Anisotropic Volume Expansion of Crystalline Silicon during

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Letter pubs.acs.org/NanoLett

Anisotropic Volume Expansion of Crystalline Silicon during Electrochemical Lithium Insertion: An Atomic Level Rationale Sung Chul Jung,† Jang Wook Choi,*,‡ and Young-Kyu Han*,† †

Division of Materials Science, Korea Basic Science Institute, Daejeon 305-806, Republic of Korea Graduate School of EEWS (WCU), Korea Advanced Institute of Science and Technology (KAIST), Daejeon 305-701, Republic of Korea

‡

S Supporting Information *

ABSTRACT: The volume expansion of silicon is the most important feature for electrochemical operations of high capacity Si anodes in lithium ion batteries. Recently, the unexpected anisotropic volume expansion of Si during lithiation has been experimentally observed, but its atomiclevel origin is still unclear. By employing first-principles molecular dynamics simulations, herein, we report that the interfacial energy at the phase boundary of amorphous LixSi/ crystalline Si plays a very critical role in lithium diffusion and thus volume expansion. While the interface formation turns out to be favorable at x = 3.4 for all of the (100), (110), and (111) orientations, the interfacial energy for the (110) interface is the smallest, which is indeed linked to the preferential volume expansion along the ⟨110⟩ direction because the preferred (110) interface would promote lithiation behind the interface. Utilizing the structural characteristic of the Si(110) surface, local Li density at the (110) interface is especially high reaching Li5.5Si. Our atomic-level calculations enlighten the importance of the interfacial energy in the volume expansion of Si and offer an explanation for the previously unsolved perspective. KEYWORDS: Lithium-ion battery, silicon anode, anisotropic volume expansion, density functional calculation, interfacial energy, molecular dynamics

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stress within the active material particles, eventually leading to the fracture and thus capacity fading.13−17 However, based on the pioneering study by Huggins18 that identified the resistance of small dimensional particles against the fracture, various nanostructured Si electrodes including nanowires,19,20 nanoparticles,21,22 and nanotubes23,24 have demonstrated significantly improved cycle lives. Other than the fracture, the significant volume change of Si causes weak contacts between Si particles and carbon conducting agents (i.e., super-P) as well as unstable solid−electrolyte interphase (SEI) formation, both of which also result in severe capacity fading.24 Overall, the significant volume change is the most important factor to deal with for successful operations of Si anodes and should thus be deeply understood. While the consensus on the importance of the volume expansion has been widely accepted, several recent experimental studies25−28 observed the anisotropic volume expansion of Si favoring the ⟨110⟩ directions, which is contradictory to the previous preconception that the volume expansion of Si would be isotropic. In fact, various theoretical models18,29,30 investigating Li diffusion-driven stresses within Si particles were developed based on the assumption of the isotropic volume expansion and are not thus fully reflective of the real electrochemical processes.

echargeable lithium-ion batteries (LIBs) have been very successful in powering diverse portable electronic devices. Beyond these small-scale applications, utilizing the superior energy and power densities, LIBs continuously expand their boundary into a variety of large-scale applications represented by sustainable transportation and utility power grids.1−3 However, these large-scale applications as well as emerging advanced portable electronic devices require LIBs with substantially increased energy densities.4,5 For example, the LIB energy density is related directly to the affordable driving distance of electrical vehicles per each charge. As an effort to meet the demand along this direction, silicon has drawn considerable attention as a next-generation anode material owing to its unparalleled theoretical capacity of 4200 mAh g−1,6 which is ∼10-fold larger than that of the conventional graphite. Beside the excellent capacity, Si holds other conspicuous advantages such as low cost, raw material abundance, and long history of investigation.7−12 Such a high specific capacity, in turn, implicates a large amount of Li insertion for the given mass of the active material, which is naturally accompanied by a great volume expansion. Indeed, Si undergoes ∼400% volume expansion upon full lithiation (Li4.4Si).6 It has been known that the large volume change of Si during Li (de)insertion makes stable cycling very difficult to achieve because the volume change triggers severe capacity fading mechanisms. The large volume expansion generates the © 2012 American Chemical Society

Received: July 23, 2012 Revised: September 5, 2012 Published: September 17, 2012 5342

