Title: A phase field crystal theory of the kinematics of dislocation lines Show Chinese title

Title: 位错线运动的相场晶体理论

Abstract: We introduce a dislocation density tensor and derive its kinematic evolution law from a phase field description of crystal deformations in three dimensions. The phase field crystal (PFC) model is used to define the lattice distortion, including topological singularities, and the associated configurational stresses. We derive an exact expression for the velocity of dislocation line determined by the phase field evolution, and show that dislocation motion in the PFC is driven by a Peach-Koehler force. As is well known from earlier PFC model studies, the configurational stress is not divergence free for a general field configuration. Therefore, we also present a method (PFCMEq) to constrain the diffusive dynamics to mechanical equilibrium by adding an independent and integrable distortion so that the total resulting stress is divergence free. In the PFCMEq model, the far-field stress agrees very well with the predictions from continuum elasticity, while the near-field stress around the dislocation core is regularized by the smooth nature of the phase-field. We apply this framework to study the rