2017/12/10 by Ananya Renuka Balakrishna, W. Craig Carter
Chemistry · Earth and Planetary Sciences · Engineering · Materials Science · Mathematics · Physics and Astronomy · #Affine transformation #Aluminum Alloy Microstructure Properties #Binary number #Chemistry #Condensed matter physics #Geometry #Hexagonal lattice #Homogeneous space #Lattice (music) #Materials science #Mathematics #Phase transition #Physics #Solidification and crystal growth phenomena #Statistical physics #Symmetry (geometry) #Transformation (genetics) #cond-mat.mtrl-sci #nanoparticles nucleation surface interactions
paper · pdf · doi:10.1103/physreve.97.043304
published as Phys. Rev. E 97, 043304 (2018) · 9 pages, 5 figures
arxiv created 2017/12/10 · openalex publication_date 2018/04/16 · arxiv updated 2018/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.