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Figure 1. Two-phase a-LixSi/c-Si interfacial systems, at x = 3.375, in which the phase boundaries are formed perpendicular to the ⟨100⟩, ⟨110⟩, and ⟨111⟩ c-Si orientations. Red and yellow balls represent the Li and Si atoms, respectively.

perpendicular to the ⟨100⟩, ⟨110⟩, and ⟨111⟩ crystalline orientations (Figure 1). These interfacial systems were simulated by periodic supercells where 140x/(1 + x) Li atoms and 140/(1 + x) Si atoms were used for the a-LixSi phase, and 160 Si atoms were used for ten atomic layers of the c-Si phase. The x was chosen to be 1.916, 2.589, 3.000, 3.375, 3.666, and 4.000 for the a-LixSi phase, corresponding to the atomic compositions of Li92Si48, Li101Si39, Li105Si35, Li108Si32, Li110Si30, and Li112Si28, respectively.

Despite multiple experimental reports25−28 on the preferential volume expansion along the ⟨110⟩ orientations, the origin of such unexpected observation has been unclear. It was reported that, among several possible factors, short-range atomic processes at the interface between amorphous lithiated Si (aLixSi) and crystalline Si (c-Si) are most limiting for the overall kinetics of lithiation process and are thus most responsible for the anisotropic behavior.31 Thus, in the present study, we focus mainly on this interface to see the interfacial orientation dependence. The Suo group32 identified the coevolution of the reaction front (i.e., the a-LixSi/c-Si interface) and the plastic deformation as a primary process during Li diffusion from a-LixSi to c-Si but did not unveil the atomic-level origin of the anisotropic volume expansion. Similarly, the Zhang group33 developed a chemomechanical model to simulate the Li insertion process but was unable to reach atomic-level interpretation. Having noticed the elusive situation in the atomic-level understanding of the anisotropic volume expansion as well as the difficulty in analyzing the amorphous phases of the lithiated Si, herein, we employed a first-principles molecular dynamics (MD) approach based on density functional theory (DFT) to simulate the interface between the c-Si and a-LixSi phases at the atomic level. Indeed, interfacial properties have been recognized as critical parameters to affect key features of nanomaterials such as morphology and growth kinetics.34−36 For the case of Li diffusion into c-Si, the calculations provide valuable information on the atomic structure, Li-to-Si atomic ratio, and Li−Si bonding characteristics at the two-phase interface. In particular, the calculated interfacial energy (γ), the work per unit area required to form the interface, elucidates the interfacial stability between the two phases. While γ gives the lowest value (most stable) at x = 3.4 for the interfaces with all of the (100), (110), and (111) orientations, the γ value at the (110) interface turned out to be much smaller than those at other interfaces, which is consistent with the experimentally observed anisotropic volume expansion along the ⟨110⟩ directions. The calculation indicates that, at x = 3.4, a larger number of Li elements exist at the (110) interface compared to the (100) and (111) counterparts such that at the (110) interface the Li-to-Si atomic ratio reaches a value as high as 5.5. Also, the relevant characteristic of the (110) surface was identified. The present study clearly suggests that the interfacial energy at the phase boundary dictates the volume expansion of Si during lithiation along the preferential direction. As an effort to examine the interfacial energy along different crystal orientations, we first constituted three two-phase a-LixSi/ c-Si interfacial systems in which the phase boundaries are formed

Figure 2. Interfacial energy γ, defined as (Etot − Ea‑LixSi − Ec‑Si)/2A, where Etot is the total energy of the a-LixSi/c-Si interfacial system, Ea‑LixSi is the total energy of a-LixSi bulk phase, Ec‑Si is the total energy of c-Si bulk phase, and A is the surface area of interface. The factor of 2 accounts for the two identical interfaces in the supercell.

