Li Segregation Induces Structure and Strength Changes at the

Sep 3, 2013 - School of Engineering, Brown University, Providence, Rhode Island ... Shiv Nadar University, Gautam Budh Nagar, Uttar Pradesh 203207, ...
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Li Segregation Induces Structure and Strength Changes at the Amorphous Si/Cu Interface Maria E. Stournara,† Xingcheng Xiao,‡ Yue Qi,*,‡,§ Priya Johari,†,∥ Peng Lu,‡ Brian W. Sheldon,† Huajian Gao,*,† and Vivek B. Shenoy†,⊥ †

School of Engineering, Brown University, Providence, Rhode Island 02912, United States General Motors Global Research & Development Center, 30500 Mound Road, Warren, Michigan 48090, United States § Department of Chemical Engineering and Materials Science, Michigan State University, East Lansing, Michigan 48824, United States ∥ Department of Physics, School of Natural Sciences, Shiv Nadar University, Gautam Budh Nagar, Uttar Pradesh 203207, India ⊥ Departments of Materials Science and Engineering & Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States ‡

S Supporting Information *

ABSTRACT: The study of interfacial properties, especially of their change upon lithiation, is a fundamentally significant and challenging topic in designing heterogeneous nanostructured electrodes for lithium ion batteries. This issue becomes more intriguing for Si electrodes, whose ultrahigh capacity is accompanied by large volume expansion and mechanical stress, threatening with delamination of silicon from the metal current collector and failure of the electrode. Instead of inferring interfacial properties from experiments, in this work, we have combined density functional theory (DFT) and ab initio molecular dynamics (AIMD) calculations with time-of-flight secondary ion mass spectrometry (TOF-SIMS) measurements of the lithium depth profile, to study the effect of lithiation on the a-Si/Cu interface. Our results clearly demonstrate Li segregation at the lithiated a-Si/Cu interface (more than 20% compared to the bulk concentration). The segregation of Li is responsible for a small decrease (up to 16%) of the adhesion strength and a dramatic reduction (by one order of magnitude) of the sliding resistance of the fully lithiated a-Si/Cu interface. Our results suggest that this almost frictionless sliding stems from the change of the bonding nature at the interface with increasing lithium content, from directional covalent bonding to uniform metallic. These findings are an essential first step toward an in-depth understanding of the role of lithiation on the a-Si/Cu interface, which may contribute in the development of quantitative electrochemical mechanical models and the design of nonfracture-and-always-connected heterogeneous nanostructured Si electrodes. KEYWORDS: Li-ion battery, Si anode, interface, density functional theory, molecular dynamics

S

ilicon has long been sought1 as a candidate anode material for lithium ion batteries due to its ultrahigh theoretical capacity, nearly 10 times greater than conventional graphite electrodes (3600 mAh/g for Si in the form of Li15Si4 as compared with 372 mAh/g for fully lithiated graphite, LiC6). However, the large volume expansion associated with silicon’s high capacity (up to 300 vol % upon full lithiation) can cause Si fracture, pulverization, and delamination from the copper current collector or from other conductive phases, such as carbon or binder, resulting in early capacity loss.2 Although nanostructured Si in the form of particles, wires, and films3−7 can enable large surface strain tolerance and mitigate Si cracking, recent theoretical studies8 and in situ TEM9 have demonstrated that nanoengineered Si electrodes can still detach from the conductive phases (for example Cu or C), resulting in capacity fade. As indicated by both experiments and modeling, capacity loss can be attributed to the loss of electric contact between particles, even without particle fragmentation; on the © 2013 American Chemical Society

other hand, capacity can be retained for numerous cycles if the fractured particles are still electronically connected.10,11 To accommodate for the loss of electrical contact with the current collector, a wide range of composite structures that retain capacity over many cycles has been studied. Examples of such structures are carbon fiber, graphene, carbon−nanotube, conductive polymer binder, and others,12−14 which combine high capacity and mechanical stability, provided by nanostructured Si, with the high electrical conductivity of carbon. Similar to other composite interfaces, the structural integrity and functionality in these heterogeneous Si materials depend on the interface properties.15−17 Designing an effective interface architecture becomes significantly more challenging as one (e.g., a-Si/Cu) or both (e.g., a-Si/a-C) of the materials across Received: June 27, 2013 Revised: August 23, 2013 Published: September 3, 2013 4759

