Lithiation-Assisted Strengthening Effect and Reactive Flow in Bulk and

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Lithiation-Assisted Strengthening Effect and Reactive Flow in Bulk and Nano-Confined Sulfur Cathodes of Lithium-Sulfur Batteries Mingchao Wang, Jingui Yu, and Shangchao Lin J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.7b05446 • Publication Date (Web): 17 Jul 2017 Downloaded from http://pubs.acs.org on July 24, 2017

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The Journal of Physical Chemistry

Lithiation-Assisted Strengthening Effect and Reactive Flow in Bulk and Nano-Confined Sulfur Cathodes of Lithium-Sulfur Batteries

Mingchao Wang, Jingui Yu and Shangchao Lin*

Department of Mechanical Engineering, Materials Science and Engineering Program, FAMUFSU College of Engineering, Florida State University, Tallahassee, Florida 32310, USA

*Corresponding author: E-mail: [email protected] (Prof. Shangchao Lin)

Abstract Lithiation of electrode materials can lead to significant microstructural evolution and changes in their mechanical behaviors in lithium batteries. Lithium-sulfur (Li-S) batteries have recently attracted extensive attention, where carbon matrices have been utilized to retain S content by restricting the dissolution of polysulfide into electrolytes. Here we systematically investigate S cathode upon unconfined and nano-confined lithiation using reactive molecular dynamics simulations. We demonstrate the great ductility of lithiated amorphous S cathode (a-LixS) governed by over-coordination sites, as well as the resulting strengthening effect of aLixS due to the formation of stronger Li-S bonds upon lithiation. Fracture and cavitation studies also indicate the dominant role of shear banding, which is facilitated by overcoordinated S “plastic carriers”, in accommodating the plastic deformation of a-LixS under tensile loading. Based on a chemo-mechanical yield function, we confirm two-dimensionally nano-confined lithiation reaction can facilitate the out-of-plane inelastic deformation (“reactive flow”) of a-LixS at a much lower level of biaxial stress. The atomistic understanding of lithiation behaviors of S cathodes provides fundamental insight into the 1 ACS Paragon Plus Environment


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optimal design of carbon-based S composite cathode with outstanding mechanical integrity, as well as the prediction of lithiation behavior of other electrode materials, such as silicon, metal oxides and graphite.

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INTRODUCTION Rechargeable lithium-ion (Li-ion) batteries have dominated in the battery market for portable electronics1 since their first commercialization in 1990s. However, their limited chargestorage capacity and energy density hinder commercial Li-ion batteries from practical applications in all-electrified vehicles and grid energy storage.2-3 Therefore, it is urgently crucial to develop new electrode materials, especially cathode materials, in battery cells with higher energy densities and longer cycling lifetime. Among those widely-explored cathodes,4 sulfur (S) has attracted increasingly more attention because of its abundance on earth, as well as low cost and high theoretical specific capacity of ~ 1670 mAhg-1, which is more than 5 times higher than those of popular cathodes (i.e., LiCoO2 and LiNiCoAlO2) current commercial Li-ion batteries.4-6 However, the commercialization of Li-S battery is still facing several technical challenges,6 such as the severe volume expansion (~ 80%) during charging/discharging cycles, as well as the polysulfide shuttle (dissolution into the electrolytes) effect in the Li-S battery system which can result in the loss of active materials and low Coulombic (charge) efficiency.7 To address these technical challenges, the most popular strategies nowadays are based on producing carbon-based S composites with favorable structures and properties.8-9 Various nanostructured carbon matrices, such as hollow carbon nanospheres and nanofibers,10-11 as well as graphene and graphene oxide sheets,12-13 have been utilized to sustain S cathode content and enhance the Li-S battery performance (i.e., charging/discharging capacity, cyclability and Coulombic efficiency). However, for such geometrically confined S cathode, the prohibition of free volume expansion by carbon matrices may generate large non-zero inner stress, and result in the breakdown of lithiated S and conductive carbon matrices. Such existing issue in carbon-based S composite cathodes was also extensively discussed by Barai et al., who have developed a lattice spring-based continuum model to study the volume 3 ACS Paragon Plus Environment


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expansion-induced mechanical degradation of carbon matrices and the corresponding effect on battery cell performence.14 Similar lithiation-induced stress has also been confirmed in silicon (Si) anodes, which can lead to small cracks and even fracture (through crack propagation) of the whole anode.15-17 Very recently, Kim et al. reported the first in situ experimental TEM observation of lithiation process of S cathode in direct contact with Li2O/Li electrolyte/anode, both confined within carbon nanotubes (CNTs) which act as cylindrical reaction vessels (as shown in Fig. 1(a)).17 This well-controlled experimental system unravels the reaction mechanism of Li-S electrochemical cells within CNTs and may help to resolve the polysulfide dissolution problem using solid rather than liquid electrolyte. Unfortunately, the lithiation-induced structural and mechanical performance of confined S cathode has not been investigated yet. In order to develop novel S cathodes and Li-S batteries (such as S cathode confined in CNTs), it is therefore necessary to understand their microstructural evolution, deformation, and stress buildup/concentration during both unconfined and confined lithiation. This is particularly true for confined S cathode where polysulfide shuttle effect induced by liquid electrolyte could be greatly reduced and neglected in the present study.


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Figure 1. (a) Schematic illustration and TEM image of nano-confined S cathode in CNT-based reaction vessel samples. Reproduced with permission of Ref.16. Copyright 2015, Wiley-VCH. (b) Schematic illustration of crystal α-phase sulfur (S) cathode, α-S, (b1) before lithiation, (b2) after unconfined lithiation (free volume expansion along all directions) and (b3) after confined lithiation (free volume expansion only along z axis). Atomistic structures of α-S in (b1), and lithiated amorphous LixS system (a-LixS) in (b2)-(b3) are shown next to the corresponding schematics. The purple arrows represent Li insertion along all axes upon (b2) unconfined lithiation and along z-axis upon (b3) confined lithiation. The blue arrows represent geometrical confinement along x and y-axes upon (b3) confined lithiation.

Recently, first-principle calculations have been carried out to study the lithiation behavior of S cathode. For example, it was found that the cyclic (ring) molecular structures of lithium polysulfides, such as Li2S8 and Li2S6, are energetically more stable than linear conformers.18 While for lithium disulfide Li2S2, its monoclinic structure19 is a semiconductor with a band gap of ~ 2.8 eV,20 and elevating temperature can increase the mobility of predominant charge carrier (hole polarons) in crystalline Li2S2 and further improve its electronic conductivity.20 Moreover, the anchoring effect of various two-dimensional materials (oxides, sulfides and chlorides)21 and dual-doped carbon22 were studied to help solve the dissolution problem in S cathode. Owing to the length- and time-scale limitations, however, the simulation cells used in those first-principle calculations cannot represent the realistic S cathode and accurately capture the underlying microstructural evolution and mechanical behavior during lithiation. To overcome the above challenges, molecular dynamics (MD) simulations using reactive force-field (ReaxFF) potentials23-24 are well suited for studying the electrochemical lithiation reaction in S cathode as well as its lithiation-dependent microstructural and mechanical properties.



