Diffusion-induced Stress Research Articles

Transient analysis of diffusion-induced stress: effect of solid reaction

The chemical reactions taking place in lithium-ion batteries can trap lithium and alter the distribution of lithium and the deformation of the electrode during electrochemical charging and discharging. In this work, we incorporate the strain generated by chemical reactions in the transient analysis of diffusion-induced stress and numerically solve the one-dimensional problem under galvanostatic and potentiostatic operations, respectively. The numerical results show that both the diffusion and local chemical reaction contribute to the expansion of the electrode. Under the potentiostatic operation, lithiation introduces a stress spike at the fixed end at the onset of the lithiation. The chemical reactions play a significant role in controlling the temporal evolution of lithium and the deformation of electrode, which needs to be taken into account in the analysis of structural durability of lithium-ion batteries.

Size-dependent effects sensitively determine buckling of a cylindrical silicon electrode particle in a lithium-ion battery

The influence of size-dependent effects on mechanical behavior of a cylindrical silicon electrode particle within a lithium-ion battery is investigated, and it is shown that these effects sensitively determine critical buckling behavior. The mathematical framework used for this investigation incorporates the bond-order-length-strength (BOLS) theory correlation in a general finite deformation theory model that includes the two-way coupling between diffusion-induced stress and stress-influenced diffusion. Additionally, the possibility of plastic flow is accounted for in the model to allow probing situations with relatively high charging rates. Significant differences, arising due to the consideration of the size-dependent effects and captured through the BOLS theory, are highlighted. In particular, it is found that, in most cases studied, both stresses and plastic stretches are amplified in magnitude. Tensile to compressive stress reversal also takes place faster on considering the BOLS theory. The modeling framework is further applied to estimate critical lengths that are safe against buckling. Thus, it is expected that the presented framework will provide an improved aid for the design of nanowire-based lithium ion battery silicon electrodes.

Low-temperature aging mechanisms of commercial graphite/LiFePO4 cells cycled with a simulated electric vehicle load profile—A post-mortem study

Abstract Reduced cycle life is one of the issues hindering the adoption of large lithium-ion battery systems in cold-climate countries. Thus, the aging mechanisms of commercial graphite/LiFePO4 (lithium iron phosphate) cells at low temperatures (room temperature, 0 °C and−18 °C) are investigated here through an extended post-mortem analysis. The cylindrical 2.3 Ah cells were cycled with a simulated battery electric vehicle load profile, and the aged cells were then disassembled inside an argon-filled glove box. A non-cycled cell was also dismantled as a reference. Half-cell testing was utilized to evaluate the degradation of the electrochemical performance of the electrodes, whereas X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectroscopy, inductively coupled plasma optical emission spectroscopy and Raman spectroscopy were used to characterize the changes in the materials properties. The full-cell performance loss was mostly seen as capacity fade whereas significant changes in the cell impedance were not observed. Depending on the cycling temperature, loss of cyclable lithium due to solid electrolyte interphase growth and/or lithium plating on the graphite electrode were observed, and they are attributed as the main mechanisms responsible for the capacity loss. Furthermore, increased disordering of the graphite electrode was observed for the cell cycled at −18 °C. The graphite disordering was hypothesized to result from diffusion-induced stress and the mechanical stress caused by severe lithium plating. In contrast, the LiFePO4 electrodes showed only minimal signs of degradation regardless of the cycling temperature.

From sand to fast and stable silicon anode: Synthesis of hollow Si@void@C yolk–shell microspheres by aluminothermic reduction for lithium storage

