Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

Guanglong Huang; David Montiel; Rebecca D. McAuliffe; Gabriel M. Veith; Katsuyo Thornton

doi:10.1016/j.commatsci.2023.112080

Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

Guanglong Huang, David Montiel, Rebecca D. McAuliffe, Gabriel M. Veith, Katsuyo Thornton

Energy Storage & Conversion

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Abstract

In this work, we present a phase-field model that captures the evolution of ionic concentrations and phase fractions during solid-state metathesis (SSM) reactions where diffusion limits the rate of transformation. The evolution of the mole fraction of each ion is obtained via governing equations that describe the reduction of a free energy, which includes an energy landscape with local minima located at compositions corresponding to stable products. We utilized two Lagrange multipliers to impose constraints of electroneutrality as well as on the sum of mole fractions, which were then eliminated to derive set of two partial differential equations that describe the dynamics of the mole fraction evolution. From these governing equations, the expressions for effective mobilities for the cations and the anions were obtained. We first study the effect of mobilities of ions on the reaction kinetics, using a simple model considering the ions with an identical absolute value of charge numbers. The simulation results show that the overall characteristic mobility, defined as the sum of the two effective ionic mobilities, provides an excellent measure of the rate at which reaction progresses and that the ratio of the effective mobilities of the anions and the cations signifies the manner by which the reaction progresses. We then generalize the model to consider ions with different charge numbers and tuned the mobility of ions based on their diffusion coefficients reported in the literature and experimental data from a thin-film experiment for the synthesis of FeS₂ to demonstrate the capability of the model to predict the phase evolution during SSM reactions. In particular, the simulation predicts nonplanar phase evolution, which is recently observed in thin-film reactions for the synthesis of FeS₂ via transmission electron microscopy. The approach can serve as a basis for models for phase transformations in other multiphase ionic mixtures, such as in all-solid-state batteries and in ionic liquids.

Original language	English
Article number	112080
Journal	Computational Materials Science
Volume	221
DOIs	https://doi.org/10.1016/j.commatsci.2023.112080
State	Published - Mar 25 2023

Funding

This work was supported as part of GENESIS: A Next Generation Synthesis Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under award No. DE-SC0019212. The computational resources were provided by the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE) Stampede2 at the TACC through allocation No. TG-DMR110007, which is supported by National Science Foundation grant number ACI-1548562. The research utilized experimental data obtained at Oak Ridge National Laboratory (ORNL), managed by UT Battelle, LLC for the U.S. Department of Energy (DOE) under contract DE-AC05-00OR22725. Finally, the authors would like to thank Vikram Gavini for the useful discussion. This work was supported as part of GENESIS: A Next Generation Synthesis Center, an Energy Frontier Research Center funded by the U.S. Department of Energy (DOE), Office of Science, Basic Energy Sciences under award No. DE-SC0019212. The computational resources were provided by the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231, and the Extreme Science and Engineering Discovery Environment (XSEDE) Stampede2 at the TACC through allocation No. TG-DMR110007, which is supported by National Science Foundation grant number ACI-1548562. The research utilized experimental data obtained at Oak Ridge National Laboratory (ORNL), managed by UT Battelle, LLC for the U.S. Department of Energy (DOE) under contract DE-AC05-00OR22725. Finally, the authors would like to thank Vikram Gavini for the useful discussion.

Funders	Funder number
Extreme Science and Engineering Discovery Environment
TACC	TG-DMR110007
Vikram Gavini
XSEDE
National Science Foundation	ACI-1548562
U.S. Department of Energy
Office of Science
Basic Energy Sciences	DE-SC0019212
Oak Ridge National Laboratory
Lawrence Berkeley National Laboratory	DE-AC02-05CH11231
UT-Battelle	DE-AC05-00OR22725

Keywords

Diffusion
Ionic compounds
Lagrange multiplier
Metathesis reaction
Phase-field model

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10.1016/j.commatsci.2023.112080

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title = "Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint",

abstract = "In this work, we present a phase-field model that captures the evolution of ionic concentrations and phase fractions during solid-state metathesis (SSM) reactions where diffusion limits the rate of transformation. The evolution of the mole fraction of each ion is obtained via governing equations that describe the reduction of a free energy, which includes an energy landscape with local minima located at compositions corresponding to stable products. We utilized two Lagrange multipliers to impose constraints of electroneutrality as well as on the sum of mole fractions, which were then eliminated to derive set of two partial differential equations that describe the dynamics of the mole fraction evolution. From these governing equations, the expressions for effective mobilities for the cations and the anions were obtained. We first study the effect of mobilities of ions on the reaction kinetics, using a simple model considering the ions with an identical absolute value of charge numbers. The simulation results show that the overall characteristic mobility, defined as the sum of the two effective ionic mobilities, provides an excellent measure of the rate at which reaction progresses and that the ratio of the effective mobilities of the anions and the cations signifies the manner by which the reaction progresses. We then generalize the model to consider ions with different charge numbers and tuned the mobility of ions based on their diffusion coefficients reported in the literature and experimental data from a thin-film experiment for the synthesis of FeS2 to demonstrate the capability of the model to predict the phase evolution during SSM reactions. In particular, the simulation predicts nonplanar phase evolution, which is recently observed in thin-film reactions for the synthesis of FeS2 via transmission electron microscopy. The approach can serve as a basis for models for phase transformations in other multiphase ionic mixtures, such as in all-solid-state batteries and in ionic liquids.",

keywords = "Diffusion, Ionic compounds, Lagrange multiplier, Metathesis reaction, Phase-field model",

author = "Guanglong Huang and David Montiel and McAuliffe, {Rebecca D.} and Veith, {Gabriel M.} and Katsuyo Thornton",

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AU - Montiel, David

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AU - Veith, Gabriel M.

AU - Thornton, Katsuyo

PY - 2023/3/25

Y1 - 2023/3/25

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ER -

Phase-field modeling of solid-state metathesis reactions with the charge neutrality constraint

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