Using first principle calculations, we uncover the underlying mechanisms explaining the brittle-to-ductile transition of LixSi electrodes in lithium ion batteries with increasing Li content. We show that plasticity initiates at x = ∼ 0.5 with the formation of a craze-like network of nanopores separated by Si–Si bonds, while subsequent failure is still brittle-like with the breaking of Si–Si bonds. Transition to ductile behavior occurs at x ⩾ 1 due to the increased density of highly stretchable Li–Li bonds, which delays nanopore formation and stabilizes nanopore growth. Collapse of the nanopores during unloading of the LixSi alloys leads to significant strain recovery.

Silicon is a promising electrode material for next-generation lithium ion batteries, since its theoretical specific capacity of ∼3579 mAh g−1 is an order of magnitude higher than conventional graphite electrodes.1 However, Si experiences a ∼300% volume expansion when fully lithiated. The inhomogeneous volume changes in the Si electrode during electrochemical cycling leads to its fracture and pulverization, resulting in loss of electrical contact and capacity fade.2,3 It has been shown that Si electrodes of small feature sizes, such as nanowires, nanoparticles, porous structures, and thin films, can remain crack-free after repeated electrochemical cycling.4–7 These structures are able to accommodate the massive volume changes due to the surprising plastic deformability of LixSi,8–13 which is in contrast to the brittle nature of unlithiated Si. Sethuraman et al. showed that lithiated Si thin-film electrodes undergo plastic deformation with the tensile yield strength decreasing from ∼1.75 GPa for Li0.3Si to ∼1 GPa for Li1.5Si.8 Kushima et al. also showed that fully lithiated Si nanowires exhibited plasticity under tension and had tensile yield strength of ∼0.72 GPa, compared to ∼3.6 GPa for pristine Si nanowires.12 These experiments, as well as others,9,13 have motivated the development of continuum plasticity theories to describe the lithiation-induced deformation of the Si electrodes.14–16 However, the nanoscale mechanisms underlying the observed plastic behavior of LixSi alloys remain unclear.

The plasticity behavior reported thus far is mainly for amorphous LixSi alloys. Recent density functional theory (DFT) calculations have uncovered metastable crystalline LixSi phases.17–19 However, these crystalline LixSi phases can only form at high temperatures of ∼415 °C when Si is lithiated in a LiCl-KCl melt.20 At room temperature, crystalline Si becomes amorphous LixSi as it is lithiated, and the structure remains amorphous even when fully delithiated.13,21 In fact, the only crystalline phase that has been observed at room temperature is when Si anode is fully lithiated to form Li15Si4. However, even this crystalline Li15Si4 phase structure occurs under carefully controlled experimental conditions, such as restricting the lithiation voltage to ∼60 mV.22 As such, this paper focuses on the plasticity response of amorphous LixSi alloys.

First-principle calculations have been used to characterize the elastic behavior of amorphous LixSi alloys,23,24 but studies specifically focusing on the plastic response have been limited to relatively low Li concentrations of up to Li0.5Si.10 In this regard, the plasticity mechanisms for LixSi can be very different following the transition from a Si dominant configuration (x < 1) to a Li dominant configuration (x > 1). Here, we show that plasticity of amorphous LixSi structures initiates at x = ∼ 0.5 with the formation of a craze-like network of nanopores and interconnected Si–Si bonds, where strain localization and breaking of these Si–Si bonds lead to sudden catastrophic failure. A sharp transition from craze plasticity to ductile behavior is also observed at intermediate lithium concentrations of x ≥ 1, due to the increased density of highly stretchable of Li–Li bonds which delays nanopore formation and stabilizes nanopore growth. We further report the possibility of significant strain recovery during unloading of these LixSi structures due to collapse of the nanopores.

