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Journal Club Theme of July 2016: Mechanics of Large-Volume-Change Materials for Rechargeable Batteries

Shuman_Xia's picture

Mechanics of Large-Volume-Change Materials for Rechargeable Batteries

Shuman Xia, Georgia Institute of Technology


The focus of this special issue is on the mechanics of rechargeable battery electrode (RBE) materials, which is a relatively new and emerging research area. There have been a few Journal Club themes and posts on iMechanica related to this topic (link 1, link 2, link3). For this special issue, I will focus on experimental research and discuss current challenges and opportunities surrounding the experimental mechanics issues of RBE materials.

1. Introduction

Global demand for low-cost, high-performance energy storage solutions has grown tremendously in recent years. These storage solutions are needed for various applications, including consumer electronics, vehicle electrification, and stationary power management. Solid-state energy materials based on charge transport and storage are critical for finding such solutions. Energy storage and release of these materials often involve a complex set of mechanical and electrochemical processes, including deformation, stress generation, mass transport, phase transformation, chemical reaction, and microstructural evolution. A fundamental understanding of the mechanics and its intricate coupling with other physical phenomena is required to achieve breakthroughs in electrical energy storage. 

The past decade has witnessed a marked increase in studies on the mechanical behaviors of high-capacity, large-volume-change RBE materials [1-17]. Significant progress has been made in the experimental measurement and modeling of diffusion-induced stresses [6, 18], lithium-concentration dependent modulus and hardness [19-21], 2D and 3D diffusion-induced deformation [22-25], time-dependent creep [21, 26], strain-rate sensitivities [27], and fracture-related properties [28-31]. In the following, I will showcase a few recent works of my group and use them as a catalyst to spark our discussion. 

2. In Situ Testing and Atomistic Modeling of Fracture in Lithiated Silicon

Nature Communications 6: 8417 (2015)

We performed an integrated experimental and computational investigation of the fracture characteristics of lithiated silicon electrodes for their use in next-generation, high-capacity lithium-ion batteries. In situ transmission electron microscopy experiments were performed to observe a striking contrast of brittle fracture versus ductile deformation in pristine and highly lithiated silicon. Quantitative nanoindentation tests were conducted on lithiated silicon thin films to reveal lithiation-induced embrittlement at low lithium concentrations, and subsequent brittle-to-ductile transition as the lithium reaction proceeds. Concurrently, we employed molecular dynamics simulations with reactive force fields to elucidate the underlying fracture mechanism mediated by lithiation-assisted atomic re-arrangement. Our work provides fundamental insights into the mechanical failure of ion-storage materials that are imperative for engineering and predictive modeling of high-performance rechargeable batteries.


Figure 1. In situ electrochemical lithiation and mechanical testing of a Si nanowire inside a transmission electron microscope (TEM). (a) In situ experimental setup of an electrochemical cell consisting of a Si nanowire working electrode, a Li2O solid electrolyte, and a bulk Li metal counter electrode. (b) Schematic illustration of mechanical testing of a partially lithitated Si nanowire using a piezopositioner. (c, d) TEM images showing the fracture of the unlithiated Si core and the large plastic deformation of the lithiated amorphous LixSi shell (scale bars, 1 micron in c and 50 nm in d).

Figures 1a and 1b show the experimental setup for in situ electrochemical lithiation and fracture testing of individual Si nanowires inside a TEM. The nano-sized electrochemical cell consisted of Si nanowires grown on a silicon substrate as the working electrode and a lithium probe as the counter electrode. A native Li2O layer on the probe surface was used as a lithium-ion conductive solid electrolyte. To drive the lithiation process, the Li probe was brought into contact with the free end of a Si nanowire, followed by the application of a bias voltage of -2 V between the working and counter electrodes. Because the surface diffusivity of Li is much higher than the bulk one, Li ions first migrated preferably along the free surfaces of the nanowire and then diffused towards the center. Due to the retardation effect of lithiation-induced stress, the lithiation front in the nanowire slowed down as it approached the center of the nanowire and eventually came to a stop. This process led to the formation of a core-shell structure with a pristine Si core and a lithiated amorphous Si shell. Following the lithiation experiment, the partially lithiated Si nanowire was used for in situ compression testing with the Li probe, as shown in Fig. 1b. As the compressive load was increased to a critical value, the nanowire buckled and the unreacted c-Si core was found to break in a brittle and catastrophic manner (Figs. 1c and 1d). In contrast, the lithiated shell underwent large deformation without cracking. This striking difference qualitatively indicates that lithiation plays a significant role in altering the fracture characteristics of silicon.


