In Situ Measurements of Strains in Composite Battery Electrodes during Electrochemical Cycling

The cyclic stress in lithium-ion battery electrodes induced by repeated charge and discharge cycles causes electrode degradation and fracture, resulting in reduced battery performance and lifetime. To investigate electrode mechanics as a function of electrochemical cycling, we utilize digital image correlation (DIC) to measure the strains that develop in lithium-ion battery electrodes during lithiation and delithiation processes. A composite graphite electrode is cycled galvanostatically (with constant current) in a custom battery cell while optical images of the electrode surface are captured in situ. The strain in the electrode is computed using an in-house DIC code. On average, an unconstrained composite graphite electrode expands 1.41 % during lithiation and contracts 1.33 % during delithiation. These strain values compare favorably with predictions based on the elastic properties of the composite electrode and the expansion of graphite-lithium intercalation compounds (G-LICs). The establishment of this experimental protocol will enable future studies of the relationship between electrode mechanics and battery performance.     

柱状电极屈曲或裂纹扩展的临界力学参数研究

柱形结构电极是近年来使用最为广泛的锂电池电极结构之一．本文以硅材料细长柱形电极为例，研究了充电电流大小、电极长径比、初始裂纹长度以及断裂韧性对于电极的屈曲现象和裂纹扩展现象发生时间的影响．计算结果表明，屈曲与裂纹扩展现象出现的先后顺序与充电电流大小无关；具有小的长径比，大的初始裂纹长度以及较小断裂韧性的电极，裂纹扩展比屈曲现象更早发生．对于硅材料，不同长径比的电极具有不同临界断裂韧性值，当材料的断裂韧性小于该临界值，在锂化过程中裂纹扩展会先于屈曲现象发生；该临界断裂韧性值随初始裂纹长度的增加而增加．本文的结论对于电极的结构设计以及材料选取具有一定指导意义．     

Phase-field model for the two-phase lithiation of silicon

As an ideal anode material, silicon has the highest lithium-ion capacity in theory, but the broader application is limited by the huge volumetric strain caused by lithium insertion and extraction. To better understand the physical process and to resolve the related reliability issue, enormous efforts have been made. Recent experiments observed sharp reaction fronts in both crystalline and amorphous silicon during the first lithiation half-cycle. Such a concentration profile indicates that the process is likely to be reaction limited. Based on this postulation, a phase-field model is developed and implemented into a finite-element code to simulate the coupled large inelastic deformation and motion of the reaction front in a silicon electrode. In contrast to most existing models, the model treats both volumetric and deviatoric inelastic deformation in silicon as a direct consequence of the lithiation at the reaction front. The amount of deviatoric deformation is determined by using the recently developed kinetic model of stress-induced anisotropic reaction. By considering the role of stress in the lithiation process, this model successfully recovers the self-limiting phenomenon of silicon electrodes, and relates it to the local geometry of electrodes. The model is also used to evaluate the energy-release rate of the surface crack on a spherical electrode, and the result suggests a critical size of silicon nanoparticles to avert fracture. As examples, the morphology evolution of a silicon disk and a Si nanowire during lithiation are also investigated.     

Strain Evolution in Lithium Manganese Oxide Electrodes

Lithium manganese oxide, LiMn₂O₄ (LMO) is a promising cathode material, but is hampered by significant capacity fade due to instability of the electrode-electrolyte interface, manganese dissolution into the electrolyte and subsequent mechanical degradation of the electrode. In this work, electrochemically-induced strains in composite LMO electrodes are measured using the digital image correlation (DIC) technique and compared with electrochemical impedance spectroscopy (EIS) measurements of surface resistance for different scan rates. Distinct, irreversible strain variations are observed during the first delithiation cycle. The changes in strain and surface resistance are highly sensitive to the electrochemical changes occurring during the first cycle and correlate with prior reports of the removal of the native surface layer and the formation of cathode-electrolyte interface layer on the electrode surface. A large capacity fade is observed with increasing cycle number at high scan rates. Interestingly, the total capacity fade scales proportionately to the strain generated after each lithiation and delithiation cycle. The simultaneous reduction in capacity and strain is attributed to chemo-mechanical degradation of the electrode. The in situ strain measurements provide new insight into the electrochemical-induced volumetric changes in LMO electrodes with progressing cycling and may provide guidance for materials-based strategies to reduce strain and capacity fade.     