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With the above in mind, we carry out reactive MD simulations to comprehensively investigate the lithiation-assisted microstructural evolution and mechanical properties of bulk S cathode under different lithiation conditions (Fig. 1(b)), as well as its underlying deformation mechanism (plasticity). The dissolution of certain polysulfide species9 into the electrolytes at the electrode-electrolyte interphase is neglected here to focus on the bulk properties of S cathode upon lithiation when it is in direct contact with solid-state electrolyte. First we demonstrate that lithiated amorphous S cathode, a-LixS (0 < x ≤ 2), possesses great ductility with increasing yield stress as x increases. Such strengthening phenomenon in a-LixS is attributed to the significant bonding network formed during unconfined lithiation. We then explore the fracture mechanics and cavitation behavior of a-LixS. It is found that the plastic deformation, accommodated by shear banding, dominates the ductile deformation of a-LixS, in which over-coordinated S atoms act as “plastic carriers” to facilitate the formation and propagation of shear bands. In addition, a chemo-mechanical yield function is utilized to understand the observed trend of in-plane (x and y-axes) biaxial tensile stress and out-of-plane (z-axis) volume expansion during confined lithiation. It is also confirmed that lithiation reaction can facilitate such plastic flow (volume expansion) of a-LixS at a much lower level of biaxial stress, which is surprisingly lower than the yield stress of a-LixS due to the combined chemo-mechanical yield mechanism.

COMPUTATIONAL METHODS Reactive MD simulations of unconfined and confined lithiation A series of reactive MD simulations were carried out here to investigate the lithiation behavior of S cathode using the massively parallelized LAMMPS package.25 Recently developed ReaxFF potential by Islam et al.24 was adopted to describe all the interatomic 6 ACS Paragon Plus Environment

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interactions in a-LixS models. A simulation timestep of 0.25 fs was chosen for all the MD simulations conducted here. Bulk α-phase S (α-S) model, which is composed of many S8 rings (as illustrated in Fig. 1(b1)), was first built with dimensions of 3.14 nm (x-axis) × 3.86 nm (yaxis) × 4.89 nm (z-axis) by duplicating the α-S unit cell by 3, 3, and 2 times along the x, y and z axis, respectively. Within the theoretical Li storage capacity of the S cathode, a stepwise Li insertion procedure26-27 was carried out to simulate the lithiation process in the S cathode and form the lithiated a-LixS system (up to x = 2 within 40 insertion steps), as illustrated in Fig. 1(b2-b3). In each insertion step, 115 Li atoms (corresponding to an incremental ∆x = 0.05 here) were randomly inserted into a previous a-LixS system (starting with the α-S system at x = 0), and each newly-formed a-Li(x+∆x)S system was first relaxed using energy minimization. Each a-Li(x+∆x)S system was then further relaxed to reach an amorphous structure by being first heated to 2000 K and then quenched down to 300 K. After the melt-and-quench procedure, each a-Li(x+∆x)S system was finally equilibrated under the NPT ensemble using the Nosé-Hoover thermostat and barostat28-29 (with coupling time constants of 25 fs and 250 fs, respectively) at 300 K for 200 ps to reach a kinetically and energetically stable a-Li(x+∆x)S system. Periodic boundary conditions (PBCs) were applied to all three axes of a-LixS models in reactive MD simulations to mimic bulk materials. In order to consider different working conditions of S cathode, two different sets of pressure-control conditions were applied to the a-LixS system to simulate both unconfined and confined lithiation process in S cathode. In the first case, a pressure coupling of 1 bar was applied to all three directions of the a-LixS model in order to simulate the unconfined lithiation of bulk S cathode with free volume expansion capability along all directions (Fig. 1(b2)), which can mimic bulk S particles located in TiO2 shells with internal void space.30 In the other case, a pressure coupling of 1 bar was applied only to the z-axis of the a-LixS model, while keeping the simulation box size along the other two directions (x and y-axes) fixed 7 ACS Paragon Plus Environment


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without pressure control, in order to mimic the confined lithiation process (free volume expansion only along the z-axis) of S cathode within a CNT reaction vessel, which is in direct contact with a Li2O/Li electrolyte/anode17 (see Fig. 1(a) and Fig. 1(b3)). Reactive MD simulations of mechanical and fracture performance In order to understand the mechanical behavior of lithiated S cathode under different working conditions, the virial theorem31-32 for atomic stresses was first utilized to evaluate the stress-strain response of bulk a-LixS models. Islam et al. compared stress-strain curves generated under strain rates from 0.0001 to 1 ps-1, and found that these stress-strain curves converge nicely when the rates are ≤ 0.01 ps-1.24 Therefore, here we adopted a relatively low strain rate of 0.001 ps-1 to obtain the stress-strain curves of unconfined a-LixS. Then, the similar virial theorem was utilized to study the lithiation-induced stress evolution in confined a-LixS. During confined lithiation, the corresponding non-zero in-plane (xy) biaxial stress in

(

equilibrated a-LixS system, σbi, can be determined as σ bi = σ xx + σ yy

)

2 , where σxx and σyy are

the normal stresses along x- and y-axis, respectively. As to explore the fracture performance of unconfined bulk a-LixS at higher Li concentration, uniaxial tension was applied to the larger bulk a-Li1.6S model with dimensions of 3.80 nm (x-axis) × 17.82 nm (y-axis) × 11.14 nm (z-axis) along z-axis at the same strain loading rate as above. Hydrostatic tension loading was applied to the bulk a-Li1.6S models with different initial void volume fractions f at the same strain loading rate along all axes. The initial voids were set as spherical and placed in the center of a-Li1.6S models with f ranging

(

from 0 to 4%. The averaged hydrostatic stress σh is calculated as σ h = σ xx + σ yy + σ zz

)

3,

where σxx, σyy and σzz are the normal stress along x-, y- and z-axis, and volumetric strain (or volume expansion rate) εvol is calculated as εvol = ∆V V ≈ ε xx + ε yy + ε zz , where ∆V and V are


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the increment and the original volume of the model respectively and εxx, εyy and εzz are the normal strains along the x, y and z-axis. The atomic strain matrix, εi, of atom i is defined as ε i = 1

