Structural transformation and embrittlement during lithiation and delithiation cycles in an amorphous silicon electrode

Acta Materialia 175 (2019) 11e20

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Structural transformation and embrittlement during lithiation and delithiation cycles in an amorphous silicon electrode Swastik Basu a, Nikhil Koratkar a, b, Yunfeng Shi b, * a b

Department of Mechanical, Aerospace and Nuclear Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA Department of Materials Science and Engineering, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

a r t i c l e i n f o

a b s t r a c t

Article history: Received 2 April 2019 Received in revised form 22 May 2019 Accepted 26 May 2019 Available online 29 May 2019

Silicon shows potential as an anode material in lithium ion batteries due to its high specific capacity, yet its considerable volume expansion during lithiation leads to fracture and pulverization. Unfortunately, neither the atomic-level structural evolution, nor the mechanical behavior of the anode during lithiation and delithiation cycles is well understood. Interestingly, the lithiation process of a-Si provides an interesting continuum from open-structured network glass to densely-packed atomic glass, which could be used to obtain useful insights regarding commonalities in glasses. Here atomic level simulation has been used to investigate one cycle of lithiation and delithiation of amorphous silicon electrode, using Grand Canonical Monte Carlo (GCMC) and molecular dynamics (MD) simulations. The atomic level structural transformation and damage accumulation of the anode during cycling has been systematically analyzed, as well as their mechanical responses in compact tension tests. There appears to be a ductilebrittle-ductile transition for the amorphous silicon anode during both the lithiation and delithiation cycle. In other words, amorphous silicon is particularly vulnerable at intermediate lithiation. The fracture behavior of lithiated silicon was found to correlate to the Poisson's ratio, due to variations in bond covalency and structural disorder. © 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

Keywords: Lithiation Delithiation Silicon Molecular dynamics Reactive force field Disorder accumulation Ductility Embrittlement Transformation

1. Introduction Rechargeable lithium ion batteries are integral to the portable, entertainment, computing, and telecommunication equipment required by today's information-rich, mobile society [1,2]. With rapid growth in the energy storage industry, lithium (Li) - ion cell production has gone up from ~26 GWh in 2011 to over ~61 GWh in 2015, and is expected to grow to ~125 GWh by 2020 [3]. In a lithium ion battery, the primary components are the anode, cathode and electrolyte. The cathode can be layered oxides such as LiCoO2 , transition metal phosphates such as LiFePO4 , or spinels such as LiMn2 O4 [4]. The liquid electrolyte generally consists of compounds such as LiBF4 , LiPF6 or LiClO4, in an organic solvent. Conventional lithium-ion batteries employ graphite-based anodes. The combined physical, chemical, electronic, and electrochemical attributes of the cathode, anode and the electrolyte affects the voltage, capacity, life, and safety of a Li ion battery [5]. Being an important material for solid-state electronics, silicon

* Corresponding author. E-mail address: [email protected] (Y. Shi). https://doi.org/10.1016/j.actamat.2019.05.055 1359-6454/© 2019 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

finds popular application in nano-electromechanical systems [6]. It is an attractive anode material for lithium ion batteries, as it has the highest known theoretical charge capacity (4200 mA h/g), which is more than ten times higher than existing graphite anodes, and much larger than various nitride and oxide materials [7]. However, silicon anodes have limited applications since silicon experiences a 400% volume expansion upon insertion of lithium, leading to cracking and pulverization of the electrode, unstable solid electrolyte interphase (SEI) formation, and consequent capacity deterioration [8]. Over the years, considerable amount of experimental work has been devoted in studying the lithium insertion process [9e19]. In addition, the lithiation processes of both crystalline silicon [20e24] and amorphous silicon [15,25e30] have been investigated theoretically. Aside from structural changes, the deformation and fracture behavior during the insertion of lithium into silicon electrodes have also been investigated [31e37]. Kushima, Huang and Li reported in situ tensile strength measurements observing a ~5-fold decrease in tensile strength and a ~2-fold increase in fracture strength from pristine silicon to lithiated Li15 Si4 alloy [35]. A number of