Figure 2 shows the calculated interfacial energies of the twophase a-LixSi/c-Si systems for each crystal orientation for the aforementioned x values. The interfacial energy γ is defined as γ = (Etot − Ea‐LixSi − Ec‐Si)/2A

where Etot is the total energy of the two-phase a-LixSi/c-Si interfacial system, Ea‑LixSi is the total energy of the a-LixSi bulk phase, Ec‑Si is the total energy of the c-Si bulk phase, and A is the surface area of interface. The factor of 2 accounts for the two identical interfaces in the supercell. All of the three interfaces exhibit parabolic-like energy curves with a common minimum around x = 3.4. The x values with minimum energies were found to be 3.43, 3.42, and 3.45 for the (100), (110), and (111) 5343

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interfaces, respectively, by a least-squares fit to the calculated data in Figure 2. These results indicate that all of the crystalline Si surfaces prefer to form the contact with the amorphous Li3.4Si alloy regardless of their interfacial orientations. Furthermore, the calculated x values with the minimum interfacial energies are in good agreement with the reported x values37,38 of 3.4 ± 0.2 and 3.5 ± 0.2 for the a-LixSi phase, both of which were determined by an in-situ X-ray diffraction technique during the two-phase lithiation reaction in c-Si. The agreement between experimental and theoretical studies strongly suggests that the calculated x value of 3.4 is a critical point that stabilizes not only the a-LixSi phase itself but also the phase boundaries with the c-Si phase. The presence of critical point offers an implication that particular concentration of Li atoms should be reached in the amorphous phases to start the disruption of c-Si surface structures and subsequently to drive the migration of the phase boundaries in the two-phase reactions, giving rise to the onset of two-phase reactions. Consequently, the critical point may be regarded as the most favorable composition for the amorphous LixSi phase during the two-phase lithiation reaction. As shown in Figure 2, the interfacial energy curves for the (100) and (111) interfaces have similar shapes, but the (111) one shows smaller values by ∼0.1 J/m2 over the entire x range. By contrast, the (110) interface exhibits a distinctive curve shape as it shows a steep parabola with a minimum γ at x = 3.4. From this curve showing a clear downward convex, it can be noted that the (110) interface is most stable in the range of 3.1 ≤ x ≤ 3.7. Such observation that the minimum γ for the (110) interface is much smaller than those for the other two interfaces suggests that around x = 3.4 the interface is more favorable to be formed in the (110) orientation. This orientation preference of the interface is indeed linked to the preferential volume expansion along the ⟨110⟩ directions because the preferred (110) interface would promote lithiation behind the interface. The anisotropic behavior is illustrated in Scheme 1 where the phase-boundary morphology

calculations describe time-averaged static situations of the phase boundary, they still offer the interfacial energy as a key parameter that dictates other related parameters and thus plays a critical role in simulating actual dynamic processes. Indeed, the interfacial energies (or surface energies) for solid/vacuum, solid/liquid, and solid/solid interfaces have been widely used to describe various complicated dynamic processes such as directional growths, morphology changes, and facet formations of various types of nanostructures.35,36,39,40 We investigated more detailed interfacial atomic structures to understand the interfacial interactions between the a-LixSi and cSi phases. We hereafter refer to the Si atoms of the a-LixSi and cSi phases as Si(a) and Si(c) atoms, respectively. The interfacial atoms are defined as (i) the first- and second-layer Si(c) atoms of the c-Si surface and (ii) the Li and Si(a) atoms bonded to the Si(c) atoms, based on the experimental observation of a very sharp phase boundary between the a-LixSi and c-Si phases.41 The interfacial atoms at the three a-LixSi/c-Si interfaces at x = 3.375 are denoted in color in Figure 3a. Based on the analyses focusing on the interfaces, the following information was obtained: (1) The Li/Si(a) atomic ratio at the interface, denoted as xinterface, varies significantly depending on the crystalline orientation of c-Si surface (Figure 4a). While the (100) and (111) interfaces show generally smaller xinterface values (y-axis) than the bulk composition values of x (x-axis), the (110) interface is opposite: xinterface is larger than x over the entire x range. In particular, it is noteworthy that xinterface for the (110) interface at x = 3.375 reaches the value as high as 5.5, indicating that the local Li density at the interface is even larger than that of Li4.4Si which corresponds to the theoretical Li capacity of Si. (2) It is anticipated that such a high Li concentration at the (110) interface is associated with the structural characteristics of the Si(110) surface. As illustrated in Figure 3b,c, at the Si(110) surface, Si atoms form a valley-like structure where each Si atom is connected with the neighboring ones in a zigzag shape constructing a parallel array of valleys. The valley-like structure in conjunction with the character of the Li−Si(c) ionic bonds that allow multiple Li−Si bonds with no designated orientation may contribute to the enhanced local Li density (Figure 3c). Our Bader charge analysis in the (110) interface region indicates that the average atomic charges are +0.8, −1.9, and −0.3 for the interfacial Li, Si(a), and Si(c) atoms, respectively, thus supporting the ionic nature of Li−Si bonds. Although it is likely that the Si(100) surface also has a valley-like structure in the top three layers (Figure 3b), the (100) surface undergoes a significant reconstruction such as dimerization upon contact with the a-LixSi phase, thus losing the original bulk-truncated structure.42 (3) The higher Si density in the first layer of the (110) surface also seems to contribute to the higher Li local density. The number of first-layer Si atoms per unit surface area is 0.067, 0.095, and 0.077/Å2 for the (100), (110), and (111) surfaces, respectively. (4) The Li density is also related closely to the Li diffusivity. It should be first noted that Li is the dominant diffusing species and the diffusion of Si is negligible, as Si is 2 orders of magnitude slower than Li in Li−Si alloy.43 It was demonstrated that the diffusivity of Li atoms in the a-LixSi alloy increases greatly as the Li concentration increases.44 Also, the experimental morphology evolution during lithiation was reproduced by using a nonlinear diffusion model, in which Li diffusivity increases sharply at high Li concentrations.26,33 Therefore, the large value of xinterface for the (110) interface can be associated with the high value of the Li