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Table 1. Structural Details of the Interface Structures: Number of Li, Si, and Cu Atoms Corresponding to Each a-LixSi and a-LixSi/Cu Intermetallic Structure, Along with the Number of Irreducible k-Points Used in the DFT Calculations in Each Casea Natoms

LixSi/Cu interfaces

a

system

x

y = x/(1 + x)

a-Si/Cu a-LiSi2/Cu a-LiSi/Cu a-Li12Si7/Cu a-Li15Si4/Cu a-Li/Cu

0 0.5 1 1.71 3.75

0 0.33 0.5 0.63 0.78 1

∞

NLi 20 40 60 75 54

NSi

NCu

optimized z length in the full-3D interface model (Å)

k-points

64 40 40 35 20

48 48 48 48 48 48

17.06 19.07 21.31 22.33

8 36 34 20 20 36

Optimal cell length along the z-direction of the 3D periodic interface model of a-LixSi/Cu is also presented.

Calculation Details. To search for equilibrium a-LixSi/Cu interfacial structures, we performed AIMD calculations at finite temperature within the framework of DFT, as implemented in the Vienna Ab Initio Simulation Package (VASP).28,29 We first performed constant volume and temperature (NVT) AIMD calculations with a Nose thermostat at 1200 K30,31 for Li and Si to mix into amorphous phases at four lithium concentrations: a-LiSi2, a-LiSi, a-Li12Si7, and a-Li15Si4, as well as for the amorphization of pure bulk Si and Li. The as-built a-LixSi structures started with unmixed Si and Li slabs in simulation cells that had their volume increased (compared with the volume of Si) by a factor of ∼1.3 for a-LiSi2, ∼ 1.66 for a-LiSi, ∼ 2.17 for a-Li12Si7,32 and ∼3.8 times for a-Li15Si433 based on previously computed equilibrium densities of these compounds. The numbers of Li and Si atoms corresponding to each concentration used in our calculations are summarized in Table 1. Starting from the initial bulk amorphous configurations, the cells were allowed to equilibrate at 1200 K for roughly 5000 MD time steps, with an MD step of 3 fs. A time of approximately 15 ps proved to be sufficient for substantial mixing in agreement with results reported in our previous work.13 Upon the end of each AIMD calculation the total energy fluctuation was minimal ( 1.7. To check the robustness of this result and to ensure that the observed variations in composition are indeed due to the presence of the interface with Cu for the slab and the 3D-interface model, we performed the same analysis for (a) the a-LixSi bulk configurations and (b) the interface models along both the x- and y-directions. Our calculations (not presented here) demonstrated infinitesimal fluctuations around the bulk Li/Si ratio for the four concentrations we tested (x = 0.5, 1, 1.71, 3.75), ensuring that the large increment observed in the interface is due to the presence of the Cu current collector. The tendency of Li segregation on the a-Si/Cu interface is experimentally demonstrated by the depth profiles of Li, Si, and Cu in a fully lithiated Si thin film on a Cu substrate with TOF-SIMS. The depth profiles for Li/Si ratio and Cu+ ions are reported in Figure 2. For comparison purposes, the Li/Si ratio

Wsep = σ1 + σ2 − γ12 =

tot Ε1tot + Ε 2tot − Ε12 Α

(1)