As an alloying type anode material, silicon is a promising alternative of graphitic carbon due to its high theoretical capacity and natural abundance. Developing an industrially viable silicon anode, however, is still a huge challenge because of several problems: First of all, the common process to synthesize a silicon anode is complicated, costly, and energy-intensive. Besides, the huge volume expansion, inevitable side reactions with the electrolyte, and low intrinsic conductivity of silicon are eventually responsible for the poor cyclability and unsatisfactory rate capability. Herein, we aim to address these issues by proposing synthesis of hollow Si@void@C yolk–shell microspheres from sand by low-temperature aluminothermic reduction, which energetically combines a cost-effective silicon source with an energy-efficient, high-yield methodology. The hollow Si@void@C yolk–shell microspheres effectively accommodate the diffusion-induced stress by providing the hollow interior and the void space. Moreover, the carbon shell not only functions as an electrolyte-blocking layer to protect the silicon yolk from undesirable side reactions and SEI formation, but also acts as a conductive framework to reduce the resistance to electron and Li+ ion transport. Benefiting from these synergistic effects, the hollow Si@void@C yolk–shell microspheres exhibit superior long-term cyclability and rate capability.

Coupled Mechanical and Electrochemical Analyses of Three-Dimensional Reconstructed LiFePO4 by Focused Ion Beam/Scanning Electron Microscopy in Lithium-Ion Batteries

Limited lifetime and performance degradation in lithium ion batteries in electrical vehicles and power tools is still a challenging obstacle which results from various interrelated processes, especially under specific conditions such as higher discharging rates (C-rates) and longer cycles. To elucidate these problems, it is very important to analyze electrochemical degradation from a mechanical stress point of view. Specifically, the goal of this study is to investigate diffusion-induced stresses and electrochemical degradation in three-dimensional (3D) reconstructed LiFePO4. We generate a reconstructed microstructure by using a stack of focused ion beam-scanning electron microscopy (FIB/SEM) images combined with an electrolyte domain. Our previous two-dimensional (2D) finite element model is further improved to a 3D multiphysics one, which incorporates both electrochemical and mechanical analyses. From our electrochemistry model, we observe 95.6% and 88.3% capacity fade at 1.2 C and 2 C, respectively. To investigate this electrochemical degradation, we present concentration distributions and von Mises stress distributions across the cathode with respect to the depth of discharge (DoD). Moreover, electrochemical degradation factors such as total polarization and over-potential are also investigated under different C-rates. Further, higher total polarization is observed at the end of discharging, as well as at the early stage of discharging. It is also confirmed that lithium intercalation at the electrode-electrolyte interface causes higher over-potential at specific DoDs. At the region near the separator, a higher concentration gradient and over-potential are observed. We note that higher over-potential occurs on the surface of electrode, and the resulting concentration gradient and mechanical stresses are observed in the same regions. Furthermore, mechanical stress variations under different C-rates are quantified during the discharging process. With these coupled mechanical and electrochemical analyses, the results of this study may be helpful for detecting particle crack initiation.

Cohesive zone model for crack propagation in crystalline silicon nanowires

A fracture of the active particle such as silicon anode results in a potential degradation in lithium-ion batteries with charge/discharge cycle. The massive volume expansion during the lithiation generates large stress which induces the cracking on its surface. We propose the finite element model to have a deep insight into the diffusion-induced stress with fracture process for crystalline silicon nanowires. This model is constructed based on the large deformation theory and cohesive zone model that can describe the failure of Si nanowires. At the beginning of lithiation, high compressive hoop stress is generated on its surface. However, further lithiation, the hoop stress near the surface become less compressive and tensile, which is associated with the “push out effect” as a result of the volume expansion of lithiated material near the phase boundary. When the diffusion induced tensile stress exceeds the fracture threshold, a crack is initiated on the surface and propagates continuously to the center of the silicon nanowire. This crack follows the phase boundary rapidly, but the crack growth speed decreases due to the neighboring compressive hoop stress generated near the phase boundary. From the observation of failure mechanism in Si, we characterize a critical size of Si nanowire, below which fracture can be averted, and we suggest a safe state of charge (safe SOC) depending on its radial size during lithiation.

