Sharp-interface formation during lithium intercalation into silicon

Meca, Esteban; Münch, Andreas; Wagner, Barbara

doi:10.1017/s0956792517000067

Cited by 7 publications

(14 citation statements)

References 35 publications

(27 reference statements)

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“…a parameter that quantifies the importance of Li attachment-detachment kinetics at the interface between the lithiated and the non-lithiated phases. This can be clearly seen in the sharp interface limit of the equations [29,30]. Parameter Y is simply the flux F nondimensionalized again with M and L 0 .…”

Section: (A) Non-dimensionalizationmentioning

confidence: 86%

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Thin-film electrodes for high-capacity lithium-ion batteries: influence of phase transformations on stress

2016

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)) on the stress evolution during the lithiation/delithiation cycle of a thin film of amorphous silicon. Based on recent work that show a two-phase process of lithiation of amorphous silicon, we formulate a phase-field model coupled to elasticity in the framework of Larché-Cahn. Using an adaptive nonlinear multigrid algorithm for the finite-volume discretization of this model, our two-dimensional numerical simulations show the formation of a sharp phase boundary between the lithiated and the amorphous silicon that continues to move as a front through the thin layer. We show that our model captures the non-monotone stress loading curve and rate dependence, as observed in recent experiments and connects characteristic features of the curve with the structure formation within the layer. We take advantage of the thin film geometry and study the corresponding one-dimensional model to establish the dependence on the material parameters and obtain a comprehensive picture of the behaviour of the system.

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Section: (A) Non-dimensionalizationmentioning

confidence: 86%

“…The scaling with of each term has been chosen to make sure that we obtain the correct asymptotic sharp-interface limit, see Meca et al [30] for details. Equations (2.5) and (2.6), together with the mechanical equilibrium condition…”

Section: The Modelmentioning

confidence: 99%

Thin-film electrodes for high-capacity lithium-ion batteries: influence of phase transformations on stress

2016

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“…In our case, the stability in the system corresponding to the sharp-interface limit has also been studied for the β = 0 case [25,38]. In a previous article [31] the authors have derived the sharp interface limit for the complete model, the main results are described in Appendix A. We obtain the following dispersion relation for perturbations of the sharp interface:…”

Section: Instability Of the Receding Frontmentioning

confidence: 94%

“…Gurtin [18] showed that such a term appears naturally when introducing ∂ t c in the list of constitutive variables, and it has been shown to guarantee a positive entropy production at the interface in the sharp-interface limit [10]. The chosen scaling from that term with ε follows similarly from the sharp-interface limit of this model (see [31]). Eqs.…”

Section: The Modelmentioning

confidence: 95%

“…In order to study this instability we use a viscous Cahn-Hilliard model [36] to model phase separation, and couple the dynamics of the concentration with elasticity using what is usually referred to as the Larché-Cahn prescription [14,24,37]. We also use the sharp-interface limit of this model [31], which is valid once phase separation has taken place. Comparing the results of the phase-field model with the sharp-interface model allows us to on the one hand validate the stability calculation and on the other hand show how the localization of the instability occurs in the phase-field model.…”

Section: Introductionmentioning

confidence: 99%

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Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity

Meca¹,

Münch²,

Wagner³

2018

Phys. Rev. E

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We study numerically and analytically the instabilities associated with phase separation in a solid layer on which an external material flux is imposed. The first instability is localized within a boundary layer at the exposed free surface by a process akin to spinodal decomposition. In the limiting static case, when there is no material flux, the coherent spinodal decomposition is recovered. In the present problem stability analysis of the time-dependent and non-uniform base states as well as numerical simulations of the full governing equations are used to establish the dependence of the wavelength and onset of the instability on parameter settings and its transient nature as the patterns eventually coarsen into a flat moving front. The second instability is related to the MullinsSekerka instability in the presence of elasticity and arises at the moving front between the two phases when the flux is reversed. Stability analyses of the full model and the corresponding sharp-interface model are carried out and compared. Our results demonstrate how interface and bulk instabilities can be analysed within the same framework which allows to identify and distinguish each of them clearly. The relevance for a detailed understanding of both instabilities and their interconnections in a realistic setting are demonstrated for a system of equations modelling the lithiation/delithiation processes within the context of Lithium ion batteries.

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Efficient Simulation of Chemical–Mechanical Coupling in Battery Active Particles

et al. 2021

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Coupling of chemistry and mechanics causes large stresses and deterioration in battery active particles, which undergo a phase change. The Cahn–Hilliard approach coupled to large deformations provides a framework to theoretically investigate the underlying physics. However, solving this model is computationally expensive, so that the current application is limited. In this article, a thermodynamically consistent phase‐field model coupling Cahn–Hilliard‐type phase separation and large deformations is developed. The model is implemented using a space and time adaptive numerical solution algorithm based on the finite element method. At the example of lithium iron phosphate, simulations are performed to investigate physical and numerical aspects of the model and the solver. The strong interrelation between chemistry, phase transformation, and mechanics is shown. In particular, the interfacial energy coefficient has a major impact on the stress inside the material. Moreover, the presented solution algorithm outperforms classical implementations. This enables the analysis of computationally demanding parameter choices and multidimensional geometries.

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Sharp-interface formation during lithium intercalation into silicon

Cited by 7 publications

References 35 publications

Thin-film electrodes for high-capacity lithium-ion batteries: influence of phase transformations on stress

Thin-film electrodes for high-capacity lithium-ion batteries: influence of phase transformations on stress

Localized instabilities and spinodal decomposition in driven systems in the presence of elasticity

Efficient Simulation of Chemical–Mechanical Coupling in Battery Active Particles

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