Figure 2. Fracture toughness measurement of lithiated Si electrodes. SEM images of indents on a lithiated electrode film (Li0.87Si) at various indentation loads showing (a) no cracking, (b) radial cracking, and (c) massive cracking (scale bar, 0.5 micron (a); scale bar, 1 micron (b); scale bar, 2 microns (c)). SEM images of indents on a lithiated electrode film with higher Li concentration (Li1.56Si) showing (d-f) no cracking under various indentation loads (Scale bar: 1 micron in (d) and (e); 2 microns in (f)). (g) Curves showing critical indentation loads as a function of the lithium concentration. (h) Fracture toughness and fracture energy of lithiated Si electrodes as a function of the lithium concentration.

The fracture toughness of LixSi alloys at five different concentrations was quantitatively evaluated by nanoindentation. Figure 2 shows the measured fracture toughness, KIc , as a function of the lithium concentration. The fracture energy was calculated as G=KIc2/E and is also presented in the figure. The fracture toughness and fracture energy of unlithiated amorphous Si are measured to be 0.51 ± 0.014 MPa·m1/2  and 2.85 ± 0.15 J/m2, respectively, which are typical values of a brittle material. As the lithium concentration increases, the fracture resistance of lithiated Si is found to first decrease, indicating lithiation-induced embrittlement. This trend is in qualitative agreement with the recent ab initio calculations which show a small amount of lithium insertion into Si substantially weakens Si bonds, and hence reduces the surface energy of the material. Upon further lithiation beyond x = 0.31, both the fracture toughness and fracture energy increase sharply with increasing lithium concentration, reaching 0.77 ± 0.03 MPa·m1/2  and 8.54 ± 0.72 J/m2 for Li1.09Si, respectively. This behavior suggests a brittle-to-ductile transition in the fracture characteristics of LixSi going from moderate to high lithium concentrations. 


Figure 3. Molecular dynamics simulations of edge crack growth in Li0.5Si and Li2.5Si specimens subjected to mode I loading.

To elucidate the experimentally observed fracture behavior of lithiated silicon, we performed molecular dynamics (MD) simulations using the reactive force field (ReaxFF) potential. In the MD simulations (Fig. 3), a thin slab of lithium-silicon alloy containing a sharp initial edge crack is stretched under displacement control at a constant rate. The far-field load is continuously monitored as the crack develops during loading. At a moderate lithium concentration (x = 0.5), the edge crack is observed to propagate instantly when the remote stress reaches a critical value of ~5.5 GPa. The far-field stress drops rapidly during the subsequent crack propagation. A close-up view of the crack-tip vicinity reveals that the fracture process is governed by nanovoid formation and coalescence at the crack tip. In contrast, a high-lithium-concentration slab (x = 2.5) tested under same mechanical condition exhibits drastically different fracture characteristics. In this case, the sharp pre-crack becomes substantially blunted and the corresponding load-displacement curve is much lower and flatter than the previous case, signifying a ductile fracture behavior at the high lithium concentration.

3. Fracture Characteristics of Lithiated Germanium as a Viable Anode Material for Lithium Ion Batteries

Journal of The Electrochemical Society 163: A90-A95 (2016)

Germanium (Ge) is a promising candidate anode material for next-generation, high-performance lithium-ion batteries. Despite its apparent promise, the mechanical properties of lithiated Ge including its fracture characteristic are largely unknown. We performed the first experimental measurement of the fracture toughness of lithiated Ge using our in-house developed nanoindentation system. The fracture toughness of lithiated Ge is found to increase monotonically with increasing lithium content, indicating a brittle-to-ductile transition of lithiated Ge as lithiation proceeds. We also compare the fracture energy of lithiated Ge with that of lithiated Si and show that, despite a slightly lower fracture energy of Ge than that of Si in the unlithiated state, Ge possesses much higher fracture resistance than Si in the lithiated state. These findings suggest that Ge anodes are intrinsically more resistant to fracture than their Si counterparts, thereby offering substantial potential for the development of durable, high-capacity, and high-rate lithium-ion batteries. The quantitative results from this work provide fundamental insights for developing new electrode materials and help to enable predictive modeling of high-performance lithium-ion batteries.


Figure 4. (a) Voltage profiles of four thin-film Ge electrodes lithiated/delithiated to various lithium concentrations. (b) Film stress evolution in the electrodes corresponding to the battery testing in (a). The two insets in (b) illustrate the development of compressive and tensile stress during lithium insertion into and extraction from the Ge electrodes, respectively.