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experimental and computational studies have indicated that silicon electrodes experience plastic deformation upon lithiation [12,24,27,28,38e41], which could affect the fracture behaviors. In early experimental results, Pharr reported that the measured fracture energy of lithiated silicon electrodes is essentially independent of the concentration of lithium [21]. However subsequent experimental and computational studies concluded that the lithiation-induced plasticity of Lix Si alloys results in high damage tolerance, and first principle calculations were used to try uncover the underlying mechanisms of brittle-to-ductile (BTD) transition observed in Lix Si electrodes [42,43]. Xueju Wang and co-workers used experiments and modelling to shed light on the high damage tolerance of lithiated Si electrodes, with nanoindentation experiments showing a BTD transition above a Li/Si ratio of 1.5. MD simulations employed for atomistic modelling of fracture in LixSi from melt-quench were limited to two compositions (Li/Si ratios of 0.5 and 2.5), attributing the brittle-to-ductile transition to decreasing fraction of covalent Si bonding and increase in delocalized metallic Li bonding [42]. In another interesting work, Haoran Wang studied four different ratios of Li to Si and provided evidence that delayed nucleation and coalescence of nanopores plays an important role in the brittle-to-ductile transition, from craze plasticity induced brittle failure at Li/Si ¼ 0.5 to nanopore nucleation and extensive ductility at Li/Si ¼ 3.75 [43]. Wang also carried out MD simulations of fracture on three compositions (LiSi2, LiSi, and Li15Si4) to demonstrate BTD transition and higher damage tolerance with increasing lithium content [44]. Bin Ding studied crack propagation and fracture on five different amorphous lithium-silicon compositions to demonstrate spontaneous nucleation of nanovoids near crack-tip at low lithium concentrations and a transition in fracture mechanism with extensive shear banding near crack-tip at higher lithium content [45]. In the above fracture MD simulations, the samples were prepared via a melting-andquenching process. To this end, the atomic structure of meltquench samples maybe significantly different from LixSi samples via lithiation/delithiation processes even with the same composition. Ekin Cubuk and Efthimios Kaxiras used first principles calculations to explore the structural transformation in lithiated amorphous silicon [26]. The works of Xueju Wang, Haoran Wang and Cubuk collectively point towards the existence of two distinct phases involved in the lithiation of a-Si. All of them observe a welldefined network of covalently bonded Si atoms in the brittle regime, and the breaking of the Si covalent bonds during tensile loading leads to sudden coalescence of neighboring nanopores, causing the failure to be brittle-like. On other hand in the ductile regime at higher lithiation, the SieSi network is highly dissolved, leading to a stable growth of nanopores. Recent theoretical work in understanding the BTD transition in metallic and oxide glasses have established the correlation between intrinsic ductility and bonding as well as structural disorder [46]. Interestingly, the BTD transition is also correlated to the Poisson's ratio, echoing empirical experimental observations [47,48]. The approach of resorting the BTD transition to characteristics of the glassy solids could in principle be applied in silicon anode to provide mechanistic understanding of its fracture behavior. In addition, the lithiation process of a-Si provides an interesting continuum from open-structured network glass to densely-packed atomic glass. Here, we investigate one cycle of lithiation and delithiation of aSi using molecular dynamics simulations. The structural and bonding variation was monitored during the lithiation-delithiation cycle. Furthermore, compact tension tests have been conducted on the anode samples over a large range of Li/Si ratios to study the fracture behavior systematically over the simulated lithiation/ delithiation process, as opposed to lithium-silicon samples