2(

J i J Ti − I ) , where Ji is the

local transformation matrix which captures the difference between the relative displacements of current and reference atomic configurations of the model. The atomic shear strain ε ishear 2 2 2 can be defined as ε ishear = ε yz2 + ε xz2 + ε xy2 + ( ε yy − ε zz ) + ( ε xx − ε zz ) + ( ε xx − ε yy )  / 6 and the  

(

atomic volumetric strain ε ivolumetric = ε xx + ε yy + ε zz

)

3 . The mapping of local atomic shear

strains in both bulk and defective a-Li1.6S were visualized using OVITO software package.3335

The microstructural properties (i.e., coordination numbers and bond-angle distributions) of

both unconfined and confined a-LixS models were characterized and analyzed by setting corresponding cutoff distances for S-S, S-Li and Li-Li bonds (see Fig. 2) in a recentlydeveloped ring statistics code RINGS.36

RESULTS AND DISCUSSION Atomic and bonding structural characteristics of a-LixS The structural characteristics of a-LixS at different Li concentrations x have been analyzed and compared at 300 K. According to the calculated radial distribution functions (RDFs) g(r) in Fig. 2(a-b), the cutoff distances for forming S-S and Li-S bonds (rS-S and rS-Li) can be determined at the valley right after the first peak in g(r). This leads to rS-S = 2.37 Å and rS-Li = 3.0 Å, which are in good agreement with those for S-S37 and S-Li38 bonds determined experimentally. The cutoff distances for Li-Li bonding, rLi-Li = 3.0 Å, referring to MD models of crystalline Li metals,24 which also agrees well with the previously reported experimental value.38 Hence these cutoff distances will be utilized to determine the coordination numbers 9 ACS Paragon Plus Environment


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of S and Li atoms. With lithiation proceeding (x increasing), Fig. 2(a) shows that the height of the first peak in g(r)S-S sharply decreases, indicating the break of S8 rings in the α-phase S (αS), while the increase of the height of the second peak in g(r)S-S reveals the long-range (nonbonded) S-S ordering, which is similar to that observed in crystalline lithium sulfide (c-Li2S). In contrast, the height of the first peak in g(r)S-Li (Fig. 2(b)) is nearly independent of x, indicating the stability of S-Li bonds in a-LixS. The reduction in the height of the second peak in g(r)S-Li also confirms the break of covalently-bonded S8 rings due to lithiation. In order to further understand the microstructural evolution of S cathode during lithiation, the time-averaged total coordination number (N̅) over all the atoms in simulation box and the bond-angle distribution are evaluated respectively. Specifically, N̅ consists of contributions from two cases when the central reference atoms are either S or Li. When S is the central atom, N̅S consists of contributions from its neighboring S and Li atoms through S-S bonding (N̅S-S) and S-Li bonding (N̅S-Li), respectively, counted using the cutoff distance of rS-S = 2.37 Å and rS-Li = 3.0 Å obtained above from RDFs. When Li is the central atom, N̅Li consists of contributions from its neighboring Li and S atoms through Li-Li bonding (N̅Li-Li) and Li-S bonding (N̅Li-S), respectively, counted using the cutoff distance of rLi-Li = 3.0 Å and rS-Li = 3.0 Å obtained above from RDFs. In Fig. 2(c), both N̅S and N̅Li initially increase with Li concentration until x = 0.8, which can be attributed to the formation of a-LixS from crystalline α-S. When x is above 0.8, N̅S keeps increasing (up to 6), while N̅Li approaches a plateau value of ~ 4. It is found that N̅S-Li plays a governing role in N̅S with x increasing, accompanied by the loss of N̅S-S. N̅Li is solely contributed by N̅Li-S up to x = 1.2. After that, the contribution from N̅Li-Li starts to emerge and increases, while the contribution from Li-S N̅Li-S decreases, and therefore, leads to a constant value of N̅Li. Here the over-coordination of S atoms (N̅S > 4), with respect to N̅S = 4 in c-Li2S, results from the heterogeneous distribution of Li. This also


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reproduces, reasonably well, the non-equilibrium nature of the lithiation process in other electrode materials, such as Si anodes.39-40 The distributions of three signature bond angles, including S-S-S, Li-S-S and Li-S-Li, are analyzed in Fig. 2(d-f) as well. Our bond angle analyses suggested that the total numbers of S-S-S and Li-S-S bond angles gradually decrease and finally vanish when Li concentrations reaching x = 1.0 and x = 1.4, respectively. Therefore, Fig. 2(d-f) only shows bond angle distributions when the S-S-S and Li-S-S bond angles are still present. The gradual Li insertion gives rise to the break of S-S-S and Li-S-S connections. However, the peak locations of their bond angle distributions stay unchanged. Specifically, S-S-S bond angle contribution exhibits a peak at ~ 109° with Li insertion, which only slightly deviates from 108.4° for α-S. Li-S-S bond angle contribution exhibits a peak at ~ 90°. On the other hand, our bond angle analyses suggested that Li-S-Li bond angles start to form when x ≥ 0.4 and the number of such bond angles continues to grow at higher x values, but the total amount is limited. With x increasing, S-Li bonds significantly dominate the a-LixS system and the total number of Li-S-Li bond angles grows accordingly. Meanwhile, there is a change of peak location from 102.8° at lower x to 74.8° at higher x. This distribution transition can be ascribed to the formation of overcoordinated S atoms from lithiation, as also confirmed by the evaluation of N̅S shown in Fig. 2(c). Generally, both under- and over-coordination sites can be regarded as f structural defects, and they exist in amorphous solids, such as amorphous silicon41-42 and glasses.43-44 As a result, they can also influence the physical properties of these amorphous solids,45-48 which will also apply to the a-LixS system considered here.



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Figure 2. (a-b) Radial distribution functions (RDFs) g(r) of (a) S-S and (b) S-Li pairs. (c) Averaged coordination number (N̅) of S and Li atoms as a function of Li concentration x. Both N̅S and N̅Li are decomposed into the contributions of different bonding types, including S-S, S-Li, Li-S and Li-Li. (df) Bond angle distributions of (d) S-S-S, (e) Li-S-S and (f) Li-S-Li angles.

