Composition dependent gradient energy coefficient: How the asymmetric miscibility gap affects spinodal decomposition in Ag-Cu?

Bence Gajdics, János J. Tomán, Z. Erdélyi

Research output: Contribution to journalArticle

Abstract

We report results for spinodal decomposition in Ag-Cu binary system. The asymmetric miscibility gap of any binary system necessarily means that the gradient energy coefficient κ is composition dependent. We demonstrate that while this composition dependence of κ does not modify the solubility curve and even the equilibrium interface profile hardly changes, the cutoff wavelength for spinodal decomposition does. Many calculations usually use composition independent gradient energy coefficient and the analytical expression for calculating the cutoff wavelength is valid also only for composition independent κ. We show that the κ-composition function can be calculated from the interaction energy V(c): κ=−1/12r0 2∂[(1−2c)V(c)]/∂c, where r0 is the interatomic distance. In this work we apply the Cahn-Hilliard theory and a 3D atomistic kinetic model, the Stochastic Kinetic Mean Field (SKMF), what we further developed purposefully. The improvement is not restricted to the Ag-Cu system, though, as the composition dependent interaction energy can be deduced e.g. from Redlich-Kister polynomials.

Original languageEnglish
Article number101665
JournalCalphad: Computer Coupling of Phase Diagrams and Thermochemistry
Volume67
DOIs
Publication statusPublished - Dec 1 2019

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Spinodal decomposition
Solubility
Chemical analysis
Wavelength
Kinetics
Polynomials

Keywords

  • Cahn-Hilliard
  • Gradient energy coefficient
  • Interface
  • Silver-copper alloy
  • Spinodal decomposition
  • Stochastic kinetic mean field (SKMF)

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Computer Science Applications

Cite this

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title = "Composition dependent gradient energy coefficient: How the asymmetric miscibility gap affects spinodal decomposition in Ag-Cu?",
abstract = "We report results for spinodal decomposition in Ag-Cu binary system. The asymmetric miscibility gap of any binary system necessarily means that the gradient energy coefficient κ is composition dependent. We demonstrate that while this composition dependence of κ does not modify the solubility curve and even the equilibrium interface profile hardly changes, the cutoff wavelength for spinodal decomposition does. Many calculations usually use composition independent gradient energy coefficient and the analytical expression for calculating the cutoff wavelength is valid also only for composition independent κ. We show that the κ-composition function can be calculated from the interaction energy V(c): κ=−1/12r0 2∂[(1−2c)V(c)]/∂c, where r0 is the interatomic distance. In this work we apply the Cahn-Hilliard theory and a 3D atomistic kinetic model, the Stochastic Kinetic Mean Field (SKMF), what we further developed purposefully. The improvement is not restricted to the Ag-Cu system, though, as the composition dependent interaction energy can be deduced e.g. from Redlich-Kister polynomials.",
keywords = "Cahn-Hilliard, Gradient energy coefficient, Interface, Silver-copper alloy, Spinodal decomposition, Stochastic kinetic mean field (SKMF)",
author = "Bence Gajdics and Tom{\'a}n, {J{\'a}nos J.} and Z. Erd{\'e}lyi",
year = "2019",
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T2 - How the asymmetric miscibility gap affects spinodal decomposition in Ag-Cu?

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AU - Tomán, János J.

AU - Erdélyi, Z.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - We report results for spinodal decomposition in Ag-Cu binary system. The asymmetric miscibility gap of any binary system necessarily means that the gradient energy coefficient κ is composition dependent. We demonstrate that while this composition dependence of κ does not modify the solubility curve and even the equilibrium interface profile hardly changes, the cutoff wavelength for spinodal decomposition does. Many calculations usually use composition independent gradient energy coefficient and the analytical expression for calculating the cutoff wavelength is valid also only for composition independent κ. We show that the κ-composition function can be calculated from the interaction energy V(c): κ=−1/12r0 2∂[(1−2c)V(c)]/∂c, where r0 is the interatomic distance. In this work we apply the Cahn-Hilliard theory and a 3D atomistic kinetic model, the Stochastic Kinetic Mean Field (SKMF), what we further developed purposefully. The improvement is not restricted to the Ag-Cu system, though, as the composition dependent interaction energy can be deduced e.g. from Redlich-Kister polynomials.

AB - We report results for spinodal decomposition in Ag-Cu binary system. The asymmetric miscibility gap of any binary system necessarily means that the gradient energy coefficient κ is composition dependent. We demonstrate that while this composition dependence of κ does not modify the solubility curve and even the equilibrium interface profile hardly changes, the cutoff wavelength for spinodal decomposition does. Many calculations usually use composition independent gradient energy coefficient and the analytical expression for calculating the cutoff wavelength is valid also only for composition independent κ. We show that the κ-composition function can be calculated from the interaction energy V(c): κ=−1/12r0 2∂[(1−2c)V(c)]/∂c, where r0 is the interatomic distance. In this work we apply the Cahn-Hilliard theory and a 3D atomistic kinetic model, the Stochastic Kinetic Mean Field (SKMF), what we further developed purposefully. The improvement is not restricted to the Ag-Cu system, though, as the composition dependent interaction energy can be deduced e.g. from Redlich-Kister polynomials.

KW - Cahn-Hilliard

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KW - Silver-copper alloy

KW - Spinodal decomposition

KW - Stochastic kinetic mean field (SKMF)

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