Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si26.svg"><mml:mrow><mml:mtext>Li</mml:mtext><mml:msub><mml:mtext>FePO</mml:mtext><mml:mn>4</mml:mn></mml:msub></mml:mrow></mml:math>

Daubner, Simon; Schneider, Daniel

doi:10.1016/j.electacta.2022.140516

Cited by 16 publications

(14 citation statements)

References 77 publications

(147 reference statements)

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“…In the general picture, the multiphase-field method [70,71] distinguishes various physical states (mostly called 'phases' in the following) based on variables φ = {φ 1 , ..., φ α , ..., φ N } T , which denote the volume fraction and can represent different materials as well as phases (crystalline polymorphs) or ordered states of the same material. Based on our previous works [51,72], we employ the Allen-Cahn model combined with a grand potential formulation where the chemical free energy f chem (φ, x) is approximated by an interpolation of phase-dependent contributions. More precisely, the chemical free energy of each phase is given by a fitting function while the energetic barrier that leads to a miscibility gap is imposed by the obstacle potential.…”

Section: Multiphase-field Simulationsmentioning

confidence: 99%

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

Daubner,

Dillenz,

Pfeiffer

et al. 2023

Preprint

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The research of new electrode materials such as sodium intercalation compounds is key to meet the challenges of future demands of sustainable energy storage. For these batteries, the intercalation behaviour on the micro-scale is governed by a complex interplay of chemical, electrical and mechanical forces strongly influencing the overall cell performance. The multiphase-field method is a suitable tool to study these multi-physics and bridge the scale from ab-initio methods to the cell level. In this work, we follow a combined approach of experiments, density functional theory (DFT) calculations and multiphase-field simulations to predict thermodynamic and kinetic properties for the P2-type NaXNi1/3Mn2/3O2 sodium-ion cathode material. Experimentally, we obtain the thermodynamic potential and diffusion coefficients at various sodium contents using electrochemical techniques and discuss limitations of the experimentally applied methods. DFT is used to identify stable phases by calculating an energy hull curve. Then, the influence of long-range dispersion interactions and the exchange-correlation functional on the voltage curve is investigated by comparison with experimental results. Finally, multiphase-field simulations are performed based on inputs from experiments and DFT. The fitting of phase-specific chemical free energies from DFT calculations and experimental data is discussed. Our results show that the single- and two-phase regions can be precisely reproduced at low C-rates close to thermodynamic equilibrium. Furthermore, the inclusion of a Butler-Volmer-type boundary condition allows to study the kinetics of the system as a competition of surface reaction, bulk diffusion and elastic deformation upon phase transformations. The model is able to predict kinetic capacity loss due to bulk diffusion limitation and the overpotential depending on charging rate.

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Section: Multiphase-field Simulationsmentioning

confidence: 99%

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

Daubner,

Dillenz,

Pfeiffer

et al. 2023

Preprint

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“…In order to develop an accurate thermodynamic description, it was essential to model the behavior of individual particles using phase-field methods, which generalize the Cahn-Hilliard formalism [55][56][57][58][59][60][61] for driven electrochemical systems 34,48,52 . This approach has led to realistic models of diffusion and reaction models for materials such as graphite 62,63 , anatase TiO2 45 , LTO 46 , LCO 9 and LFP [64][65][66][67][68] , showing excellent agreement with experiments, guiding researchers to properly understand the reasons for various peculiar behaviors occurring in phase-separating materials and helping companies in the optimization of these kinds of batteries. Recently, phase-field modeling of LFP has succeeded in reproducing a vast dataset of operando x-ray images of nanoparticles cycling at different rates pixel by pixel 69 , while learning the two-phase free-energy landscape, the reaction kinetics of coupled ion-electron transfer 70 , and the heterogeneity of surface reactivity, correlated with variations in carbon coating thickness.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of multi-sublattice battery active materials: from an extended regular solution theory to a phase-field model of LiMnFe<1-y>PO