Stress-mediated lithiation in nanoscale phase transformation electrodes

Development of high-performance phase transformation electrodes in lithium ion batteries requires comprehensive studies on stress-mediated lithiation involving migration of the phase interface. It brings out many counter-intuitive phenomena, especially in nanoscale electrodes, such as the slowing down migration of phase interface, the vanishing of miscibility gap under high charge rate, and the formation of surface crack during lithiation. However,it is still a challenge to simulate the evolution of stress in arbitrarily-shaped nanoscale electrodes, accompanied with phase transformation and concurrent plastic deformation. This article gives a brief review of our efforts devoted to address these issues by developing phase field model and simulation. We demonstrate that the miscibility gap of two-phase state is affected not only by stress but also by surface reaction rate and particle size. In addition, the migration of phase interface slows down due to stress. It reveals that the plastic deformation generates large radial expansion, which is responsible for the transition from surface hoop compression to surface hoop tension that may induce surface crack during lithiation.We hope our effort can make a contribution to the understanding of stress-coupled kinetics in phase transformation electrodes.     

In-situ Strain Field Measurement and Mechano-electro-chemical Analysis of Graphite Electrodes Via Fluorescence Digital Image Correlation

Background

Mechano-electro-chemical coupling during the ion diffusion process is a core factor to determine the electrochemical performance of electrodes. However, relationship between the mechanics and the electrochemistry has not been clarified by experiments.

Objective

In this work, we conduct an in situ, visual, comprehensive characterization of strain field and Li concentration distribution to further explore the mechano-electro-chemical relationship.

Methods

The digital image correlation characterized by fluorescent speckle and active optical imaging is developed. Combined with electrochromic-based Li concentration detection, the spatiotemporal evolution of in-plane strain and Li concentration of a graphite electrode during the lithiation and delithiation processes are measured and displayed visually via a dual optical path acquisition system.

Results

The visual results show that in-plane strain and Li concentration possess a spatially non-uniform gradient distribution along the radial direction (i.e., diffusion path) with large values outside and small values inside, and that both present obvious temporal segmentation. And mechano-electro-chemical coupling analysis reveals that the in-plane strain is not always linearly related to the concentration and infers that a high strain limits the diffusion and lithiation. The strain–concentration evolution exhibits obvious asymmetric differences between lithiation and delithiation, wherein three equations are fitted to approximately represent the evolution process between in-plane strain and concentration during the lithiation and delithiation processes

Conclusions

This work overcomes the difficulties of fine strain measurements and collaborative concentration characterization during the electrochemical process, and provides an effective experimental method and data support for further exploration of mechano-electro-chemical coupling.

     

Cracking mechanisms in lithiated silicon thin film electrodes

The massive cracking of silicon thin film electrodes in lithium ion batteries is associated with the colossal volume changes that occur during lithiation and delithiation cycles. However, the underlying cracking mechanism or even whether fracture initiates during lithiation or delithiation is still unknown. Here, we model the stress generation in amorphous silicon thin films during lithium insertion, fully accounting for the effects of finite strains, plastic flow, and pressure-gradients on the diffusion of lithium. Our finite element analyses demonstrate that the fracture of lithiated silicon films occurs by a sequential cracking mechanism which is distinct from fracture induced by residual tension in conventional thin films. During early-stage lithiation, the expansion of the lithium-silicon subsurface layer bends the film near the edges, and generates a high tensile stress zone at a critical distance away within the lithium-free silicon. Fracture initiates at this high tension zone and creates new film edges, which in turn bend and generate high tensile stresses a further critical distance away. Under repeated lithiation and delithiation cycles, this sequential cracking mechanism creates silicon islands of uniform diameter, which scales with the film thickness. The predicted island sizes, as well as the abrupt mitigation of fracture below a critical film thickness due to the diminishing tensile stress zone, is quantitatively in good agreement with experiments.     