Figure 4a shows the electrochemical profiles of four LixGe film electrodes used for fracture toughness measurement. The corresponding stress evolution in the LixGe films during the electrochemical testing are plotted in Fig. 4b. All the stress curves start with an initial compressive film stress of 0.3 GPa resulting from the sputtering process. During lithiation of the Ge films, lithium ions are inserted into the films and cause volume expansion. However, the substrate constrains the Ge films from in-plane expansion, resulting in a dramatic increase in the compressive film stress. As the lithiation proceeds, the compressive film stress first increases linearly, revealing the elastic deformation of the films. After reaching a maximum compressive stress, the LixGe films lithiated beyond x = 0.33 show a slower rate of stress change due to plastic deformation. The large compressive stress present in the films, if left unmanaged, could retard crack growth during nanoindentation and therefore impede the fracture toughness evaluation. To circumvent this problem, the Ge electrodes were delithiated for a short period immediately following the lithiation process. During the delithiation process, the substrate constrains the contraction of the films, causing the compressive film stress to be relieved to promote crack formation during subsequent nanoindentation.

Figure 5. (a) Fracture toughness and fracture energy of lithiated Ge electrodes as a function of the lithium concentration. (b) Comparison between the fracture energy of lithiated Ge electrodes and that of their Si counterparts as a function of the lithium concentration. Beyond an x value of 0.83 for LixGe and 1.56 for LixSi, the lithiated products do not show signs of indentation cracking due to the substantial toughening effects of lithiation.

After the electrochemical testing and film-stress measurement, the lithiated Ge electrodes were fracture tested by nanoindentation. Figure 5(a) shows the measured fracture toughness of the LixGe thin films at various levels of lithiation. At each degree of lithiation, indents with radial cracks were chosen for the fracture toughness evaluation using the Morris Model. The fracture toughness of unlithiated Ge is measured to be 0.218 MPa·m1/2, comparable in magnitude to that of typical brittle materials. As the degree of lithiation increases, the fracture toughness of lithiated Ge increases steadily, reaching 0.81 MPa·m1/2 for Li0.72Ge. The fracture energy curve of lithiated Ge is also seen to increase monotonically with the increase of lithium concentration. The increasing trend in fracture resistance indicates that LixGe undergoes a sharp brittle-to-ductile transition as lithiation proceeds. This transition as well as the extremely high ductility of LixGe thin films at high lithium concentrations (beyond x = 0.83) suggests that a cutoff voltage during delithiation can prevent fracture of the electrode material.

Figure 5(b) shows a direct comparison between the fracture energy of lithiated Ge obtained in this work and the previously measured fracture energy of lithiated Si. The fracture energy of pristine Si is 3 J/m2 which is slightly higher than that of unlithiated Ge of 2.33 J/m2. With a small amount of lithiation (x = ~0.03), the fracture energy of LixGe exceeds that of LixSi. The fracture energy difference between the two lithiation products at a given degree of lithiation increases as lithiation proceeds. This trend indicates that lithiated Ge is mechanically tougher than lithiated Si except at very low lithium concentrations. Furthermore, for both LixGe and LixSi, there is a critical lithium concentration, beyond which no electrode cracking is observed up to the maximum indentation load (93mN) of the nanoindentation setup. The critical values are approximately 1.56 for Si (Li1.56Si) and 0.83 for Ge (Li0.83Ge), which are also a clear indication of considerably higher fracture resistance of lithiated Ge. These quantitative results explain the robust behavior of Ge nanoparticles observed by the earlier in situ TEM observation [32]. Lithiated Ge is clearly seen to be intrinsically more resistant to crack initiation and propagation than lithiated Si. Therefore, the Ge particles experience no cracking after multiple discharge/charge cycles, while its Si counterparts undergo size-dependent fracture upon first lithiation. This attribute of Ge offers substantial potential for the development of durable, high-capacity, and high-rate anodes for advanced lithium-ion batteries. 

4. Nanoscale Deformation Measurement in Lithiated Silicon

Journal of Applied Mechanics 82: 121001 (2015)

Using in-situ TEM, we recently investigated the transport of lithium ions in amorphous silicon (a-Si) nanowires. We found a striking two-phase lithiation process for a-Si, which is contrary to the widely held view that the lithiation in a-Si is a single-phase process with gradual and smooth lithium profiles. We applied a full-field deformation measurement method, digital image correlation (DIC), to quantitatively analyze the lithiation process at the nanoscale. The DIC analysis revealed that the lithiation occurs by the movement of a sharp phase boundary between the a-Si reactant and an amorphous a-LixSi (x = 2.5) product. Such a striking amorphous-amorphous interface exists until the remaining a-Si is consumed. Then, a second step of lithiation sets in without a visible interface, resulting in the final product of a-LixSi (x = 3.75).