Our first principle calculations are performed using the Vienna Ab initio Simulation Package (VASP), with the Projector-Augmented-Wave (PAW) method and Perdew-Burke-Ernzerhof (PBE) form of the generalized gradient approximation (GGA) for exchange and correlation. We create five amorphous LixSi model structures — Si, LiSi2, LiSi, Li12Si7, and Li15Si4 — via a rapid heating and quenching scheme based on DFT formalism.25 As an example, we show the atomic configurations of the LiSi model structure in Figure 1 at various stages during the rapid heating and quenching process. We start with an initial LixSi structure created by randomly introducing Li and Si atoms within a supercell of predefined dimensions indicated in Table I to approximate a stress-free configuration (Figure 1(a)). These predefined supercell dimensions are determined based on the expected volume expansion of the LixSi alloy when lithiated.25 Using ab initio molecular dynamics (MD) as implemented in VASP, we perform an NVT calculation by subjecting each LixSi supercell to a temperature of 3000 K while keeping the box dimensions fixed; the temperature is maintained by a Nose thermostat for 5000 MD time steps, each time step corresponding to 3 fs. This temperature far exceeds the melting point of Si, Li, and their respective compounds and allows for sufficient intermixing between the Li and Si atoms in the supercell to create the amorphous structure (Figure 1(b)). The entire supercell is subsequently quenched to a target temperature of 300 K at a rate of 1 K per time step23 and is equilibrated at this temperature for a further 1000 time steps (Figure 1(c)). Both the heating and quenching processes are performed using a plane wave basis set with an energy cutoff of 300 eV. Thereafter, we relax the shape and volume of the supercell to achieve a stress-free configuration and indicate in Table I the final dimensions of the supercell for each LixSi alloy. Finally, we quantum-mechanically relax the structure to its local minimum energy state with DFT, using an atomic force tolerance of 0.01 eV/nm and a plane wave expansion kinetic energy cutoff of 400 eV (Figure 1(d)). Although our convergence analysis shows that the earlier 300 eV energy cutoff is sufficiently accurate, this larger 400 eV kinetic energy cutoff is implemented to allow for more precise calculation of the stress tensor in VASP and is used in subsequent tensile loading calculations. In all our calculations, we employ a Gamma-centered 2 × 2 × 2 and a 2 × 1 × 2 uniform Monkhorst-Pack k-point sampling taken over the Brillouin zone for pure Si and LixSi structures, respectively, which are accurate due to our relatively large supercell size. We have selectively performed calculations with 4 × 2 × 4 k-point sampling for several LixSi alloys and have found the differences in the calculated total energy to be small. The atomic configurations of the five amorphous LixSi model systems created with the above process are shown in Figure 2.

FIG. 1.

Atomic configurations for the amorphous LiSi model structure at four stages of the rapid heating and quenching process: (a) initial structure, (b) after heating at 3000 K, (c) after rapid quenching to 300 K, and (d) final amorphous structure after relaxation. The Li and Si atoms are colored in yellow and orange, respectively.

FIG. 1.

Atomic configurations for the amorphous LiSi model structure at four stages of the rapid heating and quenching process: (a) initial structure, (b) after heating at 3000 K, (c) after rapid quenching to 300 K, and (d) final amorphous structure after relaxation. The Li and Si atoms are colored in yellow and orange, respectively.

Close modal
TABLE I.

Simulation details of the five amorphous LixSi model structures.

No. of atoms
Structure Li/Si ratio Si Li Initial model dimensions (x × y × z Å3) Final stress-free model dimensions (x × y × z Å3)
Si  0.00  64  12.0 × 10.0 × 12.0  12.0 × 11.9 × 9.8 
LiSi2  0.50  100  50  12.0 × 19.0 × 12.0  12.1 × 18.6 × 11.7 
LiSi  1.00  75  75  12.0 × 17.0 × 12.0  12.0 × 17.0 × 12.0 
Li12Si7  1.71  56  96  12.0 × 17.0 × 12.0  12.1 × 16.9 × 11.9 
Li15Si4  3.75  32  120  12.0 × 17.0 × 12.0  12.0 × 16.9 × 12.2 
No. of atoms
Structure Li/Si ratio Si Li Initial model dimensions (x × y × z Å3) Final stress-free model dimensions (x × y × z Å3)
Si  0.00  64  12.0 × 10.0 × 12.0  12.0 × 11.9 × 9.8 
LiSi2  0.50  100  50  12.0 × 19.0 × 12.0  12.1 × 18.6 × 11.7 
LiSi  1.00  75  75  12.0 × 17.0 × 12.0  12.0 × 17.0 × 12.0 
Li12Si7  1.71  56  96  12.0 × 17.0 × 12.0  12.1 × 16.9 × 11.9 
Li15Si4  3.75  32  120  12.0 × 17.0 × 12.0  12.0 × 16.9 × 12.2 
FIG. 2.

Atomic configurations for the five amorphous LixSi model structures: (a) Si, (b) LiSi2, (c) LiSi, (d) Li12Si7, and (e) Li15Si4. The Li and Si atoms are colored in yellow and orange, respectively.

FIG. 2.

Atomic configurations for the five amorphous LixSi model structures: (a) Si, (b) LiSi2, (c) LiSi, (d) Li12Si7, and (e) Li15Si4. The Li and Si atoms are colored in yellow and orange, respectively.

Close modal

We subject the five amorphous LixSi structures to uniaxial straining by rigidly constraining the in-plane dimensions of the supercell in the x- and z-directions, and uniformly stretching the out-of-plane dimension in the y-direction in 2% strain increments. Each strain increment is followed by quantum-mechanical relaxation of the supercell in DFT. This more stable strain-controlled loading is used in place of conventional stress-controlled loading to allow us to trace the complete stress-strain response of the LixSi structures, including potential softening behavior. We remark that this first-principle-based approach to ascertain the stress-strain response of the LixSi alloys is highly computational-intensive. Creating each amorphous LixSi model structure of ∼150 atoms via the rapid heating and quenching approach, and deforming each structure to tensile strains of up to 40%, requires over 35 000 CPU hours on available supercomputing clusters.

Figure 3 shows the elastic modulus and yield strength of the respective LixSi structures, obtained from computations of the von Mises effective stress-strain response (black symbol). To validate our model structures, we compare our results with those from first-principle calculations10,11,23 as well as experiments.8,12,26,27 We find our measured properties to be in good agreement with these results, which suggests that these model structures are effective representations of true amorphous LixSi alloys. In particular, our results show that the elastic modulus dramatically decreases with initial increase in lithium fraction from 0 to 0.33 due to elastic softening, but later saturates. Interestingly, the elastic modulus of LiSi (lithium fraction 0.5) is even slightly higher than LiSi2 (lithium fraction 0.33), which contradicts the rule-of-mixtures predictions. This non-monotonic behavior has been reported experimentally and is likely associated with the higher density of Li–Si bonds in the LiSi structure, which affects the average inter-atomic bond stiffness.26 The calculated initial yield strength similarly displays a sharp initial decrease with initial increase in lithium content and saturates at lithium fraction of 0.5 and higher. The predicted yield strengths are in good agreement with available experimental data at high lithium fractions8,12 and are remarkably similar to those from previous DFT calculations11 even though an entirely different approach was used to create the amorphous LixSi structures.

FIG. 3.

(a) Elastic modulus and (b) initial yield strength as a function of lithium fraction from uniaxial tensile straining of the amorphous LixSi model structures (black symbols), with comparison to the literature values from first principle calculations and experiments.

FIG. 3.

(a) Elastic modulus and (b) initial yield strength as a function of lithium fraction from uniaxial tensile straining of the amorphous LixSi model structures (black symbols), with comparison to the literature values from first principle calculations and experiments.