Coupled Mechanical and Electrochemical Analyses of Reconstructed LiFePO4 By FIB/SEM in Lithium-Ion Battery

For an energy storage application such as electrical vehicles (EVs), lithium-ion batteries must overcome limited lifetime and performance degradation under specific conditions. Particularly, lithium-ion batteries show significant capacity loss at higher discharging rates (C-rates). In this work, we develop computational models incorporating coupled electrochemical-mechanical-thermal factors in order to reveal the relationship between the experimentally observed capacity loss and predicted mechanical stresses during electrochemical (dis)charging. Specifically, a multiphysics finite element model consisting of electrochemistry, heat generation, mass transport, and solid mechanics is developed to investigate thermal- and diffusion-induced stresses with the reconstructed porous microstructures of commercial LiFePO4 batteries. It has been suggested that porous microstructures in electrodes could mitigate the electrolyte reactivity for an improved battery life and safety. Therefore, the reconstructed porous microstructures from Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) images are adopted. The integrated experimental measurements and computational simulations show that: (1) lithium-ion cells electrochemically tested at 3.6C have 30% capacity loss versus cells tested at 1.2C; a corresponding stress increase of 150% is observed from the multiphysic simulations, (2) the thermal models verified by in operando temperature measurement via the fiber Bragg grating (FBG) sensor demonstrate that increasing temperature results in larger thermal stresses during (dis)charging. However, increases in thermal stress due to higher temperature played a lesser role at higher C-rates, (3) lithium ion concentration distribution is location dependent, that is, at any time and at any given C-rates, the outer layer of the particle exhibits a higher concentration than that inside the particle, and (4) higher diffusion-induced stresses are observed at the connecting areas between particles, suggesting that the higher stresses may result from higher concentration variations in the connecting area. This study presents results that include evolutions of lithium ion concentration and mechanical stresses and could help to provide insight into the decreasing electrochemical performance of lithium-ion batteries at higher C-rates.

Statistical physics-based model of mechanical degradation in lithium ion batteries

The article presents a statistical model of mechanical degradation in the negative electrode of lithium ion batteries. During battery operation, nano-cracks nucleate and grow caused by the impact of diffusion-induced stress during Li-ion intercalation. Particle agglomeration is another mechanical effect that contributes to morphological changes. The presented model employs a population balance formalism to describe the propagation of the particle density distribution function in the electrode. A set of kinetic and transport equations accounts for structure-transforming processes at the level of individual particles. These processes alter the particle density distribution function, and cause changes in battery performance. A parametric study reveals the population of small particles and the width of the initial particle size distribution (PSD) as the main parameters that determine changes in electrochemical performance and capacity fade. The model is applied to experimental data in order to isolate and quantify the impact of various degradation mechanisms.

Submicro-sized Si–Ge solid solutions with high capacity and long cyclability for lithium-ion batteries

Abstract

A coupled electrochemical–thermal–mechanical model for spiral-wound Li-ion batteries

In order to clarify the interaction of electrochemistry, thermal and diffusion-induced stress, in this work, we present a coupled electrochemical–thermal–mechanical model for spiral-wound Li batteries by coupling the mass, charge, energy and mechanics conservations as well as the electrochemical kinetics. A series of temperatures and Li concentration parameters on the reaction rate and Li+ transport are employed in this model. The results show that this model is validated for both the electrochemical performances and thermal behaviors at a constant discharge current by finite element simulation. Furthermore, the heat generation of three thermal sources and stress analysis are also discussed. This work is helpful to the battery structural design and battery thermal management.

Modeling diffusion–induced stress on two-phase lithiation in lithium-ion batteries

Abstract Capacity fade induced by chemo-mechanical degradation during charge-discharge cycles is the bottleneck in the design of high-performance batteries, especially high-capacity electrode materials. In this paper, a flexible sigmoid function is used to create the two-phase electrochemical lithiation profile, describing a sharp phase boundary that separates the pristine core from the lithiated shell of an electrode particle. According to such a phase transition, an analytical solution of the stress evolution is obtained by introducing an electrochemical reaction layer into the plastic model. Finally, based on the theory of diffusion-induced stress and the energy principle, we determine the critical thickness of radius of a lithiated layer, at which fracture occurs.