Pressure-sensitive plasticity of lithiated silicon in Li-ion batteries

Lithiation-induced plasticity is a key factor that enables Si electrodes to maintain long cycle life in Li-ion batteries. We study the plasticity of various lithiated sili-con phases based on first-principles calculations and iden-tify the linear dependence of the equivalent yield stress on the hydrostatic pressure. Such dependence may cause the compression-tension asymmetry in an amorphous Si thin film electrode from a lithiation to delithiation cycle, and leads to subsequent ratcheting of the electrode after cyclic lithiation. We propose a yield criterion of amorphous lithi-ated silicon that includes the effects of the hydrostatic stress and the lithiation reaction. We further examine the micro-scopic mechanism of deformation in lithiated silicon under mechanical load, which is attributed to the flow-defects mediated local bond switching and cavitation. Hydrostatic compression confines the flow defects thus effectively strength-ens the amorphous structure, and vice versa.     

Three-Dimensional Study of Graphite-Composite Electrode Chemo-Mechanical Response using Digital Volume Correlation

A custom built reusable cell for in situ lithiation and mechanical deformation studies while in an X-ray tomograph was demonstrated, and the strain and volume changes of a composite graphite anode were computed from 3D X-ray microcomputed tomography data via Digital Volume Correlation (DVC). The test anode was a composite electrode comprised of a porous compliant matrix, graphite as the Li⁺ host material, 5-μm ZrO₂ marker particles for use with DVC, and active carbon black to enhance electrical conductivity. The composite electrodes were hot-pressed to control their porosity, and in turn the mechanical integrity of the resulting material. This composite anode was included in a half-cell and lithiated in situ while in a tomograph, and intermittent 3D data were collected at different lithiation levels up to full gravimetric capacity. Strain measurements by DVC demonstrated relatively uniform expansion of the freestanding electrode with average normal strains in the three directions varying by 20%, while the internal shear strains were found to be negligible. The average experimental strains were about 75% of the theoretical value, as estimated by the rule of mixtures, which implies that ~25% of the normal strains in graphite, due to lithiation, are accommodated by the surrounding matrix.     

A Cahn–Hilliard-type theory for species diffusion coupled with large elastic–plastic deformations

We develop a unified framework of balance laws and thermodynamically consistent constitutive equations which couple Cahn–Hilliard-type species diffusion with large elastic–plastic deformations of a body, and account for the swelling and phase segregation caused by the diffusing species.A potential, technologically important, area of application of the theory is in the chemo-mechanical analysis of the evolution of large stresses which develop because of the volume changes associated with the diffusion of lithium ions in the active electrode particles of lithium-ion batteries during charge–discharge cycles.     

金属蜂窝夹层结构抗水下爆炸特性

金属蜂窝夹层结构是一种新型的舰船防护结构,在舰船防护领域具有广阔的应用前景,但目前缺乏对其在实际水下爆炸载荷作用下动态响应的研究。为研究金属蜂窝夹层结构在水下爆炸载荷作用下的动态响应及防护性能,设计并制备了背板加筋蜂窝夹层结构样件以及相应的浮箱,在大型露天水池中进行了水下实爆 实验;通过声固耦合算法对结构响应进行模拟,实验结果与模拟结果吻合良好,随后分析了蜂窝夹层板的变形过程及能量吸收特性,量化了载荷参数（冲击因子）及结构参数（前后面板厚度比和芯体相对密度）对结构动态响应的影响;最后,以蜂窝夹层板的面密度和后面板中心点最大变形的无量纲量为目标函数,使用NSGA-Ⅱ遗传算法对结构进行了多目标优化,得到对应的Pareto前沿。结果表明,随着冲击因子的增大,蜂窝夹层板整体变形显著增大,蜂窝芯体始终是主要的吸能构件,但其吸能占比逐渐降低;随着前后面板厚度比或芯体相对密度的增加,蜂窝夹层结构的最大变形呈现先降低后升高的趋势,同时呈现不同的变形模式,芯体相对密度对结构变形的影响更为显著;对蜂窝夹层结构开展多目标优化可有效降低结构的面密度及最大变形,优化结果可为蜂窝夹层结构的设计选型提供参考。     

Approximate analysis of progressive deformation in honeycomb structures subjected to in-plane loading

