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Title: Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys

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. 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 tomore » lattice symmetry during a phase transition process.« less

Authors:
ORCiD logo [1];  [1]
  1. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States). Dept. of Materials Science and Engineering
Publication Date:
Research Org.:
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Sponsoring Org.:
USDOE Office of Science (SC); English-Speaking Union (ESU)
OSTI Identifier:
1433486
Alternate Identifier(s):
OSTI ID: 1433279
Grant/Contract Number:  
SC0002633
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 97; Journal Issue: 4; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
36 MATERIALS SCIENCE; 25 ENERGY STORAGE; phase field models; lithium batteries; phase transition; diffusion; grain boundaries; microstructure

Citation Formats

Balakrishna, Ananya Renuka, and Carter, W. Craig. Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.97.043304.
Balakrishna, Ananya Renuka, & Carter, W. Craig. Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys. United States. doi:10.1103/PhysRevE.97.043304.
Balakrishna, Ananya Renuka, and Carter, W. Craig. Mon . "Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys". United States. doi:10.1103/PhysRevE.97.043304. https://www.osti.gov/servlets/purl/1433486.
@article{osti_1433486,
title = {Combining phase-field crystal methods with a Cahn-Hilliard model for binary alloys},
author = {Balakrishna, Ananya Renuka and Carter, W. Craig},
abstractNote = {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. 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.},
doi = {10.1103/PhysRevE.97.043304},
journal = {Physical Review E},
issn = {2470-0045},
number = 4,
volume = 97,
place = {United States},
year = {2018},
month = {4}
}

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Cited by: 2 works
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Works referenced in this record:

Phospho-olivines as Positive-Electrode Materials for Rechargeable Lithium Batteries
journal, April 1997

  • Padhi, A. K.
  • Journal of The Electrochemical Society, Vol. 144, Issue 4, p. 1188-1194
  • DOI: 10.1149/1.1837571