Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space

Yue Li; Zhijun Wang; Junjie Li; Jincheng Wang; Ke gang Wang

doi:10.1016/j.jcrysgro.2023.127312

Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space

Yue Li, Zhijun Wang, Junjie Li, Jincheng Wang, Ke gang Wang

School of Materials Sience and Engineering

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Mean-field theory has been widely applied in modelling the kinetics of microstructure evolution. Considering a free energy contribution by microstructure entropy, a Fokker-Planck equation for precipitation kinetics is variationally derived from thermodynamic principles. Using dimensionless transformation into the Lifshitz-Slyozov-Wagner space, the Fokker-Planck equation is effectively solved within a fixed radius interval and an explicit Euler scheme, which is computationally advantageous. Through comparisons with the Ni-12.5 Al at. % alloy, it is shown that the Fokker-Planck equation can represent the typical stages of precipitation kinetics, i.e., nucleation, growth, and coarsening.

Original language	English
Article number	127312
Journal	Journal of Crystal Growth
Volume	618
DOIs	https://doi.org/10.1016/j.jcrysgro.2023.127312
State	Published - 15 Sep 2023

Keywords

A1. Computer simulation
A1. Growth models
A1. Nucleation
B1. Alloys

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10.1016/j.jcrysgro.2023.127312

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title = "Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space",

abstract = "Mean-field theory has been widely applied in modelling the kinetics of microstructure evolution. Considering a free energy contribution by microstructure entropy, a Fokker-Planck equation for precipitation kinetics is variationally derived from thermodynamic principles. Using dimensionless transformation into the Lifshitz-Slyozov-Wagner space, the Fokker-Planck equation is effectively solved within a fixed radius interval and an explicit Euler scheme, which is computationally advantageous. Through comparisons with the Ni-12.5 Al at. % alloy, it is shown that the Fokker-Planck equation can represent the typical stages of precipitation kinetics, i.e., nucleation, growth, and coarsening.",

keywords = "A1. Computer simulation, A1. Growth models, A1. Nucleation, B1. Alloys",

author = "Yue Li and Zhijun Wang and Junjie Li and Jincheng Wang and Wang, {Ke gang}",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2023",

month = sep,

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doi = "10.1016/j.jcrysgro.2023.127312",

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TY - JOUR

T1 - Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space

AU - Li, Yue

AU - Wang, Zhijun

AU - Li, Junjie

AU - Wang, Jincheng

AU - Wang, Ke gang

PY - 2023/9/15

Y1 - 2023/9/15

N2 - Mean-field theory has been widely applied in modelling the kinetics of microstructure evolution. Considering a free energy contribution by microstructure entropy, a Fokker-Planck equation for precipitation kinetics is variationally derived from thermodynamic principles. Using dimensionless transformation into the Lifshitz-Slyozov-Wagner space, the Fokker-Planck equation is effectively solved within a fixed radius interval and an explicit Euler scheme, which is computationally advantageous. Through comparisons with the Ni-12.5 Al at. % alloy, it is shown that the Fokker-Planck equation can represent the typical stages of precipitation kinetics, i.e., nucleation, growth, and coarsening.

AB - Mean-field theory has been widely applied in modelling the kinetics of microstructure evolution. Considering a free energy contribution by microstructure entropy, a Fokker-Planck equation for precipitation kinetics is variationally derived from thermodynamic principles. Using dimensionless transformation into the Lifshitz-Slyozov-Wagner space, the Fokker-Planck equation is effectively solved within a fixed radius interval and an explicit Euler scheme, which is computationally advantageous. Through comparisons with the Ni-12.5 Al at. % alloy, it is shown that the Fokker-Planck equation can represent the typical stages of precipitation kinetics, i.e., nucleation, growth, and coarsening.

KW - A1. Computer simulation

KW - A1. Growth models

KW - A1. Nucleation

KW - B1. Alloys

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DO - 10.1016/j.jcrysgro.2023.127312

M3 - 文章

AN - SCOPUS:85162126944

SN - 0022-0248

VL - 618

JO - Journal of Crystal Growth

JF - Journal of Crystal Growth

M1 - 127312

ER -

Mean-field modelling of precipitation kinetics with a Fokker-Planck equation in the Lifshitz–Slyozov–Wagner space

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