where σi is the surface energy of the slab i, γ12 is the interface tot energy, Etot i is the total energy οf slab i, E12 is the total energy of the interface system with slab materials 1 and 2, and A represents the total interface area.40 This is the energy required to break bonds at the interface to completely separate along the interface normal. We calculated Wsep as a function of the Li concentration in the bulk, shown in Figure 3. Note that, to represent the change from pure Si to pure Li in this and the following sections, we define concentration y for a-LixSi, via the expression y = x/(1 + x). Hence, while x is the atomic ratio of Li/Si, y is the ratio of the Li atoms to the total number of atoms. The advantage of using y in favor of x is that for elemental Li x → ∞, while y is 1. Therefore, all of the compounds can be explored by letting y vary between 0 (Si) and 1 (Li). We computed Wsep based on the interface of a-LixSi/Cu slab models and compared those results to the ones obtained from the nonrelaxed structures. We find that relaxation is responsible for the increase of Wsep by ∼0.2 J/m2 (the interface energy is lowered by the same amount). Since the Li segregation at the interface results in higher Li concentration at the interface region than the concentration in the bulk, we also plotted the relaxed Wsep vs the interface Li concentration. As shown in Figure 3, Li segregation is responsible for small shifts of the corresponding Wsep to higher values of the Li concentration y. Upon the increase of Li, Wsep decreased by ∼16% from 1.85 J/m2 (a-Si/Cu interface) to 1.55 J/m2 (a-Li15Si4/Cu interface). If we fit Wsep as a linear function of y, we obtain two slopes to describe the rate of change of Wsep. Fitting indicates there is a sharp decrease for poorly lithiated structures below y = 0.5 (a-LiSi), with k = −0.5, followed by a five times more gradual decrease with k = −0.1. The later one reaches a plateau around a value as low as that of the pure Li/Cu interface (1.55 J/m2).

Figure 2. SIMS depth profile of Li/Si ratio through the thickness of a lithiated Si film on Cu. Since the sensitivity factors for different species are different, we normalized the Li/Si ratio using the bulk composition (Li15Si4) as the internal standard. It clearly shows that the interface has a higher Li/Si ratio than that in the bulk electrode. The high Li/Si ratio at the top surface is due to the Li trapped in the SEI layer with almost no Si.

was normalized to coincide with Li/Si = 4 in the bulk of the film, since the film is fully lithiated when Si was charged with constant potential at the end of the cycle (0.05 V), and thus this is a fully lithiated Si film. The first 30 nm below the surface is expected to be the solid electrolyte interphase (SEI) formed on the Si surface, and the significantly high Li/Si ratio (∼20 au) is attributed to the absence of Si in the SEI region. Note that the SEI region is not included in our atomic model and should not be compared with the simulation result for free LixSi surface in vacuum. The fully lithiated film (30 < x < 120 nm) is on top of the Cu current collector. The Cu presence, indicated by the Cu+ signal (zero from the top surface until 120 nm), increased quickly and reached 100% 4763

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each other, the total energy of the system will change with the relative positions of the two slabs due to the atomic configuration change at the interface. Hence, the top a-LixSi slab was moved to various positions through a lateral spatial increment of 0.5 Å along the sliding direction under the applied force, while the bottom Cu (111) slab was fixed. The direction of relative displacement of the center of mass of the two slabs was defined as the sliding direction on Cu (111), that is, [211]. As we have proposed in previous work, the valleys and hills of the Wsep profile correspond to the maxima and minima of the interfacial energy density γ12 along the sliding direction, and the energy barrier is the difference between the maxima and minima.44 Therefore, the interfacial traction during sliding is the derivative of the interface energy with respect to the sliding distance l and can be computed from Wsep as a function of the Li content x in LixSi, according to eq 1 ∂γ12 ∂l

Figure 3. Interfacial work of separation Wsep of relaxed LixSi/Cu vs y in y = x/(x + 1) for LixSi in the bulk (black diamonds), on the interface (polka dot diamonds), and Wsep of nonrelaxed LixSi/Cu (white diamonds). The slopes of the first curve, k, are highlighted as red dashed lines, indicating a sharp decrease for poorly lithiated structures below y = 0.5, with k = −0.5, followed by a more gradual decrease with k = −0.1. The overall Wsep reduction is ∼16%. Relaxation is responsible for increase of Wsep by ∼0.2 J/m2, and Li segregation on the interface is responsible for small shifts of the corresponding Wsep to higher values of the Li fraction.

