Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys
Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in...
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| Format: | Article |
| Language: | English |
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American Physical Society
2018
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| Online Access: | http://hdl.handle.net/1721.1/114765 https://orcid.org/0000-0001-7564-7173 |
| _version_ | 1826214824072183808 |
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| author | Balakrishna, Ananya Renuka Carter, W Craig |
| author2 | Massachusetts Institute of Technology. Department of Materials Science and Engineering |
| author_facet | Massachusetts Institute of Technology. Department of Materials Science and Engineering Balakrishna, Ananya Renuka Carter, W Craig |
| author_sort | Balakrishna, Ananya Renuka |
| collection | MIT |
| description | Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process. |
| first_indexed | 2024-09-23T16:12:03Z |
| format | Article |
| id | mit-1721.1/114765 |
| institution | Massachusetts Institute of Technology |
| language | English |
| last_indexed | 2024-09-23T16:12:03Z |
| publishDate | 2018 |
| publisher | American Physical Society |
| record_format | dspace |
| spelling | mit-1721.1/1147652022-10-02T07:01:27Z Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys Balakrishna, Ananya Renuka Carter, W Craig Massachusetts Institute of Technology. Department of Materials Science and Engineering Balakrishna, Ananya Renuka Carter, W Craig Diffusion-induced phase transitions typically change the lattice symmetry of the host material. In battery electrodes, for example, Li ions (diffusing species) are inserted between layers in a crystalline electrode material (host). This diffusion induces lattice distortions and defect formations in the electrode. The structural changes to the lattice symmetry affect the host material's properties. Here, we propose a 2D theoretical framework that couples a Cahn-Hilliard (CH) model, which describes the composition field of a diffusing species, with a phase-field crystal (PFC) model, which describes the host-material lattice symmetry. We couple the two continuum models via coordinate transformation coefficients. We introduce the transformation coefficients in the PFC method to describe affine lattice deformations. These transformation coefficients are modeled as functions of the composition field. Using this coupled approach, we explore the effects of coarse-grained lattice symmetry and distortions on a diffusion-induced phase transition process. In this paper, we demonstrate the working of the CH-PFC model through three representative examples: First, we describe base cases with hexagonal and square symmetries for two composition fields. Next, we illustrate how the CH-PFC method interpolates lattice symmetry across a diffuse phase boundary. Finally, we compute a Cahn-Hilliard type of diffusion and model the accompanying changes to lattice symmetry during a phase transition process. United States. Department of Energy (Grant DE-SC0002633) 2018-04-17T18:53:44Z 2018-04-17T18:53:44Z 2018-04 2018-02 2018-04-16T18:00:11Z Article http://purl.org/eprint/type/JournalArticle 2470-0045 2470-0053 http://hdl.handle.net/1721.1/114765 Balakrishna, Ananya Renuka and W. Craig Carter. "Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys." Physical Review E 97, 4 (April 2018): 043304 © 2018 American Physical Society https://orcid.org/0000-0001-7564-7173 en http://dx.doi.org/10.1103/PhysRevE.97.043304 Physical Review E Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. American Physical Society application/pdf American Physical Society American Physical Society |
| spellingShingle | Balakrishna, Ananya Renuka Carter, W Craig Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys |
| title | Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys |
| title_full | Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys |
| title_fullStr | Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys |
| title_full_unstemmed | Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys |
| title_short | Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys |
| title_sort | combining phase field crystal methods with a cahn hilliard model for binary alloys |
| url | http://hdl.handle.net/1721.1/114765 https://orcid.org/0000-0001-7564-7173 |
| work_keys_str_mv | AT balakrishnaananyarenuka combiningphasefieldcrystalmethodswithacahnhilliardmodelforbinaryalloys AT carterwcraig combiningphasefieldcrystalmethodswithacahnhilliardmodelforbinaryalloys |