prepared via melt-quench [42,44,45]. A ductile-brittle-ductile transition was observed during lithiation which reverses during delithiation. Our work shows that amorphous silicon (a-Si) is particularly vulnerable to fracture at intermediate stages of lithiation. We have established the link between the structural disorder and bonding covalency to fracture behavior of the a-Si anode. These atomistic insights on the embrittlement of a-Si anode during lithiation, and the possibility of a ductile regime could help unveil new approaches to avoid a-Si fracture and pulverization. 2. Simulation methodology To describe the LieSi system in this simulation study, we use the ReaxFF LieSi developed by Fan et al. [29] This potential provides accurate predictions for a set of fundamental properties of Lix Si alloys, such as Li composition dependent elastic modulus, volume expansion and open-cell voltage [49]. The ReaxFF parameters are optimized to reproduce heat of formation and lattice parameters of selected condensed phases to values within acceptable range of previous DFT calculations, over a wide range of composition for lithiated silicon. We perform MD simulation to investigate disorder accumulation during lithiation and delithiation cycles in an amorphous silicon (a-Si) electrode. The atomic structure of a-Si is obtained by melting diamond cubic silicon crystal, followed by quenching of the liquid to 300 K (room temperature) within a duration of 100 ps. We have used the Grand Canonical Monte Carlo (GCMC) method in LAMMPS [50] to carry out probability-driven exchange of lithium atoms with an ideal gas reservoir at the specified temperature of 300 K and at a given chemical potential. We have also created meltquench LixSi samples by quenching an equilibrated LixSi liquid from 4000 K to 300 K in 400 ps. This will be used to compare LixSi samples prepared using different procedures. For all the simulations, Newton's equations of motion were numerically integrated using the velocity-Verlet [51] algorithm with a time step of 0.5 fs. The temperature and pressure were controlled using NoseeHoover [52,53] thermostat and barostat, respectively. Periodic boundary conditions (PBC) were applied in all three directions. OVITO [54] visualization software was used to generate simulation snapshots. We study the evolution of several structural and mechanical characteristics of the system and its components in order to understand, at an atomic level, the disorder accumulation over the course of cycling of an a-Si electrode. ReaxFF being a very costly potential, smaller, periodic samples have been used to analyze the trends of bonding and structure characteristics over lithiation and delithiation, in order to study their link with the BTD transformation characteristics. For the mechanical tests, much larger slab samples ranging from 20 nm to 30 nm in length and width have been used to minimize the risk of size effect influencing our observations of BTD transitions. 3. Results and discussions 3.1. Accumulation of atomic level disorder Amorphous silicon undergoes significant expansion during lithiation, as well as contraction during delithiation. The final volume after one charging-discharging cycle is slightly higher than the initial system (density reduces by 4%). The volume and density changes have been found to be in agreement with previous studies [29]. An important structural signature which measures the degree of short range disorder over course ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi of cycling is the SieSieSi bond qthe

angle deviation (AD ¼ ðq  q0 Þ2 ) from the perfect tetrahedral angle q0 (Fig. 1) [46]. Apparently, the higher the AD, the more

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Fig. 1. Bond angle deviation as a function of Li =Si ratio.

disordered the amorphous silicon is, when compared to ideal diamond cubic silicon crystalline structure. As shown in Fig. 1, during lithiation, AD initially reduces then slightly increases. During delithiation, AD decreases slightly then increases until delithiation process completes. Upon one cycle of lithiation-delithiation, a-Si becomes more disordered, i.e., damage accumulation occurs as observed from the irreversibility of bond angle deviation. Irreversible rate-dependent structural change in the form of