Wsep E′ πc

∂Wsep ∂l

x

(3)

The critical interface shear stress is, thus, the maximum of ∂γ12/ ∂l (GPa), or τmax = ∂γ12/∂l|max, indicating the critical shear stress to initiate continuous sliding along the given sliding direction. We obtained the Wsep profile (red curves) from simulations and calculated the ∂γ12/∂l profile (blue curves) along the sliding pathway for four interfaces, ranging from low and high Li concentrations, a-LiSi2/Cu to a-Li15Si4/Cu. The maximum value of Wsep is given by the equilibrium interface structure with the minimum potential energy. Note that these values are in excellent agreement with our Wsep calculations reported in the Ideal Work of Separation at the Interface section, suggesting that the initial interface we built is indeed the most energetically stable interface. The maximum value of Wsep is 1.785 J/m2 for a-LiSi2/Cu (x = 0.5) and 1.462 J/m2 for a-Li15Si4/Cu (x = 3.75), which differs by a little more than 16%, in agreement with the discussion in the Ideal Work of Separation at the Interface section. However, the variation of the Wmax sep profile along the sliding direction for a-Li15Si4/Cu is much more flat than that for a-LiSi2/Cu. Taking the negative of the derivative of Wmax sep with respect to the sliding distance l or τ = ∂γ12/∂l leads to a very small critical shear strength τmax (Figure 4) for a-Li15Si4/Cu. The critical shear strength is 0.287 GPa for a-LiSi2/Cu and 0.034 GPa for a-Li15Si4/Cu. Note that, when Si is fully lithiated, Wmax sep is reduced by only ∼16% compared to a-LiSi2/Cu, but the critical shear strength τmax is reduced by an order of magnitude. The maximum values of τmax (Wmax sep ) in Figure 4 are listed in Table 3 and show a monotonic decrease with Li concentration. In agreement with recent experimental studies showing that patterned Si thin film electrodes on Ti substrates exhibit improved cycling stability and substantial sliding (∼30%) at the film/substrate interface,27,45 we find that the increasing presence of Li acts as a lubricant for the interface and is responsible for monotonic reduction of the interface sliding strength, τmax, from 0.287 GPa (a-LiSi2/Cu) to 0.034 GPa (a-Li15Si4/Cu). Similar to other metal/Si interfaces,15 the atomic simulation predicted τmax value of highly lithiated compounds is independent of the size of the slab and thus will be within the same order of magnitude as the experimental value reported by Soni et al. (τmax = 0.012 GPa, responsible for 30% lateral expansion of the electrode).45 Our results suggest that the sliding strength estimated from crack spacing in these experiments is some type of average of the highly lithiated configuration during cycling, while in MD it is calculated at a

For a sharp planar asymmetric crack of length 2c cleaving along the interface in a brittle manner, the critical stress of (mode I) fracture can be expressed as a function of the effective Young’s modulus E′, the crack length c, and the work of separation Wsep

σf =

=−

(2)

Considering the Si thin film on Cu substrate is close to a plane stress state, therefore E′ is the effective modulus computed by 1/E′ = 1/2(1/ECu + 1/ELixSi) with Ei being the Young’s modulus of each of the materials i across the interface.41,42 Note that, in writing eq 2, we have neglected the oscillatory behavior of an interfacial crack.43 Based on our results for Wsep and the Young’s modulus and Poisson’s ratio values reported by Shenoy et al.,24 the fracture stress (without considering other energy compensation mechanisms, such as plasticity) also decreases monotonically with increasing Li concentration. However, with increasing Li concentration (typically when x is larger than 1), a-LixSi becomes more ductile with large plastic deformation, and the macroscopic fracture toughness at the a-LixSi/Cu interface may increase as well. The reduction of Wsep in the presence of Li, although no more than ∼16%, clearly indicates slight interface weakening and may lead to easier delamination of Si from the Cu substrate during lithiation, in agreement with previous experimental studies.5,26,27 Interface Shear Strength. The interface shear, or sliding strength, is as important as the tensile strength. In this work, we use DFT to predict the interface shear strength of lithiated Si sliding at the a-LixSi/Cu interface. Since the interface shear strength cannot be immediately inferred from Wsep, that is, higher adhesion does not imply higher critical shear stress,44 we calculated the interface shear strength τmax from the variation of Wsep during sliding. When the two slabs slide against 4764

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Figure 4. Interfacial work of separation Wsep from simulations and the calculated derivative of the interface energy ∂γ12/∂l along the sliding direction [211] for LiSi2/Cu, LiSi/Cu, Li12Si7/Cu, and Li15Si4/Cu. The arrows show how the Wmax sep and τmax values were calculated. Poorly lithiated LiSi2/Cu demonstrated great fluctuations in its Wmax sep and ∂γ12/∂l values and τmax = 0.287 GPa, but Li-rich Li15Si4/Cu showed a flat profile that lead to a very small critical shear strength τmax = 0.034 GPa. For intermediate lithiated structures, the values for both Wmax sep and τmax range between the two extremes (see Table 4).

