., Challenges for Na-Ion Negative Electrodes. J. Electrochem. Soc. 2011, 158, A1011-A1014. (18) Wang, J. W.; Liu, X. H.; Mao, S. X.; Huang, J. Y., Microstructural Evolution of Tin Nanoparticles During in Situ Sodium Insertion and Extraction. Nano Lett. 2012, 12, 5897-5902. (19) Goldman, J. L.; Long, B. R.; Gewirth, A. A.; Nuzzo, R. G., Strain Anisotropies and Self‐ Limiting Capacities in Single‐Crystalline 3d Silicon Microstructures: Models for High Energy Density Lithium‐Ion Battery Anodes. Adv. Funct. Mater. 2011, 21, 2412-2422. (20) Liu, X. H.; Fan, F.; Yang, H.; Zhang, S.; Huang, J. Y.; Zhu, T., Self-Limiting Lithiation in Silicon Nanowires. ACS Nano 2013, 7, 1495-1503. (21) Liu, X. H.; Zheng, H.; Zhong, L.; Huang, S.; Karki, K.; Zhang, L. Q.; Liu, Y.; Kushima, A.; Liang, W. T.; Wang, J. W., Anisotropic Swelling and Fracture of Silicon Nanowires During Lithiation. Nano Lett. 2011, 11, 3312-3318. (22) Lee, S. W.; McDowell, M. T.; Choi, J. W.; Cui, Y., Anomalous Shape Changes of Silicon Nanopillars by Electrochemical Lithiation. Nano Lett. 2011, 11, 3034-3039. (23) Yang, H.; Huang, S.; Huang, X.; Fan, F.; Liang, W.; Liu, X. H.; Chen, L.-Q.; Huang, J. Y.; Li, J.; Zhu, T., Orientation-Dependent Interfacial Mobility Governs the Anisotropic Swelling in Lithiated Silicon Nanowires. Nano Lett. 2012, 12, 1953-1958. (24) Yang, H.; Fan, F.; Liang, W.; Guo, X.; Zhu, T.; Zhang, S., A Chemo-Mechanical Model of Lithiation in Silicon. J. Mech. Phys. Solids 2014, 70, 349-361. 26


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(25) Yang, H.; Liang, W.; Guo, X.; Wang, C.-M.; Zhang, S., Strong Kinetics-Stress Coupling in Lithiation of Si and Ge Anodes. Extreme Mech. Lett. 2015, 2, 1-6. (26) Huang, S.; Fan, F.; Li, J.; Zhang, S.; Zhu, T., Stress Generation During Lithiation of HighCapacity Electrode Particles in Lithium Ion Batteries. Acta Mater. 2013, 61, 4354-4364. (27) Choi, Y.-S.; Park, J.-H.; Ahn, J.-P.; Lee, J.-C., Interfacial Reactions in the Li/Si Diffusion Couples: Origin of Anisotropic Lithiation of Crystalline Si in Li–Si Batteries. Sci. Rep. 2017, 7, 14028. (28) Seo, J.-H.; Chou, C.-Y.; Tsai, Y.-H.; Cho, Y.; Seong, T.-Y.; Lee, W.-J.; Cho, M.-H.; Ahn, J.P.; Hwang, G. S.; Choi, I.-S., Ultrafast Chemical Lithiation of Single Crystalline Silicon Nanowires: In Situ Characterization and First Principles Modeling. RSC Adv. 2015, 5, 1743817443. (29) Kim, Y.; Park, Y.; Choi, A.; Choi, N. S.; Kim, J.; Lee, J.; Ryu, J. H.; Oh, S. M.; Lee, K. T., An Amorphous Red Phosphorus/Carbon Composite as a Promising Anode Material for Sodium Ion Batteries. Adv. Mater. (Weinheim, Ger.) 2013, 25, 3045-3049. (30) Xu, Y.; Zhu, Y.; Liu, Y.; Wang, C., Electrochemical Performance of Porous Carbon/Tin Composite Anodes for Sodium‐Ion and Lithium‐Ion Batteries. Adv. Energy Mater. 2013, 3, 128133. (31) Baggetto, L.; Keum, J. K.; Browning, J. F.; Veith, G. M., Germanium as Negative Electrode Material for Sodium-Ion Batteries. Electrochem. Commun. 2013, 34, 41-44. (32) Liu, X. H.; Wang, J. W.; Huang, S.; Fan, F.; Huang, X.; Liu, Y.; Krylyuk, S.; Yoo, J.; Dayeh, S. A.; Davydov, A. V., In Situ Atomic-Scale Imaging of Electrochemical Lithiation in Silicon. Nat. Nanotechnol. 2012, 7, 749-756.

