Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries

Cui, Zhiwei; Gao, Feng; Qu, Jianmin

doi:10.1016/j.jmps.2012.11.001

Cited by 164 publications

(117 citation statements)

References 52 publications

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“…And they mainly analyzed the effect of plastic yielding on the magnitude of stress in the amorphous silicon electrode. Cui et al 23 investigated the phase interface based on a model that accounts for the finite deformation kinematics and stress-diffusion interaction.…”

Section: Introductionmentioning

confidence: 99%

Stress analysis in cylindrical composition-gradient electrodes of lithium-ion battery

2017

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In recent years, the composition-gradient electrode material has been verified to be one of the most promising materials in lithium-ion battery. To investigate diffusion-induced stresses (DIS) generated in a cylindrical composition-gradient electrode, the finite deformation theory and the stress-induced diffusion hypothesis are adopted to establish the constitutive equations. Compared with stress distributions in a homogeneous electrode, the increasing forms of Young’s modulus E(R) and partial molar volume Ω(R) from the electrode center to the surface along the radial direction drastically increase the maximal magnitudes of hoop and axial stresses, while both of the decreasing forms are able to make the stress fields smaller and flatter. Also, it is found that the slope of -1 for E(R) with that of -0.5 for Ω(R) is a preferable strategy to prevent the inhomogeneous electrode from cracking, while for the sake of protecting the electrode from compression failure, the optimal slope for inhomogeneous E(R) and the preferential one for Ω(R) are both -0.5. The results provide a theoretical guidance for the design of composition-gradient electrode materials.

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Section: Introductionmentioning

confidence: 99%

Stress analysis in cylindrical composition-gradient electrodes of lithium-ion battery

2017

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“…The concurrent processes of Li transport, phase transformation and elasto-plastic deformation in Si anodes have inspired numerous modeling works [19][20][21][22][23][24][25] . Several groups developed models to explain the anisometric volume expansion of c-Si nanowires upon lithiation 14,18,24 .…”

Section: Introductionmentioning

confidence: 99%

Mitigating mechanical failure of crystalline silicon electrodes for lithium batteries by morphological design

Wood

et al. 2015

Phys. Chem. Chem. Phys.

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Although crystalline silicon (c-Si) anodes promise very high energy densities in Li-ion batteries, their practical use is complicated by amorphization, large volume expansion and severe plastic deformation upon lithium insertion. Recent experiments have revealed the existence of a sharp interface between crystalline Si (c-Si) and the amorphous Li x Si alloy during lithiation, which propagates with a velocity that is orientation dependent; the resulting anisotropic swelling generates substantial strain concentrations that initiate cracks even in nanostructured Si. Here we describe a novel strategy to mitigate lithiation-induced fracture by using pristine c-Si structures with engineered anisometric morphologies that are deliberately designed to counteract the anisotropy in the crystalline/amorphous interface velocity. This produces a much more uniform

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“…12,15,18,19,21,24 Based on nonequilibrium thermodynamics, Zhao et al 15,21 considered the coupled large plastic deformation and lithiation in a spherical Si electrode. Bower et al 12,18 developed a theoretical framework to incorporate finite deformation, diffusion, plastic flow, and electrochemical reaction in lithiation of Si electrodes.…”

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confidence: 99%

“…However, such non-linear diffusion model, implemented in a general finite element framework, failed to provide a characteristic length scale as the interface thickness varied with the lithiation time. Cui et al 24 and Liu et al 4 studied the lithiation of Si by considering the interfacial chemical reactions and bulk diffusion as two sequential processes. But they did not directly simulate the concurrent processes of Li diffusion and reaction.…”

mentioning

confidence: 99%

A Phase-Field Model Coupled with Large Elasto-Plastic Deformation: Application to Lithiated Silicon Electrodes

Chen

Fan

Hong

et al. 2014

J. Electrochem. Soc.

111

105

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A phase-field model, accounting for large elasto-plastic deformation, is developed to study the evolution of phase, morphology and stress in crystalline silicon (Si) electrodes upon lithium (Li) insertion. The Li concentration profiles and deformation geometries are co-evolved by solving a set of coupled phase-field and mechanics equations using the finite element method. The present phase-field model is validated in comparison with a non-linear concentration-dependent diffusion model of lithiation in Si electrodes. It is shown that as the lithiation proceeds, the hoop stress changes from the initial compression to tension in the surface layer of the Si electrode, which may explain the surface cracking observed in experiments. The present phase-field model is generally applicable to high-capacity electrode systems undergoing both phase change and large elasto-plastic deformation. As a promising anode material for lithium (Li)-ion batteries, 1-3 the theoretical Li capacity of Silicon (Si) is 4200 mAh/g (corresponding to the lithiated phase of Li 4.4 Si), which is one order of magnitude larger than the commercialized graphite anode.1,2 Recent experiments revealed that the lithiation of crystalline Si (c-Si) occurs through a two-phase mechanism, i.e., growth of lithiated amorphous Li x Si (aLi x Si, x ∼ 3.75) phase separated from the unlithiated c-Si phase by a sharp phase boundary of about 1 nm thick.4-8 An abrupt change of Li concentration across the amorphous-crystalline interface (ACI) gives rise to drastic volume strain inhomogeneity. The resulting high stresses induce plastic flow, fracture, and pulverization of Si electrodes, thereby leading to the loss of electrical contact and limiting the cycle life of Li-ion batteries. [9][10][11] Electrochemically driven mechanical degradation in high-capacity electrodes has stimulated enormous efforts on the development of chemo-mechanical models to understand how the stress arises and evolves in lithiated Si electrodes.12-15 These chemo-mechanical models often treated the lithiation-induced stress as the diffusion-induced stress by considering Li diffusion in a solid-state electrode that results in the change of composition from its stoichiometric state. Deviation from stoichiometry usually results in a volume change that generates stress if the Li distribution is non-uniform. Early chemo-mechanical models only involved a unidirectional coupling. Namely, the diffusioninduced mechanical stress was considered, whereas the effect of mechanical stress on diffusion was ignored. Both experimental and computational studies, however, have shown that the mechanical stresses play an important role in the lithiation kinetics of Si electrodes. 4,6,16,17 Recently, fully coupled chemo-mechanical models were developed to incorporate the mechanical stress into the chemical potential. [18][19][20][21][22] In these models, the local stress modulates lithiation kinetics (reaction rate and diffusivity), 4,6,23 and in turn, lithiation kinetics regulates the stress generation in lithiated ...

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Interface-reaction controlled diffusion in binary solids with applications to lithiation of silicon in lithium-ion batteries

Cited by 164 publications

References 52 publications

Stress analysis in cylindrical composition-gradient electrodes of lithium-ion battery

Stress analysis in cylindrical composition-gradient electrodes of lithium-ion battery

Mitigating mechanical failure of crystalline silicon electrodes for lithium batteries by morphological design

A Phase-Field Model Coupled with Large Elasto-Plastic Deformation: Application to Lithiated Silicon Electrodes

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