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pore structure evolution has also been observed by Kim and coworkers [55]. However, the irreversibility in that work is accompanied by significant reduction in density (probably related to the delithiation rate, temperature, sample geometry, and how the driving force for lithiation/delithiation is implemented). In comparison, the irreversibility in our simulation is best characterized by angular deviation function, with only a slight decrease in density without pore formation. To further examine disorder accumulation over the lithiation and delithiation cycle we analyze the medium range order of the structure. As a step towards understanding the medium range order of evolution of amorphous silicon structure upon lithiation, we have carried out rings statistics analysis on silicon network and cluster statistics analysis for lithium in the silicon network (Fig. 2). We have implemented the ring counting method with the shortest path criteria for primitive rings [56,57], while for the cluster analysis two lithium atoms are considered to belong to the same cluster if the separation is less than 0.25 nm. It appears that 5, 6 and 7 membered rings dominate a-Si initially, as shown in Fig. 2(a) and (b). Both larger rings and smaller rings form during the course of lithiation. During delithiation, both larger rings and smaller rings reduce, yet cannot completely recover at zero lithiation, as can be seen in Fig. 3 which tracks the progression of hexagon rings of silicon in the structure over cycling. Upon a lithiation-delithiation cycle, the population of hexagon rings reduces by almost 50% as shown in Fig. 5(a), while that of pentagon rings increases. Larger rings can also be found, which are absent initially. The cluster distribution provides important insights into whether lithium atom tends to be adjacent to existing lithium cluster during lithiation,

Fig. 2. (a, b): Rings statistics analysis of Si during lithiation and delithiation. The Y-axis scales locate on both side of the graph for clarity. (c, d): Cluster statistics analysis of Li atoms during lithiation and delithiation. The extent of lithiation and delithiation is denoted by x (LixSi). L refers to the number of lithium atoms belonging to the largest cluster.

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Fig. 3. Atomic configuration showing the progression of six-membered Si rings over the course of lithiation at Li/Si ratios of 0.5 (a), 2.0 (b), and 3.0 (c), and delithiation at Li/Si ratios of 3.0 (d), 2.0 (e), and 0.5 (f). In a network, a series of nodes (here atoms) connected sequentially without overlap is called a path, and a closed path is called a ring. The red line joining the Si atoms (enlarged in inset) represents the connection (here bonds) between the nodes forming hexagon rings. The radial cutoff criterion for the bonds is taken as 3 Å. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

Fig. 4. Atomic configuration showing the progression of the largest-sized Li clusters in Si over the course of lithiation at Li/Si ratios of 0.5 (a), 2.0 (b), and 3.0 (c); and delithiation at Li/Si ratios of 3.0 (d), 2.0 (e), and 0.5 (f). The blue atoms represent members of the largest Li cluster remaining in the system. The radial cutoff criterion for the cluster analysis is taken to be 2.5 Å. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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Fig. 5. Number of six-membered rings (a) and size of the largest Li clusters (b) as a function of Li =Si ratio over a course of lithiation and delithiation. The total number of Si atoms in the system remains constant over the addition of Li, hence the total number of Li atoms increases linearly with respect to x as shown by the black line.

Fig. 6. Local concentration distribution of Li in Lix Si at different Li/Si ratios (x ¼ Li/Si ratio) over the course of lithiation and delithiation. The information regarding the local concentrations has been obtained by dividing the simulation cell length into 60 bins with equal size and calculating the number density of Li corresponding to the specific bins. The concentration is averaged over 5 samples and an error bar has been included.

and whether isolated lithium atoms are more unstable during delithiation. As shown in Fig. 2(c) and (d), the lithium atoms tend to form a large cluster very quickly during lithiation. Therefore, incoming lithium atoms tend to locate close to existing lithium clusters in the anode. During delithiation, the large lithium cluster breaks down quickly into smaller clusters, suggesting preferential removal of lithium within the large clusters, instead of isolated lithium atoms. This can be seen from images tracking the largestsized lithium clusters in Fig. 4. This is represented quantitatively in Fig. 5(b), which shows the hysteresis of size of the largest lithium cluster during a lithiation-delithiation cycle. Between the lithiation ratios (Li/Si) of 1.5 and 3.5, the size of the largest cluster contains around 90% of the lithium atoms in the system during lithiation. However, during delithiation, greater number of smaller clusters form between Li/Si ratio of 2 and 0.5, with the size of the largest cluster not containing more than around 15% of the lithium atoms in the system. We further note that even when the lithium atoms form a large cluster, the successive stages of lithiation and delithiation show uniform distribution of local Li concentration in Lix Si (Fig. 6), in keeping with the previous studies on concentration dependent lithiation dynamics [58]. Thus we understand that the large Li cluster percolates throughout the system, keeping the local Li concentration uniform instead of segregation as Li metal. On the last note regarding the structure of LixSi, we compared

