Thermodynamics, stress, and Stefan-Maxwell diffusion in solids: application to small-strain materials used in commercial lithium-ion batteries

Baker, Daniel R.; Bower, Allan F.

doi:10.1007/s10008-015-3012-7

Cited by 13 publications

(5 citation statements)

References 44 publications

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“…12, and multi-species transport entails multiple diffusion coefficients such as, for example, the binary diffusion coefficients appearing in the Stefan-Maxwell equations. 2,16 The precise nature of lithium transport in host materials is still the subject of ongoing research, but in Ref. 7 it was observed that diffusion in graphite associated with PITT measurements in Ref.…”

Section: Theory For the Equilibrium Thermodynamicsmentioning

confidence: 99%

Thermodynamic Model for Substitutional Materials: Application to Lithiated Graphite, Spinel Manganese Oxide, Iron Phosphate, and Layered Nickel-Manganese-Cobalt Oxide

Baker

Koch²,

Xiao

et al. 2017

J. Electrochem. Soc.

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We derive and implement a method to describe the thermodynamics of electrode materials based on a substitutional lattice model. To assess the utility and generality of the method, we compare model results with experimental data for a variety of electrode materials: lithiated graphite and layered nickel-manganese-cobalt oxide (Chevrolet Bolt Electric Vehicle negative and positive electrode materials, respectively), manganese oxide (in the positive electrodes of the Gen 1 and Gen 2 Chevrolet Volt Extended Range Electric Vehicle and the positive electrode of many high-power-density batteries), and iron phosphate (Gen 1 Chevrolet Spark Electric Vehicle positive electrode material and of immediate interest for 12 and 48 V applications). An early version of the model has been applied to lithiated silicon (Li-Si). As was found in the Li-Si study, the model enables one to quantitatively represent experimental data from these different electrode materials with a small number of parameters, and, in this sense, the approach is both general and efficient. An open question is the utility of controlled-potential vs. controlled-current experiments for the elucidation of the system thermodynamics. We provide commentary on this question, and we highlight other open questions throughout this work. Central to the modeling of electrochemical systems, particularly batteries relying on solid-state diffusion within the active materials, is an accurate description of the system thermodynamics.1-4 We describe and implement a thermodynamic model for substitutional electrode materials. At the heart of the model is a simple expression for the open-circuit potential U in terms of the fraction of filled sites x within a host material. To assess the value of the model, we apply it to four electrode materials of commercial interest today: lithiated graphite, spinel manganese oxide, iron phosphate, and nickel-manganese-cobalt oxide. The model is an expanded version of that described in Ref. 12. A slight alteration is needed to describe the nickel-manganese-cobalt oxide so that inaccessible lithium can be considered (giving rise to x 0 in Table I), and we also describe how reactions between sites within the electrode material can be addressed.This document is organized as follows. First, we provide an overview of the materials and instrumentation for the experimental characterization of the electrode materials. An introduction of the thermodynamic model is then presented, followed by a detailed description of the model. A discussion of results is then presented, followed by a brief Appendix devoted to the convergence properties of the series summation employed in the U(x) model. • C under about 0.01 Torr vacuum. Other materials were dried at 100 Experimental• C under vacuum of about 0.01 Torr. Cell assembly and cycling were performed under an inert argon atmosphere with O 2 and H 2 O concentrations < 1 ppm. Cycling was performed with a Princeton Applied Research PMC 2000 potentiostat/galvanostat. For the voltammetry work on the Ni 0.6 Mn 0.2 Co ...