Figures. 6 (a) and (b) show two high-resolution TEM images taken at different time instants during an electrochemical lithiation experiment. The lithium flux was supplied from the top surface. The lithiation is seen to proceed by the movement of a sharp phase boundary between the a-Si reactant and an amorphous a-LixSi product. The growth kinetics of a-LixSi is controlled by two concurrent processes: (1) the reaction of Li with Si to form an initial product of LixSi at the phase boundary, and (2) the diffusion of the Li ions in the product phase region. We employed the local DIC method to analyze the diffusion-induced strain in the a-LixSi region behind the phase boundary. The image at t1 = 136 s (Fig. 6(a)) was chosen as the reference configuration and the image at t2 = 148 s (Fig. 6(b)) as the deformed configuration. Figs. 6(c) and (d) present the distributions of the two normal strain components obtained from DIC analysis. The two strain maps show fluctuations with statistical means and standard deviations of sxx = (-0.06 ± 2.93) × 10-3 and syy= (1.82 ± 1.49) × 10-3. This result also suggests that the diffusion-induced strain is negligibly small (relative to the measurement capability), and therefore nearly all of the lithiation-induced deformation occurs at the sharp reaction front.

Figure 6. Local DIC analysis of the lithium-diffusion-induced strain in a lithiated Si region. (a, b) Reference and deformed TEM images used for the DIC analysis. (c, d) Obtained sxx and syy strain contour plots superimposed on the reference TEM image as shown in (a).

Across the lithiation front, the reaction of Li with Si causes a change in the Li:Si molar ratio from zero to a finite value. The deformation induced by the reaction exhibits a large strain gradient at the sharp reaction front, which is unresolvable by the classical local DIC method. The use of local DIC in this case would result in underestimation of the deformation gradient. To resolve this issue, we developed a global DIC approach and applied it for quantifying the reaction-induced strain. The distributions of reaction-induced strain resulting from the global DIC analysis are presented in Figs. 7(b)-(d), and Fig. 7(e) shows the strain profiles across the a-Si/a-LixSi phase boundary. The lithiation front is seen to move steadily towards the a-Si region at a speed of 0.05 nm/s. Inside the reaction zone, the reaction-induced strain reaches a maximum value of 168%, which remains fairly constant as the lithiation proceeds. Invoking a linear relationship between the volumetric strain and lithium concentration, we obtain a molar Li:Si ratio of x = 2.33 in the reaction zone. 


Figure 7. Global DIC analysis of the reaction-induced strain at an a-Si/a-LixSi phase boundary. (a) The first image in a sequence of TEM images serving as the reference image for the global DIC analysis. (b-d) Obtained syy strain contour plots superimposed on the subsequent TEM images at various stages of lithiation. (e) Obtained strain profiles across the a-Si/a-LixSi phase boundary. Note that the strain analysis is made with respect to the reference image in (a). The width of the reaction zone with large strain increases as the lithiation proceeds.

5. Challenges and Outlook

The operation of an electrochemical energy storage system involves a set of complex mechanical and electrochemical processes, which are closely coupled to determine the system’s overall performance. The mechanical and chemical fields inside an electrode material are interrelated through a two-way coupling. The diffusion of guest atoms can change the atomic volume of the host solid. The interfacial reaction can also lead to volume changes due to the difference between the atomic volumes of the reactants and that of the reaction product. Volumetric deformation may induce a large amount of mechanical stress, if it occurs in a non-homogeneous manner or with external mechanical constraint. In contrast, mechanical stress may profoundly promote or retard the diffusion and reaction processes [33, 34]. Coupling between the electric and chemical fields has been largely overlooked in previous studies. However, recent TEM experiments [33] show a significant difference between the lithiation behaviors of silicon nanowires tested with or without an applied electric field. A fundamental understanding of the mechano-electrochemical coupling relationships is currently far from being complete and necessitates the development of new spatially and temporally resolved multiphysics measurement techniques. Advances in the experimental mechanics of electrochemically RBE materials will lead to the development of multiphysics modeling tools with unprecedented predictive capabilities, and ultimately accelerate the design, optimization, and manufacturing of energy storage devices.