Progressive deformation of honeycomb structures subjected to in-plane loading was approximately analyzed by using the collapse modes of hexagonal unit cells. The collapse modes were categorized as freely compressive, restricted compressive, and shear. Moreover, there were five characteristic deformation patterns, namely deformation bands. Average stresses of the collapsing honeycomb models were evaluated in terms of the plastic collapse stress per hinge and total number of hinges of progressively arising deformation bands. The displacements of the models were obtained by multiplying the displacement per cell with the number of collapsed cells. The present method was used to analyze progressive deformation of typical honeycomb structures. The validity of the stress–displacement relations derived for some structures was confirmed by comparing them with finite element method (FEM) results. Our method is much simpler than FEM but just as effective.     

Real-Time Stress Measurement in SiO<Subscript>2</Subscript> Thin Films during Electrochemical Lithiation/Delithiation Cycling

Oxide coatings have been shown to improve the cyclic performance of high-energy density electrode materials such as Si. However, no study exists on the mechanical characterization of these oxide coatings. Here, thin film SiO₂ electrodes are cycled under galvanostatic conditions (at C/9 rate) in a half-cell configuration with lithium metal foil as counter/reference electrode, with 1 M LiPF₆ in ethylene carbonate, diethyl carbonate, dimethyl carbonate solution (1:1:1, wt%) as electrolyte. Stress evolution in the SiO₂ thin film electrodes during electrochemical lithiation/delithiation is measured in situ by monitoring the substrate curvature using a multi-beam optical sensing method. Upon lithiation SiO₂ undergoes extensive inelastic deformation, with a peak compressive stress of 3.1 GPa, and upon delithiation the stress became tensile with a peak stress of 0.7 GPa. A simple plane strain finite element model of Si nanotube coated with SiO₂ shell was developed to understand the mechanical response of the core-shell type microstructures under electrochemical cycling; measured stress response was used in the model to represent SiO₂ constitutive behavior while Si was treated as an elastic-plastic material with concentration dependent mechanical properties obtained from the literature. The results reported here provide insights and quantitative understanding as to why the highly brittle SiO₂ coatings are able to sustain significant volume expansion (300%) of Si core without fracture and enhance cyclic performance of Si reported in the literature. Also, the basic mechanical properties presented here are necessary first step for future design and development of durable Si/SiO₂ core shell structures or SiO₂-based electrodes.     

Stochastic many-particle model for LFP electrodes

In the framework of non-equilibrium thermodynamics, we derive a new model for many-particle electrodes. The model is applied to \(\text {LiFePO}_{4}\) (LFP) electrodes consisting of many LFP particles of nanometer size. The phase transition from a lithium-poor to a lithium-rich phase within LFP electrodes is controlled by both different particle sizes and surface fluctuations leading to a system of stochastic differential equations. An explicit relation between battery voltage and current controlled by the thermodynamic state variables is derived. This voltage–current relation reveals that in thin LFP electrodes lithium intercalation from the particle surfaces into the LFP particles is the principal rate-limiting process. There are only two constant kinetic parameters in the model describing the intercalation rate and the fluctuation strength, respectively. The model correctly predicts several features of LFP electrodes, viz. the phase transition, the observed voltage plateaus, hysteresis and the rate-limiting capacity. Moreover we study the impact of both the particle size distribution and the active surface area on the voltage–charge characteristics of the electrode. Finally we carefully discuss the phase transition for varying charging/discharging rates.     

Analysis of diffusion induced elastoplastic bending of bilayer lithium-ion battery electrodes

Bilayer electrode, composed of a current collector layer and an active material layer, has great potential in applications of in-situ electrochemical experiments due to the bending upon lithiation. This paper establishes an elastoplastic theory for the lithiation induced deformation of bilayer electrode with consideration of the plastic yield of current collector. It is found that the plastic yield of current collector reduces the restriction of current collector to an active layer, and therefore, enhances in-plane stretching while lowers down the rate of electrode bending. Key parameters that influence the elastoplastic deformation are identified. It is found that the smaller thickness ratio and lower elastic modulus ratio of current collector to an active layer would lead to an earlier plastic yield of the current collector, the larger in-plane strain, and the smaller bending curvature, due to balance between the current collector and the active layer. The smaller yield stress and plastic modulus of current collector have similar impacts on the electrode deformation.     