Fig. 7. Ring statistics of three samples of the same composition of Li0.5Si: during lithiation (top, red), during delithiation (middle, green), and from melt-quench (bottom, blue). It is clear that samples via lithiation/delithiation processes are structurally very different from samples made by melt-quench. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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Fig. 8. True strain-true stress curves for the uniaxial tensile testing of the notched samples during lithiation and delithiation are shown in (a) and (b) respectively.

the lithiated and delithiated Li0.5Si samples with Li0.5Si from meltquench. Fig. 7 shows that there exists significant structural differences among the above three samples in terms of ring statistics of silicon, despite with the same composition. Six-member rings dominate the sample from lithiation, while five-member rings dominate the samples from dethiation and the melt-quench sample. The sample from delithiation has much less five-member rings than the melt-quench sample, and also contain more large rings. This result indicates the necessity of preparing LixSi using simulated lithiation/delithiation processes in studying the structure or mechanical responses of silicon anode materials in lithium ion batteries. 3.2. Mechanical properties During various stages of lithiation and delithiation, the lithiated silicon systems are subjected to room temperature relaxation, and then to various mechanical tests as shown below. The Young's modulus calculated from uniaxial tensile test simulation is found to decrease as lithiation proceeds, and then increase during subsequent delithiation, with a net reduction of around 28% due to cycle damage. The Young's modulus values obtained for the different Lix Si compounds are found to be comparable to previous results [29]. The Poisson's ratio has also been calculated from constrained tensile tests with zero transverse strain. The Poisson's ratio measured here is generally higher than the experimental values, probably due to a combination of factors such as the limited time duration in simulations and the limitation of the ReaxFF potential. However, we remain interested in the trend for the change in the elastic constants. Aside from elastic properties, we also carried out compact tension tests for lithiated silicon, with the presence of a notch in order to observe how the glassy sample resists crack propagation. The mechanical response of notched lithiated silicon sample provides a qualitative description of its ductility. The notched samples are prepared by replicating the lithiated silicon samples 8 times along X- and Z-directions such that the final slab has a length of roughly 20 nme30 nm (over the range of lithium content) with ~100,000 atoms. A notch is created at the center of the slab throughout its thickness (Y-direction). The slab is subjected to relaxation prior to mechanical tests. Tension is then applied along the Z-direction while zero stress is maintained for the other transverse directions. The temperature is maintained at 300 K. The strain rate is a constant of 5ns1 for all the samples. The stress-strain behavior of the notched samples during lithiation and delithiation are shown in Fig. 8(a and b). The original a-Si