Mechanical properties of bulk a-LixS To explore the mechanical performance of lithiated S cathode, the stress-strain (σ-ε) curves of a-LixS under tensile loading are obtained from MD simulations (see Fig. 3(a)). We can see linear elastic behaviour of a-LixS in the strain range of 0 - 3%. The Young’s modulus of a-LixS, Ea, rises with lithiation and approaches a constant value of ~ 35.5 GPa. After the following nonlinear elastic region (ε = 3 – 10%), σ-ε curves show remarkable yielding regions, demonstrating the great ductility of a-LixS. Remarkably, the stress decreases significantly in the σ-ε curve of a-Li0.8S, when ε is larger than 0.4. Such stress drop in a-Li0.8S is actually a random event, which doesn’t represent the general mechanical behavior of a-Li0.8S. This is primarily due to the random failure of such amorphous structure at certain regions with high 12 ACS Paragon Plus Environment

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local stress concentration. The yield stress of a-LixS, σY, exhibit similar trend with x to that of Ea, and reaches a plateau value of σY ≈ 1.85 GPa, but the corresponding yield strain of a-LixS, εY, shows a nearly concentration-independent trend with a consistent value of εY ≈ 0.11 (see Fig. 3(b)). The strengthening effect (increase of σY) of a-LixS can be attributed to the stronger Li-S bonding interactions, in comparison with the dominant non-bonded inter-ring interaction in α-S which results in a low Young’s modulus of 5.78 Gpa.24 As for the saturation of σY at higher Li concentration, this trend can be partially understood by the rigidity percolation in network glasses.49-50 With the increase of coordination numbers, a-LixS becomes a percolated bonding network at a certain percolation threshold (x ≈ 1.2), while the elastic stiffness (Ea) and elastic limit (σY) of a-LixS saturate at the same time. Even though further Li insertion has no influence on the elastic properties of a-LixS, it indeed plays a significant role in its plastic behavior, which will be fully analyzed later. Interestingly, the lithiation effect on the mechanical behavior of S cathode is different from that of Si anode. For instance, lithiation deteriorates the mechanical properties (i.e., Young’s modulus and yield stress) of Si anode,26, 51 and gives rise to a striking brittle-toductile transition of amorphous Li-Si alloys (a-LixSi, 0 < x ≤ 4.4).52-53 In such case, the formation of weaker ionic Li-Si bonds, in comparison with the stronger covalent Si-Si bonds, is ascribed to the lithiation-induced softening effect of a-LixSi.52



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Figure 3. (a) Stress-strain (σ-ε) curves of a-LixS at different Li concentrations (0.4 ≤ x ≤ 2.0). (b) Yield stress σY and yield strain εY as a function of Li concentration x. (c) Stress-strain (σ-ε) curves of a-Li1.6S with a pre-formed crack. The A-D points represent four typical states of defective a-Li1.6S under tension, including A: elasticity; B: yielding; C: instability; D: shear banding. The inset shows the initial atomistic structure of a-Li1.6S (yellow: S; purple: Li). (d) Atomistic configurations of a-Li1.6S with a pre-existing crack under four strain values, corresponding to the A-D points as highlighted in (c). The color map indicates the local atomic shear strain values.

We now discuss the difference between the mechanical properties of a-LixS (x > 1.2) and c-Li2S. Different from a-LixS, c-Li2S possesses much higher Young’s modulus Ecry = 34.81 GPa (see Fig. S1(a) in Supporting Information) and behaves as a typical brittle material with a fracture strength of 11.3 GPa (see Movie S1). The difference between mechanical 14 ACS Paragon Plus Environment

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performance of c-Li2S and a-LixS (x > 1.2) is consistent with that between crystalline and amorphous phases of other solids, i.e., SiC,54 LixSi,55 and TiO2.56 The presence of structural distortion and defects (under- and over-coordination sites) are responsible for the softening of their amorphous phases, leading to the much lower yield stress and wider yielding region. Fracture mechanical behavior of a-LixS We found that a-LixS (x > 1.2) exhibits a striking ductile nature with large plastic flow (in the yielding region) in comparison with c-Li2S. In order to fully understand the underlying mechanism of great ductility in a-LixS (x > 1.2), the fracture performance of a-Li1.6S (x = 1.6 is considered here as an example) within a larger simulation cell and a pre-formed crack is investigated (see Movie S2). Fig. 3(c) shows that the material’s instability associated with stress relaxation occurs after yielding. With loading elevating, a-Li1.6S enters the shear banding state with obvious plastic flow along ~ 45° with respect to the crack (as shown in Fig. 3(d)). The crack tips become blunted due to the extensive shear banding around the crack tip. This is also the fracture mechanism of some ductile amorphous solids.52, 57 In contrast, the typical fracture mechanism of some brittle amorphous solids is governed by the crack propagation induced by nanoscale void nucleation and coalescence.58-59 Therefore, the propensity of nanoscale void nucleation is proposed as a criteria for categorizing the ductile or brittle fracture of amorphous solids. Cavitation (void nucleation and expansion) process becomes spontaneous as a result of the interplay between elastic and plastic deformations in a void-free solid, when the hydrostatic stress σh (see Computational Methods) approaches a critical hydrostatic stress σcr-h.60-61 Since a-LixSi behaves as a ductile material, there should be no formation of cavitation under tensile loading in both cases with and without the pre-formed crack. To investigate the cavitation behavior of a-LixS, hydrostatic tension tests of a-Li1.6S with different initial spherical void volume fractions f are carried out (see Movies S3-S7 and 15 ACS Paragon Plus Environment


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Computational Methods). It is found that the value of σcr-h decreases from 4.42 to 3.46 GPa with f increasing from 0 to 4% (see Fig. S2). The f-dependent trend of σcr-h lies in the fact that as the hydrostatic loading rising, there is no new void nucleation owing to the small fluctuation of σh, and σh located near the larger initial void (higher f) rises faster due to the stronger stress concentration effect and reach σcr-h at lower hydrostatic loading. As a result, the stored elastic energy activates the unstable void growth through plastic expansion, accompanying with the drop of σh.61 This can also be confirmed by the 3D surface contour of the voids under hydrostatic tension. For cases with pre-formed voids (f = 1 – 4%), the voids follow a nearly homogeneous growth mode with no new void nucleation around (Fig. S3(b)-(e)). In the void-free case (f = 0%), more external work is exerted to first nucleate the initial void before continuous growth, thus leading to the higher σcr-h value (Fig. S3(a)). Different from ductile materials (e.g., a-Li1.6S here), σcr-h of brittle materials (e.g., amorphous FeP57) is insensitive to f. This is because the significant spatial heterogeneity of σh in brittle materials can facilitates the nucleation of new voids, which makes σh also independent of f.57 With the hydrostatic loading increasing in a-Li1.6S, these newly-formed voids coalesce and merge with the pre-formed void, activating their unstable growths after reaching σcr-h. In such case, the void growth process is heterogeneous with non-uniform growth rate along different directions. Structure-property relationship behind the ductility of a-LixS In addition to the fracture and cavitation behavior of a-LixS, its microstructural evolution under tension enables us to unveil the deformation mechanism of a-LixS. As discussed above, a-LixS (x > 1.2) possesses a large number of over-coordinated S atoms (N̅S > 4). Similar coordination state also exists in some popular over-coordinated networks such as amorphous Si and SiC, in which the local stiffness (a linear function of coordination state) is closely correlated with the plasticity of the material.62 To explore the relation between the 16 ACS Paragon Plus Environment