Finally, I’d like to bring everyone’s attention to a special issue on “Mechanics of Energy Materials” that Pradeep Guduru (Brown Univ), Henry Sodano (UMich) and myself are co-editing for the Journal of Experimental Mechanics. This special issue aims to exchange the latest advances in energy materials research. The focus of the special issue will be on experimental and integrated computational/experimental investigations from the mechanics and materials prospective. An open call-for-papers has been posted on iMechanica earlier (link). More about the special issue including author guidelines and submission details can be found there. The scope of the special issue is pretty broad covering a wide range of energy materials. If you have a relevant manuscript ready or close-to-ready, please give this special issue a serious consideration. 

Please feel free to leave comments or questions here. I look forward to a lively discussion with the iMechanica community. 



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hbchew's picture

interesting article and certainly an exciting new field for mechanicians. 

Shuman_Xia's picture

Thanks, Huck Beng!

Ting Zhu's picture


An excellent review!

Lithium is the ultimate anode material for Li-ion batteries. DOE is currently very interested in the Li anode. Compared to Si, I think the mechanics issues of Li anodes are more difficult to solve. Can you comment on the mechanics of Li anodes? 




Shuman_Xia's picture

Ting, thanks for bringing up this interesting subject. Lithium metal as an anode material has the highest capacity (3.86Ah/g) and has been widely used in commercial primary (i.e., non-rechargeable) lithium batteries. However, the use of lithium in rechargeable lithium-ion batteries has mainly been hindered by dendrite growth on repeated cycling. Some computational models have recently been developed to simulate this growth process. To suppress dendrite growth, many strategies have been proposed in the past. These include coating lithium anode surfaces, forming composite Li structures, applying external pressure, and replacing conventional liquid electrolytes with polymer- or ceramic-based solid electrolytes. It is undisputable that mechanics is in a key position to implement and mainstream these methods, and it’s up to us to unlock its full potential!

Hui Yang's picture





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Dear Dr. Xia,

Thank you very much for bringing this interesting topic.

High capacity anode materials, such as silicon (Si), germanium (Ge), and tin (Sn), hold the promise to revolutionize the industry of lithium-ion batteries. However, inherent to the high-capacity electrodes, Li insertion/extraction cycling induces huge volumetric expansion and stress inside the electrodes, causing fast disintegration or cracking. For instance, fully lithiated Si undergoes about 300% volume expansion. The issue is even severer when an electrode undergoes high-rate charging or discharging, which is highly desired but often induces non-uniform Li distribution in the electrode. The resulting large incompatible deformation between areas of different Li contents tends to initiate fracture, leading to the electro-chemo-mechanical failures of the electrodes. As exposed to the electrolyte through the newly cracked surfaces, the active material in the electrodes will react with the electrolyte to form solid electrolyte interfaces (SEI) on the newly cracked surfaces, resulting in the consumption of the active material in the electrodes and subsequent capacity fading of the battery. In addition, the mechanical degradation can also cause the loss of electrical contact between active materials, current collectors, and electrolytes, leading to poor cyclability. Therefore, a fundamental understanding of the degradation mechanisms in the high-capacity anodes during lithiation/delithiation cycling is crucial for the rational design of next-generation failure-resistant electrodes. Here, I would like to share some of our previous work on these aspects.


1. Orientation-dependent interfacial mobility governs the anisotropic swelling in lithiated silicon nanowires

Through a chemo-mechanical model which couples the reaction-diffusion of lithium with the lithiation-induced elasto-plastic deformation, we demonstrated that the apparent anisotropic swelling in lithiated Si is critically controlled by the orientation-dependent mobility of the core-shell interface, i.e. the lithiation reaction rate at the atomically sharp phase boundary between the crystalline core and amorphous shell.

Yang, H., Huang, S., Huang, X., Fan, F., Liang, W., Liu, X.H., Chen, L.-Q., Huang, J.Y., Li, J., Zhu, T., Zhang, S., Orientation-Dependent Interfacial Mobility Governs the Anisotropic Swelling in Lithiated Silicon Nanowires. Nano Letters, 2012. 12(4): p. 1953-1958.

Yang, H., Fan, F., Liang, W., Guo, X., Zhu, T., Zhang, S., A chemo-mechanical model of lithiation in silicon. Journal of the Mechanics and Physics of Solids, 2014. 70(0): p. 349-361.