27



(33) Balke, N.; Jesse, S.; Kim, Y.; Adamczyk, L.; Tselev, A.; Ivanov, I. N.; Dudney, N. J.; Kalinin, S. V., Real Space Mapping of Li-Ion Transport in Amorphous Si Anodes with Nanometer Resolution. Nano Lett. 2010, 10, 3420-3425. (34) Pell, E., Diffusion of Li in Si at High T and the Isotope Effect. Physical Review 1960, 119, 1014. (35) Car, R.; Parrinello, M., Unified Approach for Molecular Dynamics and Density-Functional Theory. Phys. Rev. Lett. 1985, 55, 2471. (36) Jung, S. C.; Choi, J. W.; Han, Y.-K., Anisotropic Volume Expansion of Crystalline Silicon During Electrochemical Lithium Insertion: An Atomic Level Rationale. Nano Lett. 2012, 12, 53425347. (37) Plimpton, S., Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1-19. (38) Barnard, L.; Morgan, D., Ab Initio Molecular Dynamics Simulation of Interstitial Diffusion in Ni–Cr Alloys and Implications for Radiation Induced Segregation. J. Nucl. Mater. 2014, 449, 225233. (39) Karki, B. B.; Bohara, B.; Stixrude, L., First-Principles Study of Diffusion and Viscosity of Anorthite (Caal2si2o8) Liquid at High Pressure. Am. Mineral. 2011, 96, 744-751. (40) Perdew, J. P.; Burke, K.; Ernzerhof, M., Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]. Phys. Rev. Lett 1997, 78, 1396. (41) Troullier, N.; Martins, J. L., Efficient Pseudopotentials for Plane-Wave Calculations. Phys. Rev. B 1991, 43, 1993. (42) Hoover, W. G., Canonical Dynamics: Equilibrium Phase-Space Distributions. Phys. Rev. A 1985, 31, 1695. 28


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For Table of Contents Only

29



Ultrafast sodiation of a Sn crystal Propagation Length ( μm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Page 30 of 36

12

0s 14 s Na

28 s

45 s

56 s

First-principles calculation of Na diffusion at the reaction front Na Na

a-NaxSn

8

a-NaxSn

β-Sn β-Sn

4

Amorphization of β-Sn promoting fast Na diffusion

2 µm

0 0

20

40

a-Sn

60

Diffusion Time ( s ) ACS Paragon Plus Environment

Page 31 of 36 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


b a W

probe

0s

First stage 1s 3s

Na (ΔV = 0%)

6s

9s

14 s

Second stage 20 s 28 s 36 s

a-NaSn

a-Na9Sn4

(100%)

(250%)

Na

lump

β-Sn

β-Sn

a-NaSn

pillar

Mo

lift-out grid

3 µm

Mo grid


45 s

56 s

(280%)


c

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

a

a-NaSn

b

500 nm

Sn

c Sn 500 nm

a-Na9Sn4 500 nm


Page 32 of 36

Page 33 of 36

a

b

102 Li-Si, Ref. [5] Li-Si, Ref. [6] Li-Si, Ref. [7] Li-a-Si, Ref. [8] Li-Si, This work Na-Sn, This work

2

12

101

Propagation Speed ( μm/s )

1

Propagation Length ( μm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


0

8

0

1

2

4

Si 100

Na-Sn

Si

10-1

10-2

Si Si

10-3

Li-Si Li-a-Si, φ = 4 μm, Ref. [8]

0 0

20

40

a-Si

10-4

60

102

103

Diameter of the Pillars ( nm )

Diffusion Time ( s )


104

a

Na

Page 34 of 36

t = 10 ps

a-NaxSn B

B

A A

3Å

β-Sn

y z

x

b Diffusivity of Na ( DNa, cm2/s )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

ACS Applied t=1 ps Materials t =& 5Interfaces ps

t=0s

Interface (region A) 10-4

Bulk (region B)

10-5

300 K

10-6

2.0

2.5

1000/T ( 1/K ) ACS Paragon Plus Environment

3.0

3.5

Page 35 of 36

t = 1 ps Li

t = 5 ps

y x

b

Si-Si 1 ps 5 ps 10 ps

a-LixSi

c-LixSi

4

Distance ( Å )

Na

t = 5 ps

6

z

x

d

Sn-Sn 1 ps 5 ps 10 ps

t = 10 ps

a-NaxSn

Sn

t = 20 ps

2

t = 1 ps

y

c-LixSi

Si

z

c

t = 10 ps

g (r) ( a.u. )

a

g (r) ( a.u. )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41


8


2

4

Distance ( Å )

6

8


c

0.57

Si B

2.5 eV 3.4 eV

-2

e Si-Si

Sn-Sn -4

b

ρ ( eÅ -3 )

0

1

c-Si 0

d 1.2 eV 1.8 eV

-1

Li-Si

Sn

Na-Sn

-2 2

3

4

Bond distance ( Å )

5

x

y

β-Sn

A

0.6

Si-Si

c-Si

Sn-Sn

0.15

0.4

C

D 0.2

β-Sn A

0.0

z 1

Charge density ( ρ, e/Å 3 )

Energy ( eV )

a

Energy ( eV )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41

Page 36 of 36

B

C 0

D 1

2

Distance ( Å )


3

Ultrafast Sodiation of Single-crystalline Sn Anodes - ACS Applied

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