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coordination state and ductility of a-LixS, we evaluate N̅S and N̅Li of defective a-Li1.6S under tension. Fig. 4(a) shows that both N̅S and N̅Li first slightly decrease due to bond breaking (elasticity stage), and reach plateau values within a small range of strain values (instability stage). In such instability stage, the plastic flow emerges without any changes in N̅S and N̅Li. Then, N̅S and N̅Li exhibit zig-zag fluctuations when strain further increases. Interestingly, such trend can be associated with the non-continuous formation and propagation of shear bands in a-Li1.6S. The cyclic Li-S bond breaking-and-healing process during shear band propagation results in the zig-zag fluctuations in N̅S and N̅Li. Here the over-coordination sites in a-Li1.6S act as ‘plasticity carriers’, in analogous to those in densified silica glass,63 amorphous LixSi (x > 0.5),51 and ‘liquid-like’ sites in amorphous Si,64 which facilitates the plastic deformation of a-Li1.6S.

Figure 4. (a) The averaged coordination numbers of S and Li atoms, N̅S and N̅Li, of defective (with a pre-formed crack) a-Li1.6S with respect to strain ε. The arrows show the three typical deformation stages, including elasticity, instability and shear banding. (b) The in-plane compressive biaxial stress, σbi, generated in a-LixS during confined lithiation and the compressive yield stress σY (negative in sign, but has the same magnitude as the tensile yield stress obtained from unconfined lithiation simulations under uniaxial tension) with respect to Li concentration x.



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Stress generation in a-LixS during confined lithiation Finally, we discuss the stress generation in a-LixS during confined lithiation. Due to the in-plane (xy) constraints, a compressive biaxial stress, σbi, can be generated inside a-LixS during lithiation. Fig. 4(b) shows that σbi is extremely small (in magnitude) at lower Li concentrations (x < 0.7). With further lithiation, σbi gradually increases and reaches a maximum value of 0.782 GPa in magnitude. Remarkably, σbi of a-LixS is much smaller (in magnitude) than σY of a-LixS (here we assumed that the compressive yield stress has the same magnitude as the tensile yield stress of a-LixS, following the recent computational study on Li-Si anode51) at the same x. The difference between σbi and σY can be attributed to the lithiation-induced inelastic deformation (volume expansion) along the z axis. Recently, a chemo-mechanical yield function, Ψ, was proposed to explain the Li-assisted inelastic deformation and volume expansion (also called “reactive flow” due to the concurrence of the plastic flow driven by deviatoric stress and the volume change driven by lithiation reaction51) in Si anode. Although a-LixS and a-LixSi have essentially very different reaction mechanisms, i.e., conversion reactions (covalent bond forming) in a-LixS,65 in contrast to alloying reactions (ionic bond forming) in a-LixSi,66 the general chemo-mechanical yield function, Ψ, should be still applicable to a-LixS, which can be written as:51, 67 Ψ ( sij , ζ ) =

3 sij sij + qζ 2 − σ Y2 2

(1)

where sij is the deviatoric stress that drives plastic flow only; ζ (in units of pressure) is the driving force for lithiation reaction and the associated volumetric response of S cathode (see the detailed definition in Supporting Information); q is a dimensionless positive constant, describing the relative contribution from the chemo-mechanical stress to the measured total driving force for the reactive flow; σY is lithiation-dependent yield stress under pure uniaxial mechanical loading. In general, the reactive flow is driven when Ψ ≥ 0, while it is suppressed when Ψ < 0 (see Fig. S4).


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Eq. (1) demonstrates that the reactive flow in a-LixS is both lithiation- and loadingdependent. For unconfined lithiation, as modeled by the uniaxial tension simulation along the z-axis (Fig. 3(b)), the lithiation reaction reaches equilibrium and the chemical potential of Li is balanced (ζ = 0), since a-LixS can expand freely along the x and y-axes. The reactive flow is only driven by the mechanical stress when the normal stress along the z axis, σzz, satisfies

3 s s ≡σ =σ zz Y 2 ij ij

(2)

On the other hand, for confined lithiation (Fig. 4(b)), the chemical potential of Li is imbalanced, and therefore, lithiation (delithiation) reaction is promoted with ζ > ( 1.2. Meanwhile, the plastic flow induced by sij gets weaker (Fig. 5(c-d)), and the volume expansion induced by lithiation reaction (also measured by ζ) plays a remarkable role in the total reactive flow. Fig. 5(a) shows the maximum εvol of a-LixS under confined lithiation, which leads to εvol = 0.785 at x = 2. This simulated value is very close to the ~ 80% volume expansion rate reported experimentally,6869

which also validates our MD simulations of a-LixS. The in-plane constraints in the confined 19 ACS Paragon Plus Environment


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lithiation case (Fig. 1(b3)) result in the slightly lower εvol value compared to the unconfined lithiation case.

Figure 5. (a) The evolution of volumetric strain εvol in a-LixS during confined lithiation (free volume expansion along the z-axis) and unconfined lithiation (free volume expansion along all axes). (b-d) The equilibrated atomistic configurations after confined lithiation: (b) a-Li0.3S, (c) a-Li0.9S and (d) aLi1.8S. The color map represents the local atomic shear strain values.