2. Strong coupling between lithiation kinetics and stress in lithiation of Si and Ge

Our in-situ TEM experiments along with atomistically informed continuum mechanics chemo-mechanical modeling evidenced the strong coupling between lithiation kinetics and stress generation and failure of Si and Ge electrodes. On the one hand, we showed that anisotropic lithiation in crystalline Si (c-Si) leads to anisotropic swelling and surface fracture, in contrast to isotropic lithiation, isotropic swelling, and tough behavior in c-Ge and amorphous Si (a-Si). On the other, we demonstrated that lithiation self-generated stress leads to lithiation retardation. The stronger the lithiation anisotropy, the stronger the retardation effect will be. In addition, externally applied loading can also modulate lithiation kinetics. Bending a Ge nanowire during lithiation can break the lithiation symmetry, enhancing the lithiation rate on the tensile side while suppressing it on the compressive side, both in the radial and the axial directions.

Yang, H., Fan, F., Liang, W., Guo, X., Zhu, T., Zhang, S., A chemo-mechanical model of lithiation in silicon. Journal of the Mechanics and Physics of Solids, 2014. 70(0): p. 349-361.

Liu, X.H., Fan, F., Yang, H., Zhang, S., Huang, J.Y., Zhu, T., Self-Limiting Lithiation in Silicon Nanowires. Acs Nano, 2012. 7(2): p. 1495-1503.

Liang, W., Yang, H., Fan, F., Liu, Y., Liu, X.H., Huang, J.Y., Zhu, T., Zhang, S., Tough Germanium Nanoparticles under Electrochemical Cycling. Acs Nano, 2013. 7(4): p. 3427-3433.

Yang, H., Liang, W., Guo, X., Wang, C.-M., Zhang, S., Strong kinetics-stress coupling in lithiation of Si and Ge anodes. Extreme Mechanics Letters, 2015. 2(0): p. 1-6.

Gu, M., Yang, H., Perea, D.E., Zhang, J.-G., Zhang, S., Wang, C.-M., Bending-Induced Symmetry Breaking of Lithiation in Germanium Nanowires. Nano Letters, 2014. 14(8): p. 4622-4627.



3. Self-weakening mechanism in lithiated electrodes

Besides the continuum level chemo-mechanical modelings, we also conducted molecular dynamics simulations with the reactive force field ReaxFF to investigate the fracture mechanisms of lithiated graphene and carbon nanotubes. Our simulation results reveal that Li diffusion toward the crack tip is both energetically and kinetically favored owing to the crack-tip stress gradient. The stress-driven Li diffusion results in Li aggregation around the crack tip, chemically weakening the crack-tip bond and at the same time causing stress relaxation. As a dominant factor, the chemical weakening effect manifests a self-weakening mechanism that causes the fracture of the graphene. Moreover, the variation of defect size and Li concentration sets different fracture modes of the lithiated electrodes.

Yang, H., Huang, X., Liang, W., van Duin, A.C.T., Raju, M., Zhang, S., Self-weakening in lithiated graphene electrodes. Chemical Physics Letters, 2013. 563(0): p. 58-62.

Huang, X., Yang, H., Liang, W., Raju, M., Terrones, M., Crespi, V.H., van Duin, A.C.T., Zhang, S., Lithiation induced corrosive fracture in defective carbon nanotubes. Applied Physics Letters, 2013. 103(15): p. 153901-4.



4. Experimentally and theoretically informed rational design

The previous investigations on a broad range of high-capacity energy materials have provided us the valuable insight for the rational design of new generation failure-resistant and high-performance electrodes for rechargeable batteries. For instance, we designed a hierarchically porous silicon anode to effectively alleviate the large outward volume expansion caused fracture problem of the silicon based electrode. In addition, various surface coatings were also designed to prevent the fracture of the high capacity electrodes. Furthermore, our study on the strong coupling of lithiation kinetics and stress directly motivated a novel idea of “mechanically rechargeable batteries”, leading to the successful design of a novel lithium-ion battery based mechanical energy harvesting system.

Xiao, Q., Gu, M., Yang, H., Li, B., Zhang, C., Liu, Y., Liu, F., Dai, F., Yang, L., Liu, Z., Xiao, X., Liu, G., Zhao, P., Zhang, S., Wang, C., Lu, Y., Cai, M., Inward lithium-ion breathing of hierarchically porous silicon anodes. Nat Commun, 2015. 6.

Luo, L., Yang, H., Yan, P., Travis, J.J., Lee, Y., Liu, N., Molina Piper, D., Lee, S.-H., Zhao, P., George, S.M., Zhang, J.-G., Cui, Y., Zhang, S., Ban, C., Wang, C.-M., Surface-Coating Regulated Lithiation Kinetics and Degradation in Silicon Nanowires for Lithium Ion Battery. Acs Nano, 2015. 9(5): p. 5559-5566.