Scheme 1. Schematic Diagram for the Lithiation Process in cSia

a

The dashed line represents the initial cross section of the pristine c-Si, and solid line represents the shape of a-Li3.4Si that encloses the pristine c-Si. The color box represents the local Li/Si ratio (x). The lithiation preferentially proceeds along the ⟨110⟩ orientation, accompanied by a significant volume expansion. The Li:Si local compositions in the (110) and (111) interfaces are Li5.5Si and Li3.6Si, respectively.

evolves into a shape with large-area (110) interfaces during lithiation to minimize the total interfacial energy of entire boundaries, reflecting that the interfacial energy minimization is a driving force for the orientation-dependent lithiation. The anisotropic interfacial energy therefore plays a key role for the observed anisotropic volume expansion. Although the current 5344

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Figure 3. (a) Interfacial atoms of a-LixSi/c-Si at x = 3.375, depicted as colored balls. Red and yellow balls represent the interfacial Li and Si atoms, respectively. The interfacial atoms are defined as the first- and second-layer Si(c) atoms of the c-Si surface and the Li and Si(a) atoms bonded to the Si(c) atoms. (b) Top and side views of bulk-truncated Si surfaces (upper and lower panels, respectively). Magenta and cyan balls represent the first- and second-layer Si atoms, respectively, and white balls represent the rest of the Si atoms. In the top view, only the first three Si layers are presented for clarity. (c) A schematic diagram showing the valley-like structure of the Si(110) surface. The Li−Si ionic bond character that allows multiple Li−Si bonds may contribute to the enhanced local Li density.

Figure 4. (a) Interfacial atomic ratio xinterface, defined as the ratio of interfacial Li atoms to interfacial Si(a) atoms. Dashed lines represent the reference line xinterface = x. (b) Interfacial bond ratio α, defined as the ratio of interfacial Li−Si(c) bonds to interfacial Si(a)−Si(c) bonds. The α values are larger than one irrespective of crystalline orientations, showing the predominance of Li−Si(c) bonds over Si(a)−Si(c) bonds in the interface region. We note that the xinterface and α values at x = 3.375 reach the values as high as 5.5 and 9.7, respectively, for the (110) interface.

mobility at the (110) interface, which would enhance the migration velocity of the (110) phase boundary. (5) The local Li density is also linked to the number of interfacial Li−Si(c) bonds. When the interfacial Li−Si(c)/Si(a)− Si(c) bond ratio is defined as α, the α values are larger than one

for all of the three interfaces, indicating preferred Li−Si(c) bond formation over Si(a)−Si(c) bonds at all of the interfaces (Figure 4b). Among the three interfaces, the (110) interface exhibits the largest α over the entire x range. In particular, the (110) interface shows the largest α value reaching up to 9.7 at x = 3.375, while the 5345

