Intercalation-Induced Stress

Choi, Y.-M. and S.-I. Pyun, Effects of intercalation-induced stress on lithium transport through porous LiCo02 electrode. Solid State Ionics, 1997. 99 pp. 173-183... 

Recent years have witnessed a significant effort in developing macroscopic models describing stress generation due to lithium insertion and extraction in intercalation electrode materials [41, 64-73]. In this section, different intercalation-induced stress models reported in the literature are briefly described. Modeling intercalation-induced stress requires coupling between diffusion and elasticity along with appropriate material balances. 

A.M. (2007) Numerical simulation of intercalation-induced stress in Li-ion battery electrode particles. J. Electrochem. Soc., 154 (10), A910-A916. 

As an illustration of the couphng between mechanical and other processes, we give a constitutive equation for intercalation-induced stress as... 

Intercalation-induced stresses are closely related to the diflfusion of ions inside active particles [1, 2]. Thermal stress is induced because of temperature variation due to exothermic reaction during charge/discharge. Packaging provides... 

Intercalation-induced stresses have been modeled extensively in the Hterature. A one-dimensional model was proposed to estimate stress generation in the lithium insertion process in the spherical particles of a carbon anode [24] and an LiMn204 cathode [23]. In this model, displacement inside a particle is related to species flux by lattice velocity, and total concentration of species is related to the trace of the stress tensor by compressibihty. Species conservation equations and elasticity equations are also included. A two-dimensional porous electrode model was also proposed to predict electrochemicaUy induced stresses [30]. Following the model approach of diffusion-induced stress in metal oxidation and semiconductor doping [31-33], a model based on thermal stress analogy was proposed to simulate intercalation-induced stresses inside three-dimensional eUipsoidal particles [1]. This model was later extended to include the electrochemical kinetics at electrode particle surfaces [2]. This thermal stress analogy model was later adapted to include the effect of surface stress [34]. 

Directly measuring intercalation stress in battery electrode materials is difficult because of the multiple phases of composite electrodes and also because it is usually associated with other stresses [29, 35]. In the case of cathode and anode materials, intercalation-induced stress is believed to be one of the main factors causing battery degradation, since it results in damage to reversible interaction sites and structural fatigue [14]. The active material of each electrode is usually embedded inside a binder and conductive matrix to form a porous structure as shown in Figure 26.4 (modified from [5, 6]). This combination of binder and conductive matrix provides electron conduction paths and integrates all active particles into one piece of porous composite electrode, which is then wetted by electrolyte. 

Intercalation-induced stress can be modeled by using an analogy to thermal stress. From the constitutive equation presented in Section 26.1.2.2 and the force equilibrium equation, the displacement equation can be written as... 

The one-dimensional decoupled diffusion equation without the elimination of stress-dependent terms is easier to solve numerically. With li-ion concentration obtained, intercalation-induced stresses can be calculated using the analytical expressions of Equations 26.4 and 26.5. Governing equations for one-dimensional spherical particles can be solved using the finite difference method. Governing equations for three-dimensional elHpsoidal particles are solved using the finite element analysis package GOMSOL Multiphysics. 

LiMn204 is used here to represent example calculations of intercalation-induced stresses. The volume change of 6.5% for y = 0.2 to y = 0.995 of LiyMn204 gives a strain of 0.0212. Therefore, by noting the analogy between the thermal expansion coefficient and 2/3, the partial molar volume is t2 = 3.50 x 10 m /mol. 

Figure 26.9 Implementing realistic geometry into single-particle intercalation-induced stress modeling (a) AFM images of Li (Mn204 single-particle and (b) von Mises stress distribution on the particle surface.

Intercalation-induced stress largely depends on the size of the particles and the cycling rate. It was shown that [24] the maximum tensile stress due to intercalation is on the order of 50 MPa for 5 pm (in radius) graphite electrode materials with a cychng rate of 5C. Simulations implemented on reahstic particle geometry reconstructed from 3D AFM imaging data [46] have shown that intercalation-induced stress could be as high as 110 MPa with a potential sweep rate of 0.5 mV... 

Electrode materials in most of today s commercial batteries are made of particulates. Stress generated from battery cycling varies depending on the size and shape of particles in the electrode. It has been suggested that the use of electrode particles of smaller size and larger aspect ratio help to reduce intercalation-induced stress [2]. AppHcation of this approach will require fabrication techniques that can produce the desired size and shape of particles in a controlled manner. 

Zhang, X., Sastry, A.M., and Shyy, W. (2008) Intercalation-induced stress and heat generation within single lithium-ion battery cathode particles, j. Electrochem. Soc., 155 (7), A542-A552. 

J.Y. (2005) An investigation of intercalation-induced stresses generated during lithium transport through sol-gel derived LixMn204 film electrode using a laser beam deflection method. Electrochim. Acta, 51 (3), 441-449. 

However, delamination and degradation in capacity occurred in cycled samples probably due to the intercalation-induced stress in C03O4 phase. 

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