Table 3. Interface Shear Strength τmax (GPa) Determined from the Maximum Value of Derivative of Potential Energy 2 and the Maximum Value of Work of Separation, Wmax sep (J/m ) system

τmax = ∂γ12/∂l|max (GPa)

2 Wmax sep (J/m )

a-LiSi2/Cu a-LiSi/Cu a-Li12Si7/Cu a-Li15Si4/Cu

0.287 0.211 0.098 0.034

1.785 1.582 1.518 1.462

change upon lithiation. To capture the nature of bonding, we used the electron localized function (ELF)18 to explore the bond character in the four a-LixSi/Cu intermetallic systems. ELF is a localized function of same-spin pairs, which is interpreted either as a spherical average of the Hartree−Fock same-spin pair probability47 or the excess local kinetic energy due to Pauli exclusion principle.48 The value of the ELF ranges from 0 to 1, where 1 corresponds to the localization as in covalent bonds, and 0.5 corresponds to the electron-gas-like pair probability as in metallic bonds.47 Topology analysis to ELF can effectively reveal the nature of different chemical bonds. Figure 5a shows the ELF contour plots for four optimized a-LixSi/Cu interfaces (along the Cu [110] direction perpendicular to the interfaces). The covalent and ionic bonds, indicated by the regions of red and yellow, respectively, are located between neighboring Si atoms (covalent) and between Si and Li atoms (ionic). However, as the top slabs are amorphous and the atoms are randomly distributed, it is hard to draw conclusions about a cross-section going through the center of ions to show the nature of the bonds in the 2D map. Nevertheless, it is still clear that in the bulk the covalent Si−Si bonds are replaced with ionic Li−Si bonds with increasing Li concentration in agreement with Shenoy et al.24 More importantly the interface bonding also changes from

fixed Li content. According to Wang et al.,46 although lithiation induces expansion dominantly in the vertical direction, the electrode expands radially (by 20%) as well. Clearly, the vertical expansion is a result of the electrode’s architecture, that is, the Si disk46 (square island27,44) is not confined along the z-direction. More importantly, the reported degree of expansion in ref 45 is in excellent agreement with previous measurements on square islands of Si on Ti current collector.27,45 These findings suggest that there is significant lateral expansion of the lithiated Si film as a result of the sliding of the interface, which is further supported by the our DFT calculated small value of the critical shear strength. Bonding Nature at the Interface. The reason for the weakened a-Si/Cu interface is due to the interfacial bonding 4765

