### 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=−1/12r_{0} ^{2}∂[(1−2c)V(c)]/∂c, where r_{0} 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 language | English |
---|---|

Article number | 101665 |

Journal | Calphad: Computer Coupling of Phase Diagrams and Thermochemistry |

Volume | 67 |

DOIs | |

Publication status | Published - Dec 1 2019 |

### Fingerprint

### 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

*Calphad: Computer Coupling of Phase Diagrams and Thermochemistry*,

*67*, [101665]. https://doi.org/10.1016/j.calphad.2019.101665

**Composition dependent gradient energy coefficient : How the asymmetric miscibility gap affects spinodal decomposition in Ag-Cu?** / Gajdics, Bence; Tomán, János J.; Erdélyi, Z.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Composition dependent gradient energy coefficient

T2 - How the asymmetric miscibility gap affects spinodal decomposition in Ag-Cu?

AU - Gajdics, Bence

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

KW - Gradient energy coefficient

KW - Interface

KW - Silver-copper alloy

KW - Spinodal decomposition

KW - Stochastic kinetic mean field (SKMF)

UR - http://www.scopus.com/inward/record.url?scp=85072198084&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85072198084&partnerID=8YFLogxK

U2 - 10.1016/j.calphad.2019.101665

DO - 10.1016/j.calphad.2019.101665

M3 - Article

AN - SCOPUS:85072198084

VL - 67

JO - Calphad: Computer Coupling of Phase Diagrams and Thermochemistry

JF - Calphad: Computer Coupling of Phase Diagrams and Thermochemistry

SN - 0364-5916

M1 - 101665

ER -