features pronounced yield, followed by a stress-drop during subsequent global plastic flow. It should be noted that the relatively ductile behavior for pure a-Si might be due to the small crack size used here. As the same crack size is used for all LixSi samples, we can infer the toughening or embrittlement effect during lithiation or delithiation process, based on how the sample resists the growth of the same crack. As lithiation proceeds, the lithiated silicon becomes brittle as shown both in Figs. 8(a) and Figure 9. Crack quickly propagates causing sample failure within 30% of strain. As lithiation ratio x exceeds 2, the sample becomes more ductile again. The samples with the highest lithiation ratio exhibit elastic-perfect plastic behavior. The delithiation process reverses the lithiation process, yet with different transitions in terms of the lithiation ratio. At the end of the lithiation-delithiation cycle, the a-Si sample recovers ductility, yet with a lower yield point. 3.3. Bonding characteristics According to Ref. [46], both the glassy structure and bonding covalency affect the intrinsic ductility of glassy solids. In the context of amorphous silicon, the bonding covalency refers to the strength of the angular constraints of the interatomic potential, which in turn controls the coordination number. It should be noted that the bonding covalency here does not characterize the degree of electron sharing aspect as in the traditional chemistry. One can potentially design a common potential in the Stillinger-Weber form for carbon group elements with diminishing angular constraints from carbon to lead, thus favoring close-packing over fourcoordinated open-structure. In this way, the preferred crystal structure changes from diamond cubic for carbon, silicon, germanium, alpha-tin, to body-centered tetragonal for beta-tin, then to hexagonally close-packed lead. Thus, the transition from prototypical covalent solids to metallic solids can be controlled by the strength of the angular constraint. It has been shown that strong angular constraint leads to embrittlement [47]. For the LieSi ReaxFF potential used here, the lithiated silicon system transits from a highly covalent (open structure) system to a less covalent (dense structure) one. Therefore, the bonding covalency during the lithiation-delithiation cycle needs to be characterized carefully. Here, we use the concept of total bond order (TBO) to quantify the overall bonding characteristics of the lithiated silicon system. For bond-order potentials such as ReaxFF, bond order plays a central role in controlling bond length and bond energy, as well as creating or breaking bonds during chemical reactions. In ReaxFF, bond order is defined between a pair of atoms, i.e. for each bond, and TBO of an atom is the sum of the bond orders of all the bonds

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Fig. 9. Deformation distribution morphologies for local shear for compact tension tests of samples with pre-existing cracks. The cutoff radius controls the range of neighbors that are taken into account to compute the deformation gradient tensor of an atom. Here the cutoff radius is taken to be 6 Å.

this atom involves [59]. Therefore, as the coordination number increases, the TBO of each atom increases sublinearly. Fig. 11 shows the TBO during the lithiation-delithiation cycle. The trend of TBO can be largely explained by the number of neighbors shown in

Fig. 10. The averaged TBO for silicon decreases as the number of neighboring silicon decreases, while the averaged TBO for lithium increases as the neighboring lithium increases. Hence, a higher TBO per atom represents higher number of neighbors, more close-

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Fig. 10. XeY denotes the number of nearest neighbor atoms of type Y for atom of type X. The solid line denotes lithiation, while the dashed line stands for delithiation The number of nearest neighbors is expressed as a function of x (Lix Si). As expected, the number of SieSi nearest neighbors decreases and the number of LieLi nearest neighbors increases. The number of nearest neighbors (of both types) of both Si and Li first increases and then saturates, in an observation similar to other first principle calculations [26]. However we see a steady decrease in the corresponding nearest neighbor number for both Li and Si during delithiation, signifying irreversible expansion of the Si network.

packed structure, thus lower bonding covalency. In the limit of very high Li/Si values, high TBO represents metallic bonding. The overall trend of the TBO for the entire system as shown in Fig. 11(c) decreases initially and then increases during lithiation, which is reasonable considering open network structure of amorphous silicon and dense structure of highly lithiated silicon. The TBO reverses the trend during delithiation, which reaches almost the identical value of TBO as the initial a-Si system. The TBO analysis above characterizes the transition from covalent bonding to metallic bonding during lithiation process, and vice versa. It should be noted that, LieSi bonding indeed has some ionic characteristics as observed from the atomic charge analysis in Fig. 11(d), where we see a gradual accumulation of charge on Si donated by Li. The general trend is in agreement with previous Bader charge analysis done by Chevrier [60]. However, the consideration of ionic bonding in LieSi, in addition to covalent bonding and metallic bonding, complicates the analysis on how bonding affects mechanical properties. Given the fact that LieSi bonding is negligible at both x ¼ 0 and x ¼ 3.5, we simplify the bonding characteristics of the LieSi system during lithiation/delithiation from covalent (SieSi bonding dominate at x ¼ 0) to metallic (LieLi bonding dominates at x ¼ 3.5). 3.4. Correlation from structure-bonding to mechanical properties We have reported the mechanical properties of LieSi during lithiation and delithiation, as well as the variation in structure and

