In this article, we present the behavior of two‐mode phase field crystal (2MPFC) method under a concentration dependent deformation. A mixed finite element formulation is proposed for the 2MPFC method that solves a 10th‐order parabolic equation. Lithium concentration diffusion in the electrode particle is captured by the Cahn–Hilliard (CH) equation and the host electrode material, Li_xMn₂O₄ (LMO), which has a face‐centered cubic (fcc) lattice structure, is modeled using 2MPFC. The coupling between 2MPFC and CH models brings about the concentration dependent deformation in the polycrystalline LMO electrode particle. The atomistic dynamics is assumed to operate on a faster time‐scale compared to the diffusion of lithium, thereby both the 2MPFC and CH models evolve on two different time‐scales. The coupled 2MPFC–CH system models the diffusion induced grain boundary migration in LMO capturing the charging and discharging state of the battery.

中文翻译：

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利用Cahn-Hilliard耦合双模相场晶体模型实现电池电极颗粒的相分离

在本文中，我们介绍了在浓度依赖性变形下的双模相场晶体（2MPFC）方法的行为。提出了用于求解10阶抛物线方程的2MPFC方法的混合有限元公式。电极粒子中的锂浓度扩散通过Cahn–Hilliard（CH）方程和主体电极材料Li _x Mn ₂ O ₄捕获（LMO）具有面心立方（fcc）晶格结构，使用2MPFC进行建模。2MPFC和CH模型之间的耦合在多晶LMO电极颗粒中引起浓度依赖的变形。与锂的扩散相比，假定原子动力学的运行时间更快，因此2MPFC模型和CH模型都在两个不同的时间尺度上演化。耦合的2MPFC–CH系统对LMO中由扩散引起的晶界迁移进行建模，以捕获电池的充电和放电状态。