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value of 0.98.50 The comparison of the electronegativity of these elements gives a qualitative indication of the magnitude of the relative differences in bond energies: Although in the bulk a-LixSi structure Li donated almost all its +1 valence electrons to Si, in the presence of Cu it has to redistribute the charge among bonds with both Cu and Si. Since the Cu substrate is conductive, the excess electrons will localize at the Cu surface and attract the positively charged Li ions. As Li content increases, we find a rise in excess negative charges on the Cu current collector, responsible to more attraction at the interface. Eventually, this increase (see Table 4) is responsible for Li segregation at the LixSi/Cu interface: the electrons on Si are saturated with ∼4 excess electrons from Li in bulk Li15Si4; however if each Li donates fewer electrons to Si near the Si/Cu interface, Si can coordinate with more Li ions, leading to a higher Li/Si ratio near the interface. The charge redistribution at the LixSi/Cu interface is very similar to that observed by Chou and Hwang51 at the LixSi/graphene interface, where the graphene layer becomes negatively charged and excess Li cations accumulates at the LixSi/graphene interface. We expect similar charge redistribution at the interface of LixSi and any other metal current collector, such as Si/Ti or Si/stainless steel. As the electrons in metals are not localized, but distributed homogenously and shared by all the atoms (electron cloud), a cleaved metallic surface would attract the Li charges to saturate its negative surplus. As the interface bonding changes from covalent at a-Si/Cu interface to metallic at the a-Li15Si4/Cu interface, this leads to reduction of the adhesion strength between Si and Cu discussed in the Ideal Work of Separation at the Interface section. Due to the directionality of the covalent Si−Cu bonding at the interface, breaking and forming Si−Cu bonds will cause energy peaks and valleys during sliding, as seen in the Wsep profile. On the other hand, for the more distributed metallic bonds, especially for incommensurate and disordered interfaces, the atomic interaction peaks and valleys are mostly canceled, resulting in very small critical shear stress. Thus, as Li concentration increases and its presence becomes predominant at the interface, the sliding becomes almost frictionless. Similar frictionless interfaces have been observed in atomically disordered Ni/Ni interfaces.52 Summary. In summary, we have performed AIMD and DFT simulations to study the effect of lithiation on the Si/Cu interface in Si anodes. Our results suggest more than 20% Li segregation at the interface with Cu, in good agreement with TOF-SIMS elemental depth profile measurements. We find that increasing Li concentration at the a-LixSi/Cu interface can reduce the work of separation Wsep by 16%, and the sliding strength by an order of magnitude (from 0.287 GPa at a-LiSi2/ Cu to 0.034 GPa at a-Li15Si4/Cu). This finding supports previous experimental work, which has suggested that the segregation of Li atoms in the interfacial zone is crucial for failure due to loss of electrical contact between the active material and current collector.5,26 The interfacial bonding analysis further revealed that the reduced adhesion strength of highly lithiated interfaces stems from the change in the bonding nature of the interface from covalent to metallic. More importantly, as the bonding at the interface changes from covalent Si−Cu to nondirectional metallic Li−Cu, breaking and forming bonds during sliding significantly reduces the energy difference between peaks and valleys, resulting in small critical shear stress that allows for almost frictionless sliding of the interface. Our findings provide a foundation for developing

Figure 5. ELF of LixSi/Cu structures (a). Red color represents covalent, yellow ionic, and green metallic bonding. As Li increases, there is an increase in the population of ionic Li−Si bonds in agreement with ref 24. (b) Absolute value of net charge, |qnet|, on Cu substrate. As Li concentration increases, its presence becomes predominant at the interface and the net charge on Cu increases.

mainly covalent bonds (Si−Cu) to more metallic at high Li concentration. To study the collective effect of lithiation at the interface, we also performed Bader analysis. Bader uses the so-called “zero flux surfaces” to divide atoms and defines as a zero flux surface as a 2-D surface on which the charge density is at a minimum perpendicular to the surface.49 Variation of the total electron charge on Cu substrate with lithiation is presented in Table 4 Table 4. Net Charge on the Cu Substrate Computed from the PAW-PBE Calculations Using Bader Analysisa x in a-LixSi

y = x/(1 + x)

total net charge on Cu, qnet

0 0.5 1 1.71 3.75 ∞

0 0.33 0.5 0.63 0.78 1

−0.61 −1.39 −2.72 −3.21 −4.47 −6.46

a

The calculations take into consideration both core and valence electrons.

and Figure 5b, indicating an increase in the charge on the Cu substrate with Li concentration. The results suggest that, in the presence of the Cu substrate, Li becomes an electron donor for both Cu and Si (instead of donating all its electrons to bulk Si). Thus, fewer electrons are donated to Si compared with the net amount of electrons donated to bulk a-LixSi, indicating that the Li−Si bond becomes weaker close to the a-LixSi/Cu interface. This finding is not surprising, since both Cu and Si demonstrate electronegativity values of 1.9, whereas Li has a 4766