Fig. 11. Total bond order for silicon atoms, total bond order for lithium atoms, and averaged total bond order for all atoms during lithiation and delithiation are plotted in (a), (b) and (c) respectively. (d) shows the average charge in e of the Li and Si atoms (grouped according to the number of neighboring Si atoms) at different Li/Si phases over the course of lithiation. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

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becomes more disordered, both of which point to toughening resulting in the BTD transition near x ¼ 2 to 2.5. The same analysis works well for the delithiation process. In this way, we can understand the BTD transition from a structural and bonding point of view. 4. Conclusions

Fig. 12. Plots for the Poisson's ratio, bond order and bond angle deviation during lithiation (Li/Si ratio x increases) then delithiation (x decreases). The red (green) box denotes the regions in which the Poisson's ratio, the bond order or the bond angle deviation increases (decreases). It can be seen that the embrittlement (toughening) occurs when both the total bond order and the bond angle deviation decrease (increase), accompanied with a reduction (an increase) in the Poisson's ratio. (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.)

bonding in the preceding sections. In this section, we wish to correlate the observed BTD transition to structure and bonding, as well as to the Poisson's ratio originally proposed by Ref. [47]. It should be noted that the BTD transition is reflected by the compact tension tests, instead of directly measuring the fracture energy which is difficult to accomplish in MD simulations [61]. Let us examine the BTD transition and the variation in the Poisson's ratio. It is clear that generally ductile samples exhibit higher values in the Poisson's ratio, and vice versa. In our simulations, all glassy samples (except one) lower than 0.4 Poisson's ratio during the lithiation-delithiation cycle exhibit brittle behavior, while those higher than 0.4 exhibit ductile behavior-as observed from their fracture behavior in the presence of a crack. It appears that the critical Poisson's ratio for LieSi is around 0.4, which is different from 0.31 to 0.32 in Ref. [47]. As shown in Ref. [46], the critical Poisson's ratio is indeed system-dependent. Next, we will investigate how the bonding and structural characteristics control the ductility of the glassy sample. The variation of TBO indicates that the interatomic bonding first becomes more covalent, then becomes more metallic at high level of lithiation during the lithiation process, and then reverses during the delithiation process. On the other hand, the bond angle deviation curve shows the structural disorder first decreases, then increases during lithiation, then decreases and further increases during delithiation, resulting in permanent structural damage. As both structure and bonding affect the mechanical properties, the correlation to the ductility must be made together (Fig. 12). For clarity, the regimes of embrittlement (decrease in the Poisson's ratio, TBO, and the bond angle deviation) are colored red, while the regimes of toughening (increase in the Poisson's ratio, TBO, and the bond angle deviation) are colored green. For instance, the initial lithiation from x ¼ 0 to x ¼ 0.5 leads to significant embrittlement, as the bonding covalency increases and the structure becomes more ordered. However, from x ¼ 0.5 to x ¼ 1.5, the bonding and the structure exhibit opposite trend, i.e., working against each other. Therefore, the glassy solid remains brittle, with roughly a constant Poisson's ratio. From x ¼ 1.5 to x ¼ 3.5, bonding covalency decreases while the structure