Analytical model of Li-ion diffusion-induced stress in nanowire and negative Poisson's ratio electrode under different operations

Diffusion-induced stress is one of the critical challenges in developing lithium ion battery technologies, which may lead to the huge volume expansion, nucleation of cracks, electrode mechanical degradation and even pulverization. It has been testified nanostructured electrodes with the consideration of surface effect and property of negative Poisson's ratio can restrain volumetric expansion generation and relieve the hazard of stress-induced crack nucleation. In this paper, an analytical model of diffusion-induced stress for nanowire electrode under different operations is established and a relationship between stress and the nanowire radius is formed. Through changing the morphology of nanowire electrode, the stress equations for negative Poisson's ratio electrode can be obtained. By comparing surface effect influence on diffusion-induced stress between the nanowire and negative Poisson's ratio electrodes under different operations, it is found diffusion-induced stress, especially the tensile stress, can be decreased greatly and even converted to compressive one by the nanostructured electrode and the mechanism of negative Poisson's ratio, which may improve the mechanical property of battery and be in good agreement with experimental observations. Our work provides reference conditions for the improvement of battery to mitigate the mechanical degradation and prolong the cycle life as well as avoid failure.

Life assessment prognostic modelling for multi-layered coating systems using a multidisciplinary approach

ABSTRACTThe multidisciplinary approach has been adopted to model the formation and propagation of blistering effect for evaluation of useful coating life in the multi-layered coating–substrate system. A prognostic model of de-bonding driving force has been formulated as a function of material science, solid mechanics and fracture mechanics properties to estimate critical, safe and fail conditions of the coating–substrate system. The blister growth velocity rate is also included in the developed model to estimate the blister propagation as a function of diffusion-induced stress and residual stress. The proposed prognostic modelling for the formation and propagation of blistering effect are combined to form an assessment model for the evaluation of useful coating life of the multi-layered coating–substrate system and validated through experimental observation.

A systematic investigation of cycle number, temperature and electric field strength effects on Si anode

Cycling number, crystal orientation, temperature and electric field strength play key roles in affecting the capacity and cycling ability of Li-ion battery. However, the detailed dynamic and continuous process of capacity decline mechanism from above factors need to be further understood at nanoscale. Herein, we report deformation behavior and microstructure evolution of Si anode under electric field using molecular dynamics simulations. The results show larger cycling number and electric field strength cause larger volume expansion of Si electrode, leading to the capacity loss and the reducing cycling ability as well as the decreasing structural stability. The phase transformation from diamond cubic structure to body-centred tetragonal structure and the amorphous formation depend on lithiated and delithiated depths. The crystal orientation [100] Si anode produces the volume expansion owing to a large number of nanoscale void. The various temperatures strongly affect the number and radius of nanovoid. The associated transition in the nanovoid nucleation due to the involuntary diffusion process is driven by larger cycling number or electric field strength, resulting in the irreversible capacity loss of Li-ion battery. An established analytical model suggests that diffusion-induced stress not only relies on the position of Si anode but depends upon the cycling time.

Effect of porosity and tortuosity of electrodes on carbon polymer soft actuators

This work presents an electro-mechanical model and simulation of ionic electroactive polymer soft actuators with a porous carbon electrode, polymer membrane, and ionic liquid electrolyte. An attempt is made to understand the effects of specific properties of the porous electrodes such as porosity and tortuosity on the charge dynamics and mechanical performance of the actuator. The model uses porous electrode theory to study the electrochemical response of the system. The mechanical response of the whole laminate is attributed to the evolution of local stresses caused by diffusion of ions (diffusion-induced stresses or chemical stresses). The model indicates that in actuators with porous electrode, the diffusion coefficient of ions, conductivity of the electrodes, and ionic conductivity in both electrodes and separator are altered significantly. In addition, the model leads to an obvious deduction that the ions that are highly active in terms of mobility will dominate the whole system in terms of resulting mechanical deformation direction and rate of deformation. Finally, to validate the model, simulations are conducted using the finite element method, and the outcomes are compared with the experimental data. Significant effort has been put forward to experimentally measure the key parameters essential for the validation of the model. The results show that the model developed is able to well predict the behavior of the actuator, providing a comprehensive understanding of charge dynamics in ionic polymer actuator with porous electrodes.