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Section: Theory For the Equilibrium Thermodynamicsmentioning

confidence: 99%

Thermodynamic Model for Substitutional Materials: Application to Lithiated Graphite, Spinel Manganese Oxide, Iron Phosphate, and Layered Nickel-Manganese-Cobalt Oxide

Baker

Koch²,

Xiao

et al. 2017

J. Electrochem. Soc.

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“…The cause of this apparent increase may be related to the graphite phase change and should be investigated in future work either through a multi-species reaction model [77][78][79][80] or a model that considers particle level stress induced diffusion modifications. 81,82…”

Section: Resultsmentioning

confidence: 99%

Modeling Electrochemical Transport within a Three-Electrode System

Garrick

Gao

Yang

et al. 2021

J. Electrochem. Soc.

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In support of GM’s traction battery efforts, we derive and implement a method to describe the electrochemical performance of a battery cell through the combination of a modified Newman Pseudo 2-Dimensional model and a three-electrode experimental apparatus. To assess the capability of the method, we compare model results with experimental data for a lithiated graphite and lithium nickel manganese cobalt oxide system. The model is applied to simulate the electrochemical and transport processes within the battery cell to predict the negative electrode potential and positive electrode potential with respect to a lithium iron phosphate reference electrode, as well as the terminal voltage. We also provide a commentary on the validity of the fitted parameters governing transport at the electrode level.

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“…The lithium flux inside the particle can be determined from the gradient of chemical potential 14 :

boldJ = - \frac{D}{RT} c_{m} ((), \frac{c_{s}}{c_{m}}) ((), 1 - \frac{c_{normals}}{c_{normalm}}) \nabla μ,

where c m is the maximum lithium concentration, and D is the diffusion of lithium inside the particle. From Equations () and (), ∇ μ is the difference of chemical potential between the lithiated sites and vacant sites:

\nabla μ = \nabla ((), μ_{Li - normalθ}^{0} - μ_{θ}^{0}) + italicRT \nabla ((), \ln a_{Li - normalθ} - \ln a_{θ}) - ((), Ω_{Li - normalθ} - Ω_{θ}) \nabla σ_{h} .

Since the

μ_{Li - normalθ}^{0}

and

μ_{θ}^{0}

are the standard state potentials of lithiated sites and non‐lithiated sites, respectively, Equation () can be simplified as follows:

\nabla μ = italicRT \nabla ((), \ln a_{Li - normalθ} - \ln a_{θ}) - normalΩ \nabla σ_{h} .

Taking the derivative of Equation () provides:

- F \nabla E_{eq}^{0} = R T \nabla ((), \ln a_{Li - normalθ} - \ln a_{θ}),

- F \frac{\partial E_{eq}^{0}}{\partial c_{s}} \nabla c_{s}

…”

Section: Modelling and Simulation Methodsmentioning

confidence: 99%

“…Yang introduced a mathematical relation between hydrostatic stress and atomic concentration 13 . Recently, stress‐dependent chemical potential has been applied to investigate the chemo‐mechanical behavior of Li‐ion batteries 9,14,15 . Zhang et al used the analogy of thermal stress to study the stress development in a single particle of the electrode 16 .…”

Section: Introductionmentioning

confidence: 99%

Inhomogeneous stress development at the multiparticle electrode of lithium‐ion batteries

Ali

Iqbal

Lee

2021

Intl J of Energy Research

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The active particle at the electrode of Li-ion batteries is surrounded by other particles and binders. During the lithiation/delithiation process, these surrounding materials mechanically constrain expansion and contraction of the particle. Since electrochemical and mechanical responses mutually influence each other, the constraining condition can finally affect cell performance. In this paper, we investigate the mechanical and electrochemical responses at the particle and cell levels with consideration of the coupling effect of electrochemistry and mechanics. To study the effect of mechanical constraints on cell

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Thermodynamics, stress, and Stefan-Maxwell diffusion in solids: application to small-strain materials used in commercial lithium-ion batteries

Cited by 13 publications

References 44 publications

Thermodynamic Model for Substitutional Materials: Application to Lithiated Graphite, Spinel Manganese Oxide, Iron Phosphate, and Layered Nickel-Manganese-Cobalt Oxide

Thermodynamic Model for Substitutional Materials: Application to Lithiated Graphite, Spinel Manganese Oxide, Iron Phosphate, and Layered Nickel-Manganese-Cobalt Oxide

Modeling Electrochemical Transport within a Three-Electrode System

Inhomogeneous stress development at the multiparticle electrode of lithium‐ion batteries

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