Luo, L., Zhao, P., Yang, H., Liu, B., Zhang, J.-G., Cui, Y., Yu, G., Zhang, S., Wang, C.-M., Surface Coating Constraint Induced Self-Discharging of Silicon Nanoparticles as Anodes for Lithium Ion Batteries. Nano Letters, 2015. 15(10): p. 7016-7022.

Kim, S., Choi, S.J., Zhao, K., Yang, H., Gobbi, G., Zhang, S., Li, J., Electrochemically driven mechanical energy harvesting. Nat Commun, 2016. 7.



Thank you very much for reading up to this point. I look forward to your and other’s comments.


Shuman_Xia's picture

Hui, thank you very much for your comprehensive review. In your Nano Letters paper, you showed that mechanical stress could induce symmetry breaking of lithiation in germanium nanowires. In your more recent Nature Communications paper, it was demonstrated that the same stress-diffusion coupling occurs in lithiated silicon and could be harnessed for mechanical energy harvesting. This is a very creative and stimulating idea. I just wondered if you have ever considered or tried using germanium for making energe harvesting devices. Germanium has much higher Li diffusivity than silicon. Intuitively, it may exhibt greater stress-duffusion coupling and therefore offer higher envery harvesting effeciency. Any thought?

Sulin Zhang's picture

Hi Shuman, 

In our Nature Communication paper, we used nano-thick thin-film Si as the electrodes. Because of the nanoscale size, surface diffusion is domaint (and fast). Ge is certainly better; but more expensive. From a cost-effectiveness point of view, we shall seek for different forms of Si (such as nano porous Si) to improve the rate capability of the device, while make it potentially commercializable.  

Shuman_Xia's picture

Thanks for your explanation, Sulin. This makes perfect sense.

Matt Pharr's picture

Hi Shuman,

Thanks for the excellent review and excellent work in the area!  We have done a number of related experiments in the field and in general have found similar results to those you have provided in this review.  For instance, we have found values for the fracture energies of lithiated silicon and lithiated germanium that are similar to yours (in terms of order of magnitude at the very least) [1-2].  Likewise, we have also found that germanium is a good alternative to silicon in terms of its enhanced resistance to fracture [2]. Still, there are some small differences among studies from literature.  For instance, in our studies on the fracture energy of lithiated silicon, we did not find a substantial change in the fracture energy as a function of lithium concentration [1]. We found similar results in terms of the fracture energy of lithiated germanium but did find that the flow stress in lithiated germanium is significantly smaller than in silicon for the same loading conditions (same state of charge, charging rate, and film thickness) [2].  As a result, the crack driving forces at these same conditions are substantially smaller for germanium as compared to silicon (since crack driving force scales with the square of the stress), rendering germanium a good alternative to silicon in terms of avoiding fracture during cycling [2].

It is great to see general agreement among the experiments in literature, despite taking quite different approaches to the measurements!  However, I am curious about your thoughts on the slight differences among our observations.  One potential explanation:  the properties (flow stress, perhaps fracture energy?) depend on the loading rate.  For instance, it has been found that these materials readily creep [3-5].  As a result, if we load faster, we develop more stress.  In our experiments, we use relatively slow charging rates (e.g., C/16) which effectively impose small loading rates on the electrodes.  In comparing to your experiments, in which you perform in-situ TEM (which typically involve very high charging rates) or nanoindentation experiments (which impose much larger strain-rates than in our experiments), it is possible that larger stresses develop.  The results of studies [3]-[5] imply different physics (e.g., atomic arrangement) at different loading rates – could this lead to varying fracture energy at varying loading rates?

Other potential explanations are different materials, for instance by different approaches to fabrication of the electrodes, or different models used to calculate the values (e.g., analysis by Beuth for fracture of a film on a substrate, Morris model for fracture during indentation, etc.).  Any thoughts here?



[1]  Pharr, Suo, and Vlassak.  “Measurements of the fracture energy of lithiated silicon electrodes of Li-ion batteries,” Nano Letters, 13 (11), 2013.

[2]  Pharr, Choi, Lee, Oh, and Vlassak.  “Measurements of stress and fracture in germanium electrodes of lithium-ion batteries during electrochemical lithiation and delithiation,” Journal of Power Sources, 304, 2016.

