Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys
Name
PhysRevE.97.043304.pdf
Size
4.26 MB
Format
Adobe PDF
Checksum (MD5)
1049f3c4f2a07edeb207baebd36960f9
Author(s)
Balakrishna, Ananya Renuka
Carter, W Craig
Date Issued
April 2018
Journal
Physical Review E
Publisher
American Physical Society
Citation
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
Version
Final published version
Abstract
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.
MIT Department
Massachusetts Institute of Technology. Department of Materials Science and Engineering
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Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1103/PhysRevE.97.043304