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α values are only 2.4 and 5.4 for the (100) and (111) interfaces, respectively. This implies that the interfacial Si(c) atoms of the (110) surface have more chances of reacting with Li atoms and thus being decoupled from the surface, suggesting an easier disruption of the Si(110) surface structure and consequently a higher rate of Li−Si reaction at the (110) phase boundary. At x = 3.375, the highest α value as well as the aforementioned largest Li local density is commensurate with the steep parabolic curve of the (110) interfacial energies that shows the minimum at the same x value. In summary, we have employed first-principles MD simulations to investigate the electrochemical lithiation process of Si in the atomic level. In particular, the present study focuses on the a-LixSi/c-Si interface and its dependence on the crystal orientation. While the interfacial energy γ indicates that the formation of the interface is most preferred at x = 3.4 for all of the three interfaces examined, the γ value for the (110) interface turns out to be much smaller than those for the other two interfaces, which offers an atomic-level explanation for the experimentally observed anisotropic volume expansion along the ⟨110⟩ directions. The extraordinary high Li concentration (Li5.5Si) at the (110) interface is associated with the structural characteristic of the Si(110) surface. The present investigation clearly delivers the importance of the interfacial energy and thus provides an in-depth understanding on the volume expansion of Si, which is the key feature for stable cycling of high capacity Si anodes in the ever-expanding LIB field. Also, the microscopic perspective for the a-LixSi/c-Si(110) interface developed throughout the present study should be readily applicable to other high capacity alloy-based electrodes that could have the dependence of crystal orientation during volume expansion. First-Principles Molecular Dynamics Calculations. Our DFT calculations were performed within the Perdew−Burke− Ernzerhof (PBE) exchange and correlation functionals45 and the projector augmented wave (PAW) method,46,47 as implemented in the Vienna ab initio simulation package (VASP).48 The electronic wave functions were expanded in a plane-wave basis set of 271.6 eV. We treated 1s22s1 for Li and 3s23p2 for Si as the valence electron configurations. A 2 × 2 × 1 k-point mesh was used for Brillouin-zone integrations. The calculated lattice constant of bulk silicon is 5.472 Å, which is in good agreement with the experimental value of 5.430 Å.49 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.50,51 During the MD run, a 1 × 1 × 1 k-point mesh was used to reduce the enormous computational costs. The two-phase interfacial systems were modeled with periodic supercells including the a-LixSi and c-Si phases separated by flat phase boundaries. Our interface modeling procedure consisted of three sequential steps. First, for a given x, we determined the volume of the a-LixSi phase. To generate the a-LixSi phase, we employed a “liquid-quench” technique52 in which heating, equilibration, and cooling were carried out in series using the MD simulations. Second, using the determined volume, we prepared, for each x, three a-LixSi phases with different supercell sizes in order to attach the a-LixSi supercells to the three different c-Si supercells for the (100), (110), and (111) surfaces. The liquid-quench method was again used to generate the three aLixSi phases. Lastly, we attached the prepared a-LixSi phases to the c-Si surfaces to construct three interfacial systems of a-LixSi/ c-Si(100), a-LixSi/c-Si(110), and a-LixSi/c-Si(111). Each a-

LixSi/c-Si system was equilibrated by sufficient MD steps at 300 K to describe a realistic interfacial system. Overall three-step procedures for each x require ∼43 ps MD runs. It should be mentioned that the present model based on the interface with planar geometry is consistent with the recent transmission electron microscopy (TEM) characterization41 that indeed observed that the phase boundary moves while preserving the flat geometry. Detailed processes at each step are described in the Supporting Information.

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ASSOCIATED CONTENT

S Supporting Information *

Computational details, detailed procedure for two-phase interface modeling, and Bader charge analysis results. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Fax +82-42-865-3610; e-mail [email protected] (J.W.C.), [email protected] (Y.-K.H.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.W.C. acknowledges the financial support by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) ((NRF-2010-C1AAA001-0029031, NRF2012M1A2A2026587, and NRF-2012-R1A2A1A01011970) and the World Class University Program (R-31-2008-000-10055-0). Y.-K.H. acknowledges the financial support by the National Research Foundation of Korea Grant funded by the Korean Government (MEST, NRF-2010-C1AAA001-0029018) and by KBSI grant T32413.

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dx.doi.org/10.1021/nl3027197 | Nano Lett. 2012, 12, 5342−5347