Concentration of electric field near electrodes on piezoelectric layer

This paper aims at the study of electric field concentration near the edge of the electrodes for a piezoelectric layer. For simplicity, attention is focussed on a piezoelectric layer that is bonded to a rigid, conductive substrate and then covered by a pair of conductive electrodes on the surface. The analysis is performed within the scope of linear piezoelectricity. Fourier transform technique is applied to reduce the boundary value problem to a pair of dual integral equations. An analytical solution to the integral equations is obtained by using an iteration method. Numerical results for distributions of stresses and electric fields are displayed and discussed.     

Cyclic plasticity and shakedown in high-capacity electrodes of lithium-ion batteries

Of all materials, silicon has the highest capacity to store lithium, and is being developed as an electrode for lithium-ion batteries. Upon absorbing a large amount of lithium, the electrode swells greatly, with a volumetric change up to 300%. The swelling is inevitably constrained in practice, often leading to stress and fracture. Evidence has accumulated that the swelling-induced stress can be partially relieved by plastic flow, and that electrodes of small feature sizes can survive many cycles of lithiation and delithiation without fracture. Here we simulate a particle of an electrode subject to cyclic lithiation and delithiation. A recently developed theory of concurrent large swelling and finite-strain plasticity is used to co-evolve fields of stress, deformation, concentration of lithium, and chemical potential of lithium. We identify three types of behavior. When the yield strength is high and the charging rate is low, the entire particle deforms elastically in all cycles. When the yield strength is low and the charging rate is high, the particle (or part of it) undergoes cyclic plasticity. Under intermediate conditions, the particle exhibits the shakedown behavior: part of the particle flows plastically in a certain number of initial cycles, and then the entire particle remains elastic in subsequent cycles. We discuss the effect of the three types of behavior on the capacity and the electrochemical efficiency.     

Size-dependent fracture of Si nanowire battery anodes

We use a unique transmission electron microscope (TEM) technique to show that Si nanowires (NWs) with diameters in the range of a few hundred nanometers can be fully lithiated and delithiated without fracture, in spite of the large volume changes that occur in this process. By analyzing the stresses associated with lithiation and delithiation we conclude that the process does not occur by the growth of discrete crystalline phases; rather it occurs by amorphization of the Si NWs followed by diffusion of Li into the structure. By accounting for the large deformation associated with this process and by including the effects of pressure gradients on the diffusion of Li, we show that Si NWs with diameters less than about 300 nm could not fracture even if pre-existing cracks were present in the NW. These predictions appear to be in good agreement with the experiment.     

Balancing particle properties for practical lithium-ion batteries

As a state-of-the-art secondary battery, lithium-ion batteries (LIBs) have dominated the consumer electronics market since Sony unveiled the commercial secondary battery with LiCoO₂ as the negative electrode material in the early 1990s. The key to the efficient operation of LIBs lies in the effective contact between the Li-ion-rich electrolyte and the active material particles in the electrode. The particle properties of the electrode materials affect the lithium ion diffusion path, diffusion resistance, contact area with the active material, the electrochemical performance and the energy density of batteries. To achieve satisfied comprehensive performance and of LIBs, it is not only necessary to focus on the modification of materials, but also to balance the properties of electrode material particles. Therefore, in this review, we analyze the influence of particle properties on the battery performance from three perspectives: particle size, particle size distribution, and particle shape. A deep understanding of the effect and mechanism of particles on electrodes and batteries will help develop and manufacture practical LIBs.     

Strong dependency of lithium diffusion on mechanical constraints in high-capacity Li-ion battery electrodes

The effect of external constraints on Li diffusion in high-capacity Li-ion battery electrodes is investigated us- ing a coupled finite deformation theory. It is found that thin- film electrodes on rigid substrates experience much slower diffusion rates compared with free-standing films with the same material properties and geometric dimensions. More importantly, the study reveals that mechanical driving forces tend to retard diffusion in highly-constrained thin films when lithiation-induced softening is considered, in contrast to the fact that mechanical driving forces always enhance diffusion when deformation is fully elastic. The results provide further proof that nano-particles are a better design option for next-generation alloy-based electrodes compared with thin films.