Stress relaxation through interdiffusion in amorphous lithium alloy electrodes

Gao, Yixin; Cho, M.; Zhou, Min

doi:10.1016/j.jmps.2012.09.004

Cited by 31 publications

(10 citation statements)

References 60 publications

(94 reference statements)

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“…The diffusion of lithium in electrodes is driven by chemical potential gradient, and the radial flux J ( R , t) is proportional to the gradient of chemical potential μ , as [11]where D is the diffusivity, R g is the gas constant, and T is the temperature. μ is defined as the deviation of total energy density to the concentration and can be written as…”

Section: Methodsmentioning

confidence: 99%

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A developed expression of chemical potential for fast deformation in nanoparticle electrodes of lithium-ion batteries

2019

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In this paper, we propose a developed expression of chemical potential without the assumption of low deformation rate to account for the diffusion induced stress and the distribution of Li concentration in nanoparticle electrodes of lithium-ion batteries. The difference between the developed and traditional expressions on the stress evolution in a spherical nanoparticle electrode made of silicon is analyzed under both potentiostatic and galvanostatic operations, using the derived diffusion equation and the finite deformation theory. The numerical result suggests that the difference between these two expressions of chemical potential is significant under potentiostatic operation, rather than that under galvanostatic operation. A critical radius, where there is no difference between the Li flux caused by these two expressions of chemical potential as well as the Cauchy hydrostatic stress during most of the lithiated process, is firstly reported in this work.

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Section: Methodsmentioning

confidence: 99%

“…We focus on the stress-dependent part of the chemical potential τ ( E e , C), which is the derivative of strain energy density W with respect to the concentration of lithium C. Traditionally, Π( X , t) is considered to be Helmholtz free energy density and therefore this step is carried out for fixed deformation written as [11]…”

Section: Methodsmentioning

confidence: 99%

A developed expression of chemical potential for fast deformation in nanoparticle electrodes of lithium-ion batteries

2019

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“…Little work has yet explored time‐dependent mechanical behavior in LiSi x materials: Ref. predicted relaxation times in lithiated phases on the order of minutes to hours, and Refs. and reported measurements of creep over the timescale of several minutes.…”

Section: Time‐dependent Behaviormentioning

confidence: 99%

“…To that end, the mechanics of lithiation of silicon have been the subject of numerous studies, for example Refs. . Several groups modeled strain in Si during lithiation and made indirect observations of experimental particle and cylinder‐shaped systems .…”

Section: Introductionmentioning

confidence: 99%

Observations of stress accumulation and relaxation in solid‐state lithiation and delithiation of suspended Si microcantilevers

Brown

Lee

Xiao

et al. 2016

Physica Status Solidi (a)

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Motion of microfabricated cantilevers is demonstrated as an in situ technique for mechanical characterization during the solid‐state electrochemical lithiation and delithiation of silicon. The composite cantilevers consist of suspended single‐crystal silicon cantilevers, onto which LiAlF4 electrolyte, Li2WO4 lithium reservoir, and Ag electrode layers are deposited. Using white light interferometry, the cantilevers are observed to deflect downward as the silicon is charged with lithium (lithiation), but the cantilevers experience little motion as the lithium is discharged (delithiation). An analytical cantilever‐bending model featuring a moving phase boundary is developed to describe motion of the beams and explore stress profiles within the lithiated layer. Cantilever deflection during lithiation allows comparison to several models for stress within the LiSix layer. Specifically, a purely elastic model overestimates cantilever motion, as does a plastic bending model. The observed cantilever deflection distances are appropriate for a model of gradual accumulation of stress during charging, best fit with an exponential function indicating compressive stress of more than 1 GPa at the Si‐LiSix phase boundary. After both charge and discharge cycles, the cantilevers relax upwards, indicating that this material system experiences time‐dependent stress relaxation and continues to restructure itself after both lithiation and delithiation. During lithiation (black lines), microcantilevers are observed to deflect downward with increasing charge, while similar behavior is not observed during delithiation (gray lines). This experimental technique was demonstrated using a model solid electrolyte system supported on Si microcantilevers, and resulted in observation of stress relaxation without current flow.

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“…7,8 To overcome this failure mode, extensive effort has been devoted to understand the underline mechanisms of Li insertion into Si. 9,10 Based on experimental observations, the authors 11,12 have developed a lithiation model that accounts for the interfacial chemical interactions between Li and Si by introducing an electrochemical Biot number b ¼ k e f V m h 0 =D 0 , where k e f is the rate of chemical reaction at the Si/Li x Si interface, D 0 is the rate of bulk diffusion of Li in Li x Si, V m is the molar volume of Si, and h 0 is a characteristic length of the anode. Clearly, b characterizes the ratio between the rate of interfacial chemical reaction and the rate of Li diffusion in Si.…”

mentioning

confidence: 99%

Two-phase versus two-stage versus multi-phase lithiation kinetics in silicon

Cui

Gao

2013

Applied Physics Letters

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Communication: Enhanced oxygen reduction reaction and its underlying mechanism in Pd-Ir-Co trimetallic alloys A hybrid kinetic Monte Carlo method for simulating silicon films grown by plasma-enhanced chemical vapor deposition In situ atomic force microscopy observation on the decay of small islands on Au single crystal in acid solutionWe classify the lithiation process into three types, namely, two-phase, two-stage, and multi-phase lithiation. We found that under a given charging rate, smaller electrochemical Biot number of b will likely to result in two-phase lithiation, while larger b may lead to multi-phase lithiation. For the film anode, intermediate b, or intermediate charging rate, will yield two-stage lithiation, and the Li concentration during the first stage of the lithiation is determined by the relationship between b and the charging rate (or more precisely the Li flux supplied to the Si/Li x Si phase interface). Such twostage lithiation does not occur in the particle or fiber anode. V C 2013 AIP Publishing LLC.

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Stress relaxation through interdiffusion in amorphous lithium alloy electrodes

Cited by 31 publications

References 60 publications

A developed expression of chemical potential for fast deformation in nanoparticle electrodes of lithium-ion batteries

A developed expression of chemical potential for fast deformation in nanoparticle electrodes of lithium-ion batteries

Observations of stress accumulation and relaxation in solid‐state lithiation and delithiation of suspended Si microcantilevers

Two-phase versus two-stage versus multi-phase lithiation kinetics in silicon

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