Anisotropic Cahn-Hilliard free energy and interfacial energies for binary alloys with pairwise interactions
Abstract
The original Cahn-Hilliard derivation of the contribution of compositional inhomogeneity to the free energy of a binary alloy with pairwise interactions is extended to include higher-order inhomogeneity terms. For alloys on a cubic lattice, the coefficient of the first inhomogeneity is a second-rank tensor and reduces to a scalar, but it is shown that the second order and the third order inhomogeneity terms are weighted by fourth-rank and sixth-rank tensors, thus resulting in anisotropic contributions. Furthermore, each interaction shell generates a unique set of inhomogeneity coefficients that is determined by the set of vectors connecting an atom to its neighbors on that shell. These coefficients are calculated for fcc and bcc alloys with interactions up fourth nearest neighbors. Phase field simulations based on these extended Cahn-Hilliard free energies are performed to measure interface free energies along specific crystallographic directions as a function of temperature, and to obtain the equilibrium shape of precipitates. Interface free energies, and the resulting anisotropies, are compared to those obtained by discrete models and Monte Carlo simulations.
- Publication Date:
- Research Org.:
- Univ. of Illinois at Urbana-Champaign, IL (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1853401
- Alternate Identifier(s):
- OSTI ID: 1797504
- Grant/Contract Number:
- SC0019875
- Resource Type:
- Accepted Manuscript
- Journal Name:
- Acta Materialia
- Additional Journal Information:
- Journal Volume: 215; Journal Issue: C; Journal ID: ISSN 1359-6454
- Publisher:
- Elsevier
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 36 MATERIALS SCIENCE
Citation Formats
Bellon, P., and Li, Q. Anisotropic Cahn-Hilliard free energy and interfacial energies for binary alloys with pairwise interactions. United States: N. p., 2021.
Web. doi:10.1016/j.actamat.2021.117041.
Bellon, P., & Li, Q. Anisotropic Cahn-Hilliard free energy and interfacial energies for binary alloys with pairwise interactions. United States. https://doi.org/10.1016/j.actamat.2021.117041
Bellon, P., and Li, Q. Thu .
"Anisotropic Cahn-Hilliard free energy and interfacial energies for binary alloys with pairwise interactions". United States. https://doi.org/10.1016/j.actamat.2021.117041. https://www.osti.gov/servlets/purl/1853401.
@article{osti_1853401,
title = {Anisotropic Cahn-Hilliard free energy and interfacial energies for binary alloys with pairwise interactions},
author = {Bellon, P. and Li, Q.},
abstractNote = {The original Cahn-Hilliard derivation of the contribution of compositional inhomogeneity to the free energy of a binary alloy with pairwise interactions is extended to include higher-order inhomogeneity terms. For alloys on a cubic lattice, the coefficient of the first inhomogeneity is a second-rank tensor and reduces to a scalar, but it is shown that the second order and the third order inhomogeneity terms are weighted by fourth-rank and sixth-rank tensors, thus resulting in anisotropic contributions. Furthermore, each interaction shell generates a unique set of inhomogeneity coefficients that is determined by the set of vectors connecting an atom to its neighbors on that shell. These coefficients are calculated for fcc and bcc alloys with interactions up fourth nearest neighbors. Phase field simulations based on these extended Cahn-Hilliard free energies are performed to measure interface free energies along specific crystallographic directions as a function of temperature, and to obtain the equilibrium shape of precipitates. Interface free energies, and the resulting anisotropies, are compared to those obtained by discrete models and Monte Carlo simulations.},
doi = {10.1016/j.actamat.2021.117041},
journal = {Acta Materialia},
number = C,
volume = 215,
place = {United States},
year = {Thu Jun 03 00:00:00 EDT 2021},
month = {Thu Jun 03 00:00:00 EDT 2021}
}
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