Close modal

Figure 4(a) examines the evolution of the axial stress σ22 versus strain ϵ22 for four LixSi structures. We observe the expected brittle-failure response for unlithiated Si, which undergoes an instantaneous loss of stress-carrying capacity after yielding. The LiSi2 structure, however, undergoes appreciable plasticity beginning at ϵ22 = ∼ 0.1 but experiences a sudden loss of stress-carrying capacity at ϵ22 = 0.2. The LiSi and Li15Si4 structures also undergo significant plasticity and continue to remain load-bearing even at strains beyond ϵ22 > 0.3, implying that such structures are truly ductile. To quantify the evolving damage in these LixSi structures, we calculate the nanopore volume V at each strain increment. Since the equilibrium bond distance for Si–Si, Li–Si, and Li–Li bonds is 2.4 Å, 2.7 Å, and 2.7 Å, respectively, we define the “porous” regions to be at least 2 Å away from the nearest Si and Li atoms. We subdivide the supercell of each LixSi structure into regular (0.02)3 nm3 grid elements and sum up the grid elements which are within the porous region to obtain V; we confirm that V does not appreciably change with further refinement of the subdivision volume. The evolving porosity f of each LixSi structure, indicative of the damage extent, is then obtained by normalizing V with the current deformed volume of the supercell V0 in Figure 4(b). Observe that unlithiated Si has the largest initial porosity due to its open sp3 tetrahedral structure. Increasing Li content significantly decreases this free volume, and a fully dense undeformed structure is achieved for LiSi and Li15Si4. The porosity for unlithiated Si increases linearly with ϵ22 due to elastic stretching of the Si–Si bonds but experiences a sudden jump at the failure point due to breaking of Si–Si bonds. For LiSi2, appreciable increase in f only occurs during plastic deformation ϵ 22 > 0 . 1 . Like unlithiated Si, a substantial jump in f coincides with the sudden loss of stress-carrying capacity, which indicates catastrophic brittle-failure of the LiSi2 structure despite its ability to deform plastically. In contrast, the structures for LiSi and Li15Si4 remain fully dense up to ϵ22 > 0.15; the nucleated nanopores subsequently undergo very stable growth even at applied strains beyond ϵ22 > 0.3.

FIG. 4.

Evolution of the (a) axial stress σ22 and (b) porosity f versus the applied strain ϵ22 for four LixSi structures subjected to uniaxial straining.

FIG. 4.

Evolution of the (a) axial stress σ22 and (b) porosity f versus the applied strain ϵ22 for four LixSi structures subjected to uniaxial straining.

Close modal

Figure 5 shows the details of the porosity (damage) distribution within the LiSi2, LiSi, and Li15Si4 structures; the nanopores in each configuration are represented by a collection of blue spheres, each of diameter 0.02 nm. We also display the covalent Si–Si bonds as brown lines; each Si–Si bond pair is operationally defined as having a bond distance of ≤2.6 Å per our bond analysis later discussed in Section III B. For LiSi2, no significant nanopore growth is observed during the initial elastic deformation (compare ϵ22 = 0 and 0.08). The onset of plasticity, however, induces rapid nanopore growth (ϵ22 = 0.16). The resulting structure comprises of interpenetrating nanopores and Si–Si covalent bonds which closely resembles the network of microvoids and fibrils in polymer crazing.28 Like polymer crazing, this network of strong Si–Si covalent bonds (fibrils) prevents the neighboring nanopores from coalescing; damage is therefore delocalized, as seen by the spread of discrete nanopores in the structure. At this point, the LiSi2 structure is still load-bearing, since the Si–Si bonds stretch but do not break. This mechanism of plastic deformation by nanoscale crazing absorbs fracture energy and likely increases the toughness of the LiSi2 structure. Once sufficient tensile load is applied to locally break the Si–Si covalent bonds (fibrils), the sudden coalescence of neighboring nanopores causes failure to be brittle-like (ϵ22 = 0.24). With increasing Li concentrations, craze plasticity is no longer possible since the chains of Si–Si atoms are no longer continuous (Figures 5(b) and 5(c)). These discontinuous Si–Si chains also result in the lower tensile yield strengths of LiSi and Li15Si4. The extensive ductility of these structures, on the other hand, can be attributed to the delayed nucleation and subsequent stable growth of nanopores. Even when nanopore link-up occurs, as in ϵ22 = 0.32 for Li15Si4, the coalescence process occurs gradually, compared to that in LiSi2, and the structure continues to be load-bearing. We further observe that the covalent Si–Si bonds for all three LixSi structures remain largely intact during the deformation process, except at the final failure point of LiSi2, implying that the nanopores grow by either the breaking of weaker Li–Si or Li–Li bonds.

FIG. 5.