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(14) Magasinski, A.; et al. High-performance lithium-ion anodes using a hierarchical bottom-up approach. Nat. Mater. 2010, 9 (4), 353−358. (15) Xia, S.; et al. Strength characterization of Al/Si interfaces: A hybrid method of nanoindentation and finite element analysis. Acta Mater. 2009, 57 (3), 695−707. (16) Lane, M. Interface fracture. Annu. Rev. Mater. Res. 2003, 33, 29− 54. (17) Martin, L.; et al. First principles calculations of solid-solid interfaces: an application to conversion materials for lithium-ion batteries. J. Mater. Chem. 2012, 22 (41), 22063−22071. (18) Liao, H.; et al. Interfacial Mechanics of Carbon Nanotube@ Amorphous-Si Coaxial Nanostructures. Adv. Mater. 2011, 23 (37), 4318−4322. (19) Howe, J. Y.; et al. Improving microstructure of silicon/carbon nanofiber composites as a Li battery anode. J. Power Sources 2013, 221, 455−461. (20) Magasinski, A.; et al. Toward Efficient Binders for Li-Ion Battery Si-Based Anodes: Polyacrylic Acid. ACS Appl. Mater. Interfaces 2010, 2 (11), 3004−3010. (21) Sun, C.-F.; et al. A beaded-string silicon anode. ACS Nano 2013, 7 (3), 2717−24. (22) Liu, G.; et al. Polymers with Tailored Electronic Structure for High Capacity Lithium Battery Electrodes. Adv. Mater. 2011, 23 (40), 4679−4683. (23) Qi, Y.; et al. Threefold Increase in the Young’s Modulus of Graphite Negative Electrode during Lithium Intercalation. J. Electrochem. Soc. 2010, 157 (5), A558−A566. (24) Shenoy, V. B.; Johari, P.; Qi, Y. Elastic softening of amorphous and crystalline Li-Si Phases with increasing Li concentration: A firstprinciples study. J. Power Sources 2010, 195 (19), 6825−6830. (25) Wang, X. G.; Smith, J. R. Si/Cu interface structure and adhesion. Phys. Rev. Lett. 2005, 95, 15. (26) Maranchi, J. P.; et al. Interfacial properties of the a-Si/Cu: active-inactive thin-film anode system for lithium-ion batteries. J. Electrochem. Soc. 2006, 153 (6), A1246−A1253. (27) Haftbaradaran, H.; et al. Method to deduce the critical size for interfacial delamination of patterned electrode structures and application to lithiation of thin-film silicon islands. J. Power Sources 2012, 206, 357−366. (28) Kresse, G.; Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comput. Mater. Sci. 1996, 6 (1), 15−50. (29) Kresse, G.; Furthmuller, J. Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys. Rev. B 1996, 54 (16), 11169−11186. (30) Balke, N.; et al. Real Space Mapping of Li-Ion Transport in Amorphous Si Anodes with Nanometer Resolution. Nano Lett. 2010, 10 (9), 3420−3425. (31) Johari, P.; Qi, Y.; Shenoy, V. B. The Mixing Mechanism during Lithiation of Si Negative Electrode in Li-Ion Batteries: An Ab Initio Molecular Dynamics Study. Nano Lett. 2011, 11 (12), 5494−5500. (32) Green, M.; et al. Structured silicon anodes for lithium battery applications. Electrochem. Solid State Lett. 2003, 6 (5), A75−A79. (33) Beattie, S. D.; et al. Si electrodes for li-ion batteries - A new way to look at an old problem. J. Electrochem. Soc. 2008, 155 (2), A158− A163. (34) Chou, C.-Y.; Hwang, G. S. Surface effects on the structure and lithium behavior in lithiated silicon: A first principles study. Surf. Sci. 2013, 612, 16−23. (35) Kresse, G.; Joubert, D. From ultrasoft pseudopotentials to the projector augmented-wave method. Phys. Rev. B 1999, 59 (3), 1758− 1775. (36) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77 (18), 3865− 3868. (37) Feynman, R. P. Forces in molecules. Phys. Rev. 1939, 56 (4), 340−343.

quantitative models for failure and detachment of the anode− current collector interface and for subsequent development of flaw-tolerant anode architectures.

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ASSOCIATED CONTENT

* Supporting Information S

Surface energy calculation details and normalized surface energies (Figure S1). This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Authors

*E-mail: [email protected]. *E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We gratefully acknowledge the support by the GM-Brown Collaborative Research Laboratory on Computational Materials Science, the National Science Foundation, the Department of Energy and the Assistant Secretary for Energy Efficiency and Renewable Energy (Office of Vehicle Technologies of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231, Subcontract No. 7056410) under the Batteries for Advanced Transportation Technologies (BATT) Program.

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