In summary, lithiation and delithiation of a-Si has been studied in detail for an atomic level understanding of damage accumulation and the mechanistic underpinnings of the BTD transformation during the process. Our study points to the key roles played by bonding covalency (reflected by the total bond order) and structural disorder (reflected by the bond angle deviation) in giving rise to brittle and ductile regimes over the course of cycling a-Si electrode. There also appears to be a correlation between the fracture behavior and the Poisson's ratio, consistent with prior experimental and computational observations. In addition, our simulation shows that a-Si in the intermediate lithiation regime is the most brittle, which should be either mitigated by charging/discharging schedule or avoided. Acknowledgments We gratefully acknowledge the support from the National Science Foundation under Grant No. 1510828. We appreciate the generous help from Dr. Van Duin from Pennsylvania State University for the SieLi ReaxFF potential. We are also thankful for stimulating discussions with Dr. Liping Huang, Shravan Suresh, Lu Li, Siddharth Sundararaman, Yanming Zhang at Rensselaer. The MD simulations were carried out in the Center for Computational Innovations (CCI) at Rensselaer. References [1] J.-M. Tarascon, M. Armand, Issues and challenges facing rechargeable lithium batteries, Nature 414 (2001) 359e367. [2] K. Takada, Progress and prospective of solid-state lithium batteries, Acta Mater. 61 (2013) 759e770. [3] Lithium-ion Battery Market - Global Industry Analysis, Size, Share, Growth, Trends and Forecast 2016 - 2024, Transpar. Mark. Rep., 2016, pp. 1e142. [4] M.S. Whittingham, Lithium batteries and cathode materials, Chem. Rev. 104 (2004) 4271e4301. [5] C. Liu, Z.G. Neale, G. Cao, Understanding electrochemical potentials of cathode materials in rechargeable batteries, Mater. Today 19 (2016) 109e123. [6] H. Zhao, N.R. Aluru, Molecular dynamics simulation of bulk silicon under strain, Interact. Multiscale Mech. 1 (2008) 303e315. [7] C.K. Chan, H. Peng, G. Liu, K. McIlwrath, X.F. Zhang, R. a Huggins, Y. Cui, Highperformance lithium battery anodes using silicon nanowires, Nat. Nanotechnol. 3 (2008) 31e35. [8] U. Kasavajjula, C. Wang, A.J. Appleby, Nano- and bulk-silicon-based insertion anodes for lithium-ion secondary cells, J. Power Sources 163 (2007) 1003e1039. [9] M.N. Obrovac, L. Christensen, Structural changes in silicon anodes during lithium insertion/extraction, Electrochem. Solid State Lett. 7 (2004) A93eA96. c, J.M. Tarascon, C.P. Grey, [10] B. Key, R. Bhattacharyya, M. Morcrette, V. Sezne Real-time NMR investigations of structural changes in silicon electrodes for lithium-ion batteries, J. Am. Chem. Soc. 131 (2009) 9239e9249. [11] X.H. Liu, J.W. Wang, S. Huang, F. Fan, X. Huang, Y. Liu, S. Krylyuk, J. Yoo, S. a. Dayeh, A.V. Davydov, S.X. Mao, S.T. Picraux, S. Zhang, J. Li, T. Zhu, J.Y. Huang, In situ atomic-scale imaging of electrochemical lithiation in silicon, Nat. Nanotechnol. 7 (2012) 749e756. [12] V.A. Sethuraman, M.J. Chon, M. Shimshak, V. Srinivasan, P.R. Guduru, In situ measurements of stress evolution in silicon thin films during electrochemical lithiation and delithiation, J. Power Sources 195 (2010) 5062e5066. [13] W. Wan, Q. Zhang, Y. Cui, E. Wang, First principles study of lithium insertion in bulk silicon, J. Phys. Condens. Matter 22 (2010) 415501. [14] C. Arrouvel, S.C. Parker, M. Saiful Islam, Lithium insertion and transport in the TiO2-B anode material: a computational study, Chem. Mater. 21 (2009) 4778e4783. [15] S. Huang, T. Zhu, Atomistic mechanisms of lithium insertion in amorphous silicon, J. Power Sources 196 (2011) 3664e3668. [16] A. Ostadhossein, E.D. Cubuk, G.A. Tritsaris, E. Kaxiras, S. Zhang, A.C.T. van Duin, Stress effects on the initial lithiation of crystalline silicon nanowires: reactive

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