[3] Boles, Thompson, Kraft, and Monig, “In situ tensile and creep testing of lithiated silicon nanowires,” Applied Physics Letters, 103, 2013.

[4] Pharr, Suo, and Vlassak, “Variation of stress with charging rate due to strain-rate sensitivity of silicon electrodes of Li-ion batteries,” Journal of Power Sources, 270, 2014.

[5] Berla, Lee, Cui, and Nix, “Mechanical behavior of electrochemically lithiated silicon,” Journal of Power Sources, 273, 2015.


Shuman_Xia's picture

Matt, congratulations on your new faculty position! It’s indeed great to see we have found similar results from very different approaches. You have made some very good points to explain the slight difference between our observations at elevated Li concentrations. I agree that the loading rate plays an important role in the fracture properties of lithiated electrode materials. The lithiated materials in our TEM and nanoindentation experiments were mechanically loaded within a few minutes, while your samples were loaded at a much lower rate using electrochemical lithiation. Another possible cause I have thought about is the difference in the stress states between our samples. Your electrode films were subjected to biaxial stress during fracture testing. For our TEM and nanoindentation samples, the stress state was close to uniaxial state. In conventional fracture mechanics of metals, the stress state at a crack tip is known to have a great influence on the fracture toughness due to its effect on microvoid nucleation and coalescence. Similarly, lithiated materials may exhibits some kind of stress-state dependence but its physical origin may differ from metallic fracture and warrants further investigation.

Matt Pharr's picture

Thanks for your response!  I completely agree with you that a better physical explanation of the mechanism of fracture of these materials is vital. Perhaps we can do some experiments to investigate microstructural features associated with the fracture process and in turn shine some light on differences among other experimental observations at the macro-level.

Sulin Zhang's picture

Hi Shuman,

A very nice review on the experimental side of the mechanics of anodes for lithium ion batteries. I am pround to see that our mechanicians have done a great job in evovling the field and helping electrochemists understand the electrochemical behavior of the large-volume-change anode materials. 

Two borthering, but valid questions remain. One is the SEI formation, the other is the pore formation (ubiquitous in almost all the anode materials) during delithiation. The first question is obvious but our mechanicians rarely touch it (constantly complained by electrochemists in our proposals). The second question is less obvious, but we often see that the lithiation behavior (for exmaple, amorphous Si) is very different during the first and subsequent cycles, indicating its importance. Can our experimentalists help solving these problems before moving to other battery forms (such as Li-air) ? 


Shuman_Xia's picture

Very nice points, Sulin. Microstructure evolution such as pore formation is of vital importance for battery cyclability. I read your recent Nature Communications paper on hierarchically porous silicon anodes and were quite amazed by the superior performance of these anodes. Regarding your point on SEI, I agree that it is indeed a far less studied research area. A big challagenge from the experimental point of view is that SEI suffers from decomposition once it's removed from liquid electrolyte. Ideally, the chemo-mechanical properties of SEI films need to be studied in situ and in operando. However, this remains difficult with the current experimental capabilities. A possible solution may lie in integrating experimental measurement with large scale atomistic modeling to provide a comprehensive picture of SEI formation and evolution. 

Hello Shuman and Sulin

Thanks for pointing the importance of SEI formation. Unfortunately formation of SEI layer and  influence of  its mechanical and electrochemical properties on the battery performance need to be study more.  I agreed with Dr. Shuman that new in-situ experimental methods is required to investigate the chemo-mechanical properties of the SEI layer. Recently, Guduru and his co-workers published a journal in the adv. energy mat., 2016, 6, 16000099. They used the AFM technique to track the formation of SEI layer on the silicon electrode, and their results showed that irreversible SEI formation takes place dominantly during the first lithiation cycle.  Another new technique to probe the irreversible changes in the electrodes is the in-situ strain measurements. Recently, E. Jones and I published a paper about the irreversible changes in the graphite electrode (JES 163 A1965 2016). Irreversible strain generated during cycling increases with increasing surface area and cycling time. It means that at a given voltages, SEI layer forms thicker at slow scan rates.  Interestingly, choice of binder has a great influence on the irreversible strain generation, suggest that SEI layer formation is affected by type of polymer binder.   Dr. Shuman, I am wondering that did you have a chance to investigate the influence of SEI layer on fracture toughness of the electrodes yet ? I also want to specially thank Dr. Shuman for organizing the special edition in the SEM journal. 





Hello Shuman and Sulin

Thanks for pointing the importance of SEI formation. Unfortunately I agreed with Dr. Shuman that 

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