Vasileiadis

Ombrini

Wagemaker

et al. 2023

Preprint

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Phase separation during the lithiation of redox-active materials is a critical factor affecting battery performance, including energy density, charging rates, and cycle life. Accurate physical descriptions of these materials are necessary for understanding underlying lithiation mechanisms, performance limitations, and optimizing energy storage devices. This work presents an extended regular solution model that captures mutual interactions between sublattices of multi-sublattice battery materials, typically synthesized by metal substitution. We apply the model to phospho-olivine materials and demonstrate its quantitative accuracy in predicting the composition-dependent redox shift of the plateaus of LiMnyFe1−yPO4 (LFMP), LiCoyFe1−yPO4 (LFCP), LiCoxMnyFe1−x−yPO4 (LFMCP), as well as their phase separation behavior. Furthermore, we develop a phase-field model of LFMP that consistently matches experimental data and identifies LiMn0.4Fe0.6PO4 as a superior composition that favors a solid solution phase transition, making it ideal for high-power applications.

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“…There is a broad field of applications for coupling the phase‐field with a concentration field. Previously, this coupling has been applied, for example, to corrosion of steels (e.g., Mai et al., 2016), solidification of alloys (e.g., Steinmetz et al., 2018) including advective effects (e.g., Laxmipathy et al., 2019), polymer solutions (e.g., H. Zhang et al., 2021), charging of battery systems (e.g., Daubner et al., 2022), hydrogen fuel cells (e.g., Hoffrogge et al., 2021), and martensitic phase transformation (e.g., Schoof et al., 2019), just to name a few.…”

Section: Introductionmentioning

confidence: 99%

Phase‐Field Simulations of Epitaxial Crystal Growth in Open Fractures With Reactive Lateral Flow

Späth

Selzer

Busch

et al. 2023

Water Resources Research

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Fluid flow in fracture porosity in the Earth's crust is in general accompanied by crystallization or dissolution depending on the state of saturation. The evolution of the microstructure in turn affects the transport and mechanical properties of the rock, but the understanding of this coupled system is incomplete. Here, we aim to simulate spatio‐temporal observations of laboratory experiments at the grain scale (using potash alumn), where crystals grow in a fracture during reactive flow, and show a varying growth rate along the fracture due to saturation differences. We use a multiphase‐field modeling approach, where reactive fluid flow and crystal growth is computed and couple the chemical driving force for grain growth to the local saturation state of the fluid. The supersaturation of the fluid is characterized by a concentration field which is advected by fluid flow and in turn affects the crystal growth with anisotropic growth kinetics. The simulations exhibit good agreement with the experimental results, providing the basis for upscaling our results to larger scale computations of combined multi‐physical processes in fractured porous media for applications as groundwater protection, geothermal, and hydrocarbon reservoir prediction, water recovery, or storing H2 or CO2 in the subsurface.

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Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of LiFePO4

Cited by 16 publications

References 77 publications

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

Thermodynamics of multi-sublattice battery active materials: from an extended regular solution theory to a phase-field model of LiMnFe<1-y>PO

Phase‐Field Simulations of Epitaxial Crystal Growth in Open Fractures With Reactive Lateral Flow

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Modeling intercalation in cathode materials with phase-field methods: Assumptions and implications using the example of LiFePO4

Cited by 16 publications

References 77 publications

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

Combined study of phase transitions in the P2-type NaXNi1/3Mn2/3O2 cathode material: experimental, ab-initio and multiphase-field results

Thermodynamics of multi-sublattice battery active materials: from an extended regular solution theory to a phase-field model of LiMnFe&lt;1-y&gt;PO

Phase‐Field Simulations of Epitaxial Crystal Growth in Open Fractures With Reactive Lateral Flow

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Thermodynamics of multi-sublattice battery active materials: from an extended regular solution theory to a phase-field model of LiMnFe<1-y>PO