Influence of local velocity on diffusion-induced stress and axial reaction force in a hollow cylindrical electrode of lithium-ion batteries with cosidering expasion rate of medium

Silicon, as the next-generation cathode material in lithium-ion batteries, exhibits excellent electrochemical performances compared with traditional cathode material, such as high capacity and cheap price. However, its cycling performances are greatly affected by the volume change of silicon due to the insertion of Li atoms. Lots of work focuses on the analysis of diffusion-induced stresses in electrode, but the convection term is seldom considered in analyzing the diffusion-induced stress in an electrode. In this paper, a mathematical model is established, where the convection term is taken into consideration in the diffusion process. The mechanics equations and diffusion equation are derived based on continuum mechanics and the diffusion theory. Diffusion-induced stress, axial reaction force and the critical buckling time in a hollow cylindrical electrode under galvanostatic charging are calculated. The effects of local velocity, ratio of the outer radius to inner radius, charging rate, material parameters and lithiation induced softening factors on stress field and the critical buckling time are studied. According to the results, it is found that the influence of local velocity on stress distribution increases with the increasing of Li concentration, and the contribution of local velocity to axial reaction force is insignificant. Compared with the results without local velocity, the tensile hoop stress of inner surface is large, and compressive stress at the outer surface is small. The axial reaction force and the critical buckling time are calculated with different ratios of outer radius to inner radius. As the radius ratio increases, the axial reaction force and critical buckling time decrease. The effects of three main material parameters (elastic modulus, diffusion coefficient, partial molar volume) on axial reaction force are discussed. The dimensionless force is independent of elastic modulus due to stress varying linearly with Young's modulus. The critical time is inversely proportional to diffusion coefficient. As the partial molar volume increases, which indicates larger volume change induced by the intercalation of the same quantity of Li-ions, the critical buckling time drops and the effect of local velocity on stress field increases. It takes less time for axial reaction force to reach the critical buckling force at a higher charging rate. The elastic properties of silicon in the lithiation process should be a function of Li concentration due to the formation of Li-Si alloy. The elastic modulus is assumed to be a linear function of Li concentration. The hollow cylindrical electrodes with increasing absolute value of lithiation induced softening factor have lower maximum axial reaction force. However, the lithiation induced softening factor has a limited effect on the critical buckling time due to the fact that the Li concentration at critical buckling time is relatively small.

Model of Stress Generation in Anodic Aluminum Oxide Films: Part I. Origin of Stress at the Film Interfaces

Stress builds up near the interfaces of anodic aluminum oxide layers prior to formation of self-organized arrays of pores. Pore initiation may result from a viscous flow instability driven by interfacial stress gradients. We examined the mechanism of interfacial stress generation through a model of coupled viscous flow and ionic migration during growth of planar anodic aluminum oxide layers. In the model, diffusion-induced stress is produced at the oxide-solution interface because deposition of new oxide is constrained by strong adsorption of electrolyte oxyanions. Stress distributions were calculated for barrier oxide growth in phosphoric acid, using values of ion migration parameters and oxide viscosity from independent experimental results. Both the stress layer thickness of a few nanometers and the magnitude of the interfacial stress agreed with those found experimentally. The model also correctly predicted transitions between compressive and tensile stress at the oxide-solution and metal-oxide interfaces at critical current densities. The thin stress layer at the solution interface can be viewed as effective surface tension dependent on the local current density. The current distribution on a nonplanar interface would induce surface tension gradients resulting in shear and normal stress in the oxide, and these in turn could drive oxide flow leading to self-organized porous films.