Distribution of nanopores (filled with blue spheres) within each (a) LiSi2, (b) LiSi, and (c) Li15Si4 supercell at four applied strains ϵ 22 . Atomic configurations are filtered to include Si–Si bonds (brown lines).

FIG. 5.

Distribution of nanopores (filled with blue spheres) within each (a) LiSi2, (b) LiSi, and (c) Li15Si4 supercell at four applied strains ϵ 22 . Atomic configurations are filtered to include Si–Si bonds (brown lines).

Close modal

The distinct transitions in the plastic behavior of LixSi structures with increasing Li content above can be explained in terms of the density and type of bonds present: covalent Si–Si bonds, ionic Li–Si bonds, and metallic Li–Li bonds, in order of decreasing bond strength. We performed a pair distribution analysis for each of these bond types in the LiSi2, LiSi, and Li15Si4 structures, akin to a partial radial distribution function analysis.24,25,29 Figure 6 shows the nearest-neighbor bond length distributions (b), normalized by the equilibrium bond distance (b0) which is taken to be 2.4 Å, 2.7 Å, and 2.7 Å for Si–Si, Li–Si, and Li–Li bonds, respectively. The Si–Si bond lengths in all the deformed LixSi structures are found to be limited to within ∼5% bond extension: the peak number of Si–Si bonds lies within 1 ≤ b/b0 ≤ 1.05 even after significant deformation. In contrast, the Li–Si bond stretch is shown to depend on the Li content. A significant number of Li–Si bonds (>50) are stretched to ∼15% for LiSi2 but are stretched to only ∼10% for Li15Si4. According to Pauling’s rule,30 the electrostatic Li–Si bond strength, defined by the charge on the ion versus the coordination number, is the same for LiSi2, LiSi, and Li15Si4. This infers that the Li–Si bonds in all three alloys can be stretched to the same extent. The fact that the Li–Si bonds in Li15Si4 are not stretched to the fullest extent possible suggests that most of the strain is accommodated by the Li–Li bonds instead. Compared to Si–Si and Li–Si bonds, the Li–Li bonds are the most stretchable. For example, the few Li–Li bonds for LiSi2 can be locally stretched to 25% strains, corresponding to the distribution peak at b/b0 = 1.25 under deformation. For LiSi and Li15Si4, the peak Li–Li bond distribution continuously shifts to the right with deformation, and a significant proportion of Li–Li bonds is now stretched to 20%-30%. These highly stretchable Li–Li bonds are responsible for the increased ductility of the LixSi structures with increasing Li content. In addition, much sharper Li–Li, Li–Si, and Si–Si bond length distribution peaks are observed for Li15Si4, compared to LiSi and LiSi2, implying more delocalized deformation behavior at higher Li concentrations. This can be attributed to the delocalized nature of metallic bonds itself, as well as the high mobility of Li ions29 to accommodate the strain-induced deformation. Given the low density of Si–Si bonds in the Li15Si4 structure, much of the strength comes from the Li–Si ionic bonds. In contrast, the absence of significant proportion of Li–Li bonds in LiSi2 implies that ductility will be limited, though its tensile strength — originating from the high density of interconnected Si–Si bonds — will be the highest.

FIG. 6.

Distributions of the nearest-neighbor Si–Si, Li–Si, and Li–Li bond lengths (b) normalized with respect to the equivalent bond lengths (b0) for LiSi2, LiSi, and Li15Si4 structures at three applied strains (ϵ22). The symbols reflect the number of Si–Si, Li–Si, and Li–Li atom pairs in the respective supercells which are within 5% deviation from the corresponding b/b0 values.

FIG. 6.

Distributions of the nearest-neighbor Si–Si, Li–Si, and Li–Li bond lengths (b) normalized with respect to the equivalent bond lengths (b0) for LiSi2, LiSi, and Li15Si4 structures at three applied strains (ϵ22). The symbols reflect the number of Si–Si, Li–Si, and Li–Li atom pairs in the respective supercells which are within 5% deviation from the corresponding b/b0 values.