Furthermore, the lithiation dependence of biaxial stress σbi in a-LixS is distinct from that in a-LixSi. As reported in previous studies, σbi in a-LixSi first increases to a maximum value (2 GPa at x ≈ 0.451 and 6 GPa at x ≈ 0.7526) and then decreases gradually and reaches σbi ≈ 0.9 GPa at x = 3.75.26 Such disparate trends in σbi can be well explained using Eq. (3), in which the intrinsic σY dominates the magnitude of σbi. In such case, the different lithiation-assisted mechanical behaviors observed, i.e., the strengthened ductility in a-LixS (from weaker S-S to stronger Li-S bonding network), compared to the brittle-to-ductile transition in a-LixSi52 (from stronger Si-Si to weaker Li-Si bonding network), result in their different yield stresses σY, and consequently, different biaxial stresses σbi. Notably, such difference between Si anode and S cathode can offer fundamental insight into predicting the lithiation-induced mechanical 20 ACS Paragon Plus Environment

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performance of other electrode materials, such as metal oxides and graphite. Similar to Si anode, metal oxide anodes may exhibit a brittle-to-ductile transition upon lithiation due to their brittle nature. In contrast, graphite anode may display similar strengthening effect to that in S cathode, resulting from the formation of stronger ionic Li-C interactions than the original weaker van der Waals interactions.70 These proposed lithiation behaviors can be further confirmed by MD simulations, and will enable the optimal design of these electrode materials with excellent mechanical integrity. Current atomistic understanding of mechanical and fracture performance of lithiated S cathodes and the underlying structure-property relationship actually provides useful guidance for the optimal design of nanostructured carbon-based S cathodes with good mechanical integrity. For instance, since the lithiation-induced biaxial stress is moderate, one-dimensional hollow carbon nanofibers and nanotubes will not introduce significant inner stress concentrations, and therefore, largely suppress mechanical degradation by allowing free reactive flow along the longitudinal direction. In other nanostructured carbon matrices such as nanospheres, however, three-dimensional constraints applied by the enclosing structure may accelerate their mechanical degradation upon lithiation.

CONCLUSIONS In summary, we conducted reactive MD simulations to study the microstructural evolution and mechanical behaviors of a-LixS under different lithiation conditions and the underlying mechanism for its chemo-mechanically coupled plastic deformation during lithiation. The findings reported here are generally applicable for understanding unconfined bulk S cathode interphasing with solid-state electrolyte or confined S cathode with minimal polysulfide shuttling/dissolution into liquid electrolyte. Uniaxial tension tests first revealed 21 ACS Paragon Plus Environment


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the great ductility of a-LixS and the increase of yield stress upon lithiation. Such strengthening effect results from the transition of the bonding network from non-bonded to covalently bonded interactions. We then investigated the fracture and cavitation behavior of a-Li1.6S due to the saturation of yield stress in order to unveil the deformation mechanism in a-LixS. Both fracture and cavitation failure patterns of a-Li1.6S demonstrated the dominant role of shear banding in accommodating the plastic deformation under mechanical loading. In such case, the over-coordinated sites (S atoms) serve as “plastic carriers”, and assist the non-continuous formation and propagation of shear bands in a-LixS, as confirmed by the observed zig-zag change of coordination number under loading. Moreover, we explored the confined lithiation behavior of a-LixS and evaluated the corresponding in-plane biaxial stress and out-of-plane volume expansion (“reactive flow”). Based on a chemo-mechanical yield function, it was confirmed that such reactive flow in a-LixS is both lithiation- and loading-dependent. The lithiation reaction enhances the reactive flow of a-LixS at a much lower level of biaxial stress, which is, unexpectedly, lower than the yield stress of a-LixS due to the combined chemomechanical yield mechanism. Our atomistic understanding of lithiation-induced fracture mechanical behaviors of S cathode materials will shed light not only on the optimal design of carbon-based S composite cathodes with outstanding mechanical integrity, but also on the modeling of lithiation behaviors of other electrode materials, such as silicon, metal oxides and graphite.

ASSOCIATED CONTENT Supporting Information These materials are available free of charge via the Internet at http://pubs.acs.org. Supporting figures, simulation movies (in AVI) showing the uniaxial tension of c-Li2S (colored by the atomic volumetric strain) and a-Li1.6S with pre-formed crack (colored by 22 ACS Paragon Plus Environment

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the atomic shear strain), as well as hydrostatic tension of a-Li1.6S with different initial void volume fractions (left: colored by the atomic volumetric strain; right: 3D outer surface contour of the voids).

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected].

ACKNOWLEDGEMENTS The authors would like to acknowledge the startup funding from the Energy and Materials Initiative from the Florida State University as well as the computational resources provided by Extreme Science and Engineering Discovery Environment (XSEDE) projects TGDMR160044 and TG-DMR160125. This research was also supported by an intramural award from the FSU Provost’s Office and the Office of Postdoctoral Affairs (OPDA).

REFERENCES (1) Goodenough, J. B. Evolution of strategies for modern rechargeable batteries. Acc. Chem. Res. 2013, 46, 1053-1061. (2) Tarascon, J. M.; Armand, M. Issues and challenges facing rechargeable lithium batteries. Nature 2001, 414, 359-367. (3) Arico, A. S.; Bruce, P.; Scrosati, B.; Tarascon, J.-M.; van Schalkwijk, W. Nanostructured materials for advanced energy conversion and storage devices. Nat. Mater. 2005, 4, 366377. (4) Nitta, N.; Wu, F.; Lee, J. T.; Yushin, G. Li-ion battery materials: Present and future. Mater. Today 2015, 18, 252-264. (5) Yang, Y.; Zheng, G.; Cui, Y. Nanostructured sulfur cathodes. Chem. Soc. Rev. 2013, 42, 3018-3032.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(6) Sun, Y.; Liu, N.; Cui, Y. Promises and challenges of nanomaterials for lithium-based rechargeable batteries. Nat. Energy 2016, 1, 16071. (7) Mikhaylik, Y. V.; Akridge, J. R. Polysulfide shuttle study in the Li/S battery system. J. Electrochem. Soc. 2004, 151, A1969-A1976. (8) Bruce, P. G.; Freunberger, S. A.; Hardwick, L. J.; Tarascon, J.-M. Li-O2 and Li-S batteries with high energy storage. Nat. Mater. 2012, 11, 19-29. (9) Manthiram, A.; Fu, Y.; Chung, S.-H.; Zu, C.; Su, Y.-S. Rechargeable lithium–sulfur batteries. Chem. Rev. 2014, 114, 11751-11787. (10) Li, W.; Liang, Z.; Lu, Z.; Yao, H.; Seh, Z. W.; Yan, K.; Zheng, G.; Cui, Y. A sulfur cathode with pomegranate-like cluster structure. Adv. Energy Mater. 2015, 5, 1500211. (11) Jayaprakash, N.; Shen, J.; Moganty, S. S.; Corona, A.; Archer, L. A. Porous hollow carbon@sulfur composites for high-power lithium–sulfur batteries. Angew. Chem. Int. Ed.

2011, 123, 6026-6030. (12) Liu, X. H.; Zheng, H.; Zhong, L.; Huang, S.; Karki, K.; Zhang, L. Q.; Liu, Y.; Kushima, A.; Liang, W. T.; Wang, J. W. et al. Anisotropic swelling and fracture of silicon nanowires during lithiation. Nano Lett. 2011, 11, 3312-3318. (13) Wang, H.; Yang, Y.; Liang, Y.; Robinson, J. T.; Li, Y.; Jackson, A.; Cui, Y.; Dai, H. Graphene-wrapped sulfur particles as a rechargeable lithium–sulfur battery cathode material with high capacity and cycling stability. Nano Lett. 2011, 11, 2644-2647. (14) Barai, P.; Mistry, A.; Mukherjee, P. P. Poromechanical effect in the lithium–sulfur battery cathode. Extreme Mech. Lett. 2016, 9, 359-370. (15) Berla, L. A.; Lee, S. W.; Ryu, I.; Cui, Y.; Nix, W. D. Robustness of amorphous silicon during the initial lithiation/delithiation cycle. J. Power Sources 2014, 258, 253-259. (16) Ryu, I.; Lee, S. W.; Gao, H.; Cui, Y.; Nix, W. D. Microscopic model for fracture of crystalline Si nanopillars during lithiation. J. Power Sources 2014, 255, 274-282. (17) Kim, H.; Lee, J. T.; Magasinski, A.; Zhao, K.; Liu, Y.; Yushin, G. In situ TEM observation of electrochemical lithiation of sulfur confined within inner cylindrical pores of carbon nanotubes. Adv. Energy Mater. 2015, 5, 1501306. (18) Chen, J.-J.; Yuan, R.-M.; Feng, J.-M.; Zhang, Q.; Huang, J.-X.; Fu, G.; Zheng, M.-S.; Ren, B.; Dong, Q.-F. Conductive lewis base matrix to recover the missing link of Li2S8 during the sulfur redox cycle in Li-S battery. Chem. Mater. 2015, 27, 2048-2055. (19) Paolella, A.; Zhu, W.; Marceau, H.; Kim, C.-S.; Feng, Z.; Liu, D.; Gagnon, C.; Trottier, J.; Abdelbast, G.; Hovington, P. et al. Transient existence of crystalline lithium disulfide Li2S2 in a lithium-sulfur battery. J. Power Sources 2016, 325, 641-645. 24 ACS Paragon Plus Environment

Page 24 of 29

Page 25 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(20) Liu, Z.; Balbuena, P. B.; Mukherjee, P. P. Revealing charge transport mechanisms in Li2S2 for Li–sulfur batteries. J. Phys. Chem. Lett. 2017, 8, 1324-1330. (21) Zhang, Q.; Wang, Y.; Seh, Z. W.; Fu, Z.; Zhang, R.; Cui, Y. Understanding the anchoring effect of two-dimensional layered materials for lithium–sulfur batteries. Nano Lett. 2015, 15, 3780-3786. (22) Pang, Q.; Tang, J.; Huang, H.; Liang, X.; Hart, C.; Tam, K. C.; Nazar, L. F. A nitrogen and sulfur dual-doped carbon derived from polyrhodanine@cellulose for advanced lithium–sulfur batteries. Adv. Mater. 2015, 27, 6021-6028. (23) Senftle, T. P.; Hong, S.; Islam, M. M.; Kylasa, S. B.; Zheng, Y.; Shin, Y. K.; Junkermeier, C.; Engel-Herbert, R.; Janik, M. J.; Aktulga, H. M. et al. The ReaxFF reactive force-field: Development, applications and future directions. Npj Comput. Mater.

2016, 2, 15011. (24) Islam, M. M.; Ostadhossein, A.; Borodin, O.; Yeates, A. T.; Tipton, W. W.; Hennig, R. G.; Kumar, N.; van Duin, A. C. T. ReaxFF molecular dynamics simulations on lithiated sulfur cathode materials. Phys. Chem. Chem. Phys. 2015, 17, 3383-3393. (25) Plimpton, S. Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 1995, 117, 1-19. (26) Feifei, F.; Shan, H.; Hui, Y.; Muralikrishna, R.; Dibakar, D.; Vivek, B. S.; Adri, C. T. v. D.; Sulin, Z.; Ting, Z. Mechanical properties of amorphous LixSi alloys: A reactive force field study. Model. Simul. Mater. Sci. Eng. 2013, 21, 074002. (27) Sitinamaluwa, H. S.; Wang, M. C.; Will, G.; Senadeera, W.; Zhang, S.; Yan, C. Lithium concentration dependent structure and mechanics of amorphous silicon. J. Appl. Phys.

2016, 119, 245103. (28) Nosé, S. A unified formulation of the constant temperature molecular dynamics methods. J. Chem. Phys. 1984, 81, 511-519. (29) Hoover, W. G. Canonical dynamics: Equilibrium phase-space distributions. Phys. Rev. A

1985, 31, 1695-1697. (30) Wei Seh, Z.; Li, W.; Cha, J. J.; Zheng, G.; Yang, Y.; McDowell, M. T.; Hsu, P.-C.; Cui, Y. Sulphur–TiO2 yolk–shell nanoarchitecture with internal void space for long-cycle lithium–sulphur batteries. 2013, 4, 1331. (31) Tsai, D. H. The virial theorem and stress calculation in molecular dynamics. J. Chem. Phys. 1979, 70, 1375-1382. (32) Zhou, M. A new look at the atomic level virial stress: On continuum-molecular system equivalence. Proc. R. Soc. A 2003, 459, 2347-2392. 25 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

(33) Falk, M. L.; Langer, J. S. Dynamics of viscoplastic deformation in amorphous solids. Phys. Rev. E 1998, 57, 7192-7205. (34) Shimizu, F.; Ogata, S.; Li, J. Theory of shear banding in metallic glasses and molecular dynamics calculations. Mater. Trans. 2007, 48, 2923-2927. (35) Alexander, S. Visualization and analysis of atomistic simulation data with OVITO–The Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 2010, 18, 015012. (36) Le Roux, S.; Jund, P. Ring statistics analysis of topological networks: New approach and application to amorphous GeS2 and SiO2 systems. Comput. Mater. Sci. 2010, 49, 70-83. (37) Bhattacharyya, R.; Pal, D.; Chakrabarti, P. Disulfide bonds, their stereospecific environment and conservation in protein structures. Protein Eng. Des. Sel. 2004, 17, 795808. (38) Sutton, L. E. Tables of Interatomic Distances and Configuration in Molecules and Ions: Supplement 1956-59; Chemical Society: London, U.K., 1965. (39) Ge, M.; Rong, J.; Fang, X.; Zhou, C. Porous doped silicon nanowires for lithium ion battery anode with long cycle life. Nano Lett. 2012, 12, 2318-2323. (40) Zhao, K.; Pharr, M.; Cai, S.; Vlassak, J. J.; Suo, Z. Large plastic deformation in highcapacity lithium-ion batteries caused by charge and discharge. J. Am. Ceram. Soc. 2011, 94, s226-s235. (41) Pantelides, S. T. Defects in amorphous silicon: A new perspective. Phys. Rev. Lett. 1986, 57, 2979-2982. (42) Ishimaru, M.; Munetoh, S.; Motooka, T. Generation of amorphous silicon structures by rapid quenching: A molecular-dynamics study. Phys. Rev. B 1997, 56, 15133-15138. (43) Williams, Q.; Jeanloz, R. Spectroscopic evidence for pressure-induced coordination changes in silicate glasses and melts. Science 1988, 239, 902-905. (44) Skuja, L. Optically active oxygen-deficiency-related centers in amorphous silicon dioxide. J. Non-Cryst. Solids 1998, 239, 16-48. (45) Vedula, R. P.; Anderson, N. L.; Strachan, A. Effect of topological disorder on structural, mechanical, and electronic properties of amorphous silicon nitride: An atomistic study. Phys. Rev. B 2012, 85, 205209. (46) Štich, I.; Car, R.; Parrinello, M. Amorphous silicon studied by ab initio molecular dynamics: Preparation, structure, and properties. Phys. Rev. B 1991, 44, 11092-11104. (47) Chakravarty, S.; Georgiev, D. G.; Boolchand, P.; Micoulaut, M. Ageing, fragility and the reversibility window in bulk alloy glasses. J. Phys. Condens. Matter 2005, 17, L1.


Page 26 of 29

Page 27 of 29

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(48) Smedskjaer, M. M.; Mauro, J. C.; Youngman, R. E.; Hogue, C. L.; Potuzak, M.; Yue, Y. Topological principles of borosilicate glass chemistry. J. Phys. Chem. B 2011, 115, 12930-12946. (49) Phillips, J. C. Topology of covalent non-crystalline solids I: Short-range order in chalcogenide alloys. J. Non-Cryst. Solids 1979, 34, 153-181. (50) Thorpe, M. F. Continuous deformations in random networks. J. Non-Cryst. Solids 1983, 57, 355-370. (51) Zhao, K.; Tritsaris, G. A.; Pharr, M.; Wang, W. L.; Okeke, O.; Suo, Z.; Vlassak, J. J.; Kaxiras, E. Reactive flow in silicon electrodes assisted by the insertion of lithium. Nano Lett. 2012, 12, 4397-4403. (52) Ding, B.; Li, X.; Zhang, X.; Wu, H.; Xu, Z.; Gao, H. Brittle versus ductile fracture mechanism transition in amorphous lithiated silicon: From intrinsic nanoscale cavitation to shear banding. Nano Energy 2015, 18, 89-96. (53) Huang, S.; Zhu, T. Atomistic mechanisms of lithium insertion in amorphous silicon. J. Power Sources 2011, 196, 3664-3668. (54) Xue, K.; Niu, L.-S. Understanding the changes in mechanical properties due to the crystalline-to-amorphization transition in SiC. J. Appl. Phys. 2009, 106, 083505. (55) Shenoy, V. B.; Johari, P.; Qi, Y. Elastic softening of amorphous and crystalline Li–Si Phases with increasing Li concentration: A first-principles study. J. Power Sources 2010, 195, 6825-6830. (56) Xu, Y.; Wang, M.; Hu, N.; Bell, J.; Yan, C. Atomistic investigation into the mechanical behaviour of crystalline and amorphous TiO2 nanotubes. RSC Adv. 2016, 6, 28121-28129. (57) Murali, P.; Guo, T. F.; Zhang, Y. W.; Narasimhan, R.; Li, Y.; Gao, H. J. Atomic scale fluctuations govern brittle fracture and cavitation behavior in metallic glasses. Phys. Rev. Lett. 2011, 107, 215501. (58) Singh, I.; Guo, T. F.; Murali, P.; Narasimhan, R.; Zhang, Y. W.; Gao, H. J. Cavitation in materials with distributed weak zones: Implications on the origin of brittle fracture in metallic glasses. J. Mech. Phys. Solids 2013, 61, 1047-1064. (59) Gu, X. W.; Jafary-Zadeh, M.; Chen, D. Z.; Wu, Z.; Zhang, Y.-W.; Srolovitz, D. J.; Greer, J. R. Mechanisms of failure in nanoscale metallic glass. Nano Lett. 2014, 14, 5858-5864. (60) Huang, Y.; Hutchinson, J. W.; Tvergaard, V. Cavitation instabilities in elastic-plastic solids. J. Mech. Phys. Solids 1991, 39, 223-241.



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(61) Faleskog, J.; Shih, C. F. Micromechanics of coalescence—I. Synergistic effects of elasticity, plastic yielding and multi-size-scale voids. J. Mech. Phys. Solids 1997, 45, 2150. (62) Boolchand, P.; Zhang, M.; Goodman, B. Influence of one-fold-coordinated atoms on mechanical properties of covalent networks. Phys. Rev. B 1996, 53, 11488-11494. (63) Yuan, F.; Huang, L. Brittle to ductile transition in densified silica glass. Sci. Rep. 2014, 4, 5035. (64) Demkowicz, M. J.; Argon, A. S. High-density liquidlike component facilitates plastic flow in a model amorphous silicon system. Phys. Rev. Lett. 2004, 93, 025505. (65) Lin, Z.; Liang, C. Lithium-sulfur batteries: From liquid to solid cells. J. Mater. Chem. A

2015, 3, 936-958. (66) McDowell, M. T.; Lee, S. W.; Nix, W. D.; Cui, Y. 25th anniversary article: Understanding the lithiation of silicon and other alloying anodes for lithium-ion batteries. Adv. Mater. 2013, 25, 4966-4985. (67) Brassart, L.; Suo, Z. Reactive flow in solids. J. Mech. Phys. Solids 2013, 61, 61-77. (68) Zhang, F.-F.; Zhang, X.-B.; Dong, Y.-H.; Wang, L.-M. Facile and effective synthesis of reduced graphene oxide encapsulated sulfur via oil/water system for high performance lithium sulfur cells. J. Mater. Chem. 2012, 22, 11452-11454. (69) Rauh, R. D.; Shuker, F. S.; Marston, J. M.; Brummer, S. B. Formation of lithium polysulfides in aprotic media. J. Inorg. Nucl. Chem. 1977, 39, 1761-1766. (70) Wang, F.; Graetz, J.; Moreno, M. S.; Ma, C.; Wu, L.; Volkov, V.; Zhu, Y. Chemical distribution and bonding of lithium in intercalated graphite: Identification with optimized electron energy loss spectroscopy. ACS Nano 2011, 5, 1190-1197.


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TOC Graphic


Lithiation-Assisted Strengthening Effect and Reactive Flow in Bulk and

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