Effects of plastic deformation in current collector on lithium diffusion and stress in bilayer lithium-ion battery electrode

Lithium-ion batteries (LIBs) have already become indispensable energy storage devices, as they can meet urgent requirements for higher energy and power density in the applications ranging from portable electronics to electric vehicles. However, in the process of charging and discharging of LIB, the diffusion-induced stress associated with inhomogeneous Li concentration in the electrode may cause the electrode material to damage, and then further degrade storage capacity and cycling performance of LIB. Therefore, it is important to quantitatively understand the mechanism relating to the stress evolution in electrode during electrochemical cycling, which will be conducive to developing effective methods of relieving the diffusion induced stress. In this work, a bilayer electrode model is proposed by taking into account Li diffusion, built-in stress, concentration-dependent material properties and elastoplastic deformation of current collector. Based on the established model, the influences of the possible plastic deformation in the current collector on the lithium diffusion and stress evolution of bilayer electrode during charging are investigated. The numerical results show that the plastic deformation of current collector can weaken the constraint between current collector and active layer, which leads to a smaller electrode curvature and more homogeneous lithium concentration in the active layer. The relaxation effect of the plastic deformation not only significantly relieves the stresses at the bottom and top surface of active layer, but also promotes the diffusion of lithium into active layer, which can improve the structural reliability of the electrode and increase the effective capacity of the active layer. Furthermore, the influences of the yield strength and plastic modulus of the current collector are discussed. The results indicate that the constraint between the current collector and active layer becomes weaker with reducing yield strength and plastic modulus of current collector, respectively. In other words, the further stress relaxation in the electrode indicates that the capacity can be enhanced upon reducing the yield strength and plastic modulus of current collector, respectively. Considering our results, it is expected that a bilayer electrode composed of the current collector with smaller mechanical strength enjoys simultaneous improvement in battery usable capacity and structural reliability. Consequently, the results of this paper provide a route to improving the cycle performance of bilayer lithium-ion battery electrode.

Physics-Based and Control-Oriented Modeling of Diffusion-Induced Stress in Li-Ion Batteries

Advanced battery management systems must take into account all key factors that contribute to significant degradation in order to ensure safe operation and to prolong battery useful life. One of the most important battery degradation mechanisms is the stress induced fracture. This has been observed on cathode electrodes during experiments, and may lead to partial or complete electrical isolation of the particles from the electrode. A physics-based stress model considering the nonlinear variation of lattice constant is presented and validated against experimental data. The effect of stress on diffusion dynamics is investigated. Stresses under the linear lattice constant and nonlinear lattice constant are compared. Stresses at different SOCs are also studied. SOC operating window which avoids the maximum stresses are determined. A physics-based, control-oriented, and highly computationally efficient model is also developed to predict the particle level stress in lithium ion batteries. This physics-based control-oriented model enables accurate estimation of stress levels inside the cathode particles while being computationally efficient enough to be implemented on an inexpensive micro-controller. With the accurate prediction of the stress level in the electrode particles, vehicles can be optimized to operate more efficiently with the aim of protecting battery health and prolonging battery life.

Unveiling the Role of CeO2 Atomic Layer Deposition Coatings on LiMn2O4 Cathode Materials: An Experimental and Theoretical Study.

An atomic layer deposition (ALD) coating on active materials of a lithium ion battery is a more effective strategy for improving battery performance than other coating technologies. However, substantial uncertainty still remains about the underlying physics and role of the ALD coating in improving battery performance. Although improvement in the stability and capacity of CeO2 thin film coated particles for batteries has been reported, a detailed and accurate description of the mechanism has not been provided. We have developed a multiphysics-based model that takes into consideration stress mechanics, diffusion of lithium ion, and dissolution of transition-metal ions of spinel LiMn2O4 cathode. The model analyzes how different coating thicknesses affect diffusion-induced stress generation and, ultimately, crack propagation. Experimentally measured diffusivity and dissolution rates were incorporated into the model to account for a trade-off between delayed transport and prevention of side reactions. Along with experimental results, density functional theory results are used to explain how a change in volume, due to dissolution of active material, can affect battery performance. The predicted behavior from the model is well-matched with experimental results obtained on coated and uncoated LiMn2O4-Li foil cells. The proposed approach and explanations will serve as important guidelines for thin film coating strategies for various battery materials.