Close modal

The correlation between the bond type/density in the structure versus the formation and growth of nanopores can be understood by considering the proportion of Si–Si, Si–Li, and Li–Li bonds in each structure as a function of the applied strain in Figure 7. In obtaining these results, we define the Si–Si, Si–Li, and Li–Li bonds in the respective LixSi structures to have maximum b/b0 of 1.1, 1.15, and 1.35, respectively, based on our bond analysis above. Observe that majority of the bonds in LiSi2, LiSi, and Li12Si7 are of Li–Si type, while Li–Li bonds are dominant for Li15Si4. The results further show a clear transition in the dominant nanopore formation/growth mechanism, from the initial breaking of Li–Si bonds for LiSi2, LiSi, and Li12Si7 to the breaking of Li–Li bonds for Li15Si4. This trend can be explained by examining the weakest-link in the structure. Covalent Si–Si bonds are undoubtedly the strongest, and the proportion of Si–Si bonds across all LixSi structures does not change much with deformation. Compared to the Si–Si bonds, the ionic Li–Si bonds for LiSi2 and LiSi structures are much weaker; breaking of these bonds, as shown by the decrease in the proportion of Li–Si bonds, allows the nanopores to nucleate and grow. For Li12Si7, the proportion of Li–Si bonds decreases up to ϵ22 = ∼ 0.2, beyond which the breaking of Li–Li bonds becomes the dominant nanopore growth mechanism; this transition is consistent with the ability of Li–Li bonds to tolerate local strains of ∼20%-30%. For Li15Si4, the nanopore growth is solely caused by the breaking of these weaker, metallic Li–Li bonds; these Li–Li bonds are able to tolerate significant strains before breaking, which retards nanopore formation and stabilizes its growth.

FIG. 7.

Evolution of the proportion of Si–Si, Li–Si, and Li–Li bonds with deformation in four LixSi structures, obtained by normalizing the current number of bonds of the same type by the total number of bonds in the undeformed structure. The Si–Si, Li–Si, and Li–Li bonds in the respective structures are defined to have maximum b/b0 of 1.1, 1.15, and 1.35, respectively.

FIG. 7.

Evolution of the proportion of Si–Si, Li–Si, and Li–Li bonds with deformation in four LixSi structures, obtained by normalizing the current number of bonds of the same type by the total number of bonds in the undeformed structure. The Si–Si, Li–Si, and Li–Li bonds in the respective structures are defined to have maximum b/b0 of 1.1, 1.15, and 1.35, respectively.

Close modal

Continuum plasticity approaches to model the deformation response of LixSi alloys are based on classical elasto-plastic or visco-plastic assumptions.14,15 Our results, however, demonstrate that the ability of LixSi alloys to undergo plasticity stems from the breaking of Li–Si and/or Li–Li bonds which results in nanopore formation and growth; this necessitates the development of Gurson-type porous material models31 to correctly describe the plastic response of these alloys. In addition, unlike continuum plasticity theories where the plastic part of the deformation is permanent, unloading the LixSi structure can allow the nanopores to shrink and in turn the broken bonds to reform.

Figures 8(a) and 8(b) shows the axial stress-strain loading and unloading profiles for LiSi and Li15Si4 — two structures that undergo substantial plasticity during tensile deformation. Unloading the LiSi structure from strains of ϵ 22 UL = 0 . 16 and 0.32 results in axial plastic strains of ϵp = 0.02 and 0.05, respectively, which are remarkably smaller than expected due to the ability of the nanopores to shrink and some bonds to reform. The atomic configurations during the unloading process from ϵ 22 UL = 0 . 16 in Figure 8(c) show the reforming of Li–Si bonds (A-B) during the collapse of the nanopore. The gradual unloading stress-strain response of LiSi from a highly porous state ( ϵ 22 UL = 0 . 32 ) is due to stiffening of the structure with decreasing porosity. This is in contrast to Li15Si4 which unloads with a constant stiffness over a substantial portion of the deformation due to the much lower porosity. Interestingly, kinks are consistently observed in the unloading stress-strain curves for Li15Si4 near the point of collapse of the nanopores. These kinks reflect the competition between the loss of surface energy associated with the collapse of the nanopores and the increased elastic strain energy due to the stretching of newly reformed Li–Li bonds across the surface of the nanopores. The atomic configurations for ϵ 22 UL = 0 . 26 in Figure 8(d) show rearrangement of Li atoms (H) to enable bonding across the void surface; this process causes local Li–Li bond stretching (H-L and K-L) which contributes to a sudden, albeit small, increase in σ22 as the structure is unloaded. We remark that the axial strain for Li15Si4 is almost fully recovered when the structure is unloaded from strains of up to ϵ 22 UL = 0 . 26 . At higher strains of ϵ 22 UL = 0 . 34 , however, large axial plastic strain of ϵp = 0.1 is observed when the structure is first unloaded to σ22 = 0, since the existing nanopores shrink but do not completely close.

FIG. 8.

((a) and (b)) Loading and unloading axial stress-strain response for LiSi and Li15Si4 structures. ((c) and (d)) Deformed atomic configurations of LiSi and Li15Si4 structures when unloaded from strains of ϵ 22 UL = 0 . 16 and 0.26, respectively. The Li and Si atoms are colored in yellow and orange, while the nanopores are filled with blue spheres.

FIG. 8.

((a) and (b)) Loading and unloading axial stress-strain response for LiSi and Li15Si4 structures. ((c) and (d)) Deformed atomic configurations of LiSi and Li15Si4 structures when unloaded from strains of ϵ 22 UL = 0 . 16 and 0.26, respectively. The Li and Si atoms are colored in yellow and orange, while the nanopores are filled with blue spheres.

Close modal

In summary, bond-breaking-induced nanopore nucleation, growth, and coalescence play the key role in the plastic deformation of LixSi alloys: from craze plasticity resulting in brittle failure response (LiSi2) to extensive ductility (Li15Si4) resulting from the high density of stretchable Li–Li bonds which delays nanopore nucleation and stabilizes nanopore growth. The nanopores evolve by the breaking of Li–Si bonds at low to moderate Li concentrations and by the breaking of Li–Li bonds at high Li concentrations. In addition, the LixSi structures are capable of exhibiting substantial strain recovery when unloaded within certain deformation limits. These newly uncovered plasticity mechanisms have important implications in the design of nanostructured Si electrodes to mitigate fracture and failure.

The authors acknowledge the support of National Science Foundation Grant Nos. NSF-CMMI-1300805 and NSF-CMMI-1300458, as well as computational time provided by TACC Grant No. TG-MSS130007, and Blue Waters sustained-petascale computing project which is supported by the National Science Foundation (Award Nos. OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.

1.
U.
Kasavajjula
,
C.
Wang
, and
A. J.
Appleby
,
J. Power Sources
163
,
1003
(
2007
).
2.
J. P.
Maranchi
,
A. F.
Hepp
,
A. G.
Evans
,
N. T.
Nuhfer
, and
P. N.
Kumta
,
J. Electrochem. Soc.
153
,
A1246
(
2006
).
3.
H.
Wang
,
B.
Hou
,
X.
Wang
,
S.
Xia
, and
H. B.
Chew
,
Nano Lett.
15
,
1716
(
2015
).
4.
S. W.
Lee
,
M. T.
McDowell
,
L. A.
Berla
,
W. D.
Nix
, and
Y.
Cui
,
Proc. Natl. Acad. Sci. U. S. A.
109
,
4080
(
2012
).
5.
X. H.
Liu
,
L.
Zhong
,
S.
Huang
,
S. X.
Mao
,
T.
Zhu
, and
J. Y.
Huang
,
ACS Nano
6
,
1522
(
2012
).
6.
J.
Graetz
,
C. C.
Ahn
,
R.
Yazami
, and
B.
Fultz
,
Electrochem. Solid-State Lett.
6
,
A194
(
2003
).
7.
T.
Takamura
,
S.
Ohara
,
M.
Uehara
,
J.
Suzuki
, and
K.
Sekine
,
J. Power Sources
129
,
96
(
2004
).
8.
V. A.
Sethuraman
,
M. J.
Chon
,
M.
Shimshak
,
V.
Srinivasan
, and
P. R.
Guduru
,
J. Power Sources
195
,
5062
(
2010
).
9.
V. A.
Sethuraman
,
V.
Srinivasan
,
A. F.
Bower
, and
P. R.
Guduru
,
J. Electrochem. Soc.
157
,
A1253
(
2010
).
10.
K. J.
Zhao
,
W. L.
Wang
,
J.
Gregoire
,
M.
Pharr
,
Z. G.
Suo
,
J. J.
Vlassak
, and
E.
Kaxiras
,
Nano Lett.
11
,
2962
(
2011
).
11.
K.
Zhao
,
G. A.
Tritsaris
,
M.
Pharr
,
W. L.
Wang
,
O.
Okeke
,
Z.
Suo
,
J. J.
Vlassak
, and
E.
Kaxiras
,
Nano Lett.
12
,
4397
(
2012
).
12.
A.
Kushima
,
J. Y.
Huang
, and
J.
Li
,
ACS Nano
6
,
9425
(
2012
).
13.
M. J.
Chon
,
V. A.
Sethuraman
,
A.
McCormick
,
V.
Srinivasan
, and
P. R.
Guduru
,
Phys. Rev. Lett.
107
,
045503
(
2011
).
14.
A. F.
Bower
,
P. R.
Guduru
, and
V. A.
Sethuraman
,
J. Mech. Phys. Solids
59
,
804
(
2011
).
15.
L.
Brassart
and
Z.
Suo
,
J. Mech. Phys. Solids
61
,
61
(
2013
).
16.
H. B.
Chew
,
B.
Hou
,
X.
Wang
, and
S.
Xia
,
Int. J. Solids Struct.
51
,
4176
(
2014
).
17.
A. J.
Morris
,
C. P.
Grey
, and
C. J.
Pickard
,
Phys. Rev. B
90
,
054111
(
2014
).
18.
V. L.
Chevrier
,
J. W.
Zwanziger
, and
J. R.
Dahn
,
J. Alloys Compd.
496
,
25
(
2010
).
19.
W. W.
Tipton
,
C. R.
Bealing
,
K.
Mathew
, and
R. G.
Hennig
,
Phys. Rev. B
87
,
184114
(
2013
).
20.
C. J.
Wen
and
R. A.
Huggins
,
J. Solid State Chem.
37
,
271
(
1981
).
21.
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
, and
J. Y.
Huang
,
Nat. Nanotechnol.
7
,
749
(
2012
).
22.
J.
Li
and
J. R.
Dahn
,
J. Electrochem. Soc.
154
,
A156
(
2007
).
23.
V. B.
Shenoy
,
P.
Johari
, and
Y.
Qi
,
J. Power Sources
195
,
6825
(
2010
).
24.
C.-Y.
Chou
,
H.
Kim
, and
G. S.
Hwang
,
J. Phys. Chem. C
115
,
20018
(
2011
).
25.
P.
Johari
,
Y.
Qi
, and
V. B.
Shenoy
,
Nano Lett.
11
,
5494
(
2011
).
26.
B.
Hertzberg
,
J.
Benson
, and
G.
Yushin
,
Electrochem. Commun.
13
,
818
(
2011
).
27.
L. A.
Berla
,
S. W.
Lee
,
Y.
Cui
, and
W. D.
Nix
,
J. Power Sources
273
,
41
(
2015
).
28.
P. A.
O’Connell
and
G. B.
Mckenna
,
Encyclopedia of Polymer Science and Technology
, 3rd ed. (
John Wiley and Sons, Inc.
,
Hoboken, New Jersey
,
2004
).
29.
J.
Pan
,
Q.
Zhang
,
J.
Li
,
M. J.
Beck
,
X.
Xiao
, and
Y.-T.
Cheng
,
Nano Energy
13
,
192
(
2015
).
30.
L.
Pauling
,
The Nature of the Chemical–Bond and the Structure of Molecules and Crystals–An Introduction to Modern Structural Chemistry
(
Cornell University Press
,
1960
), Vol.
16
.
31.
A. L.
Gurson
,
J. Eng. Mater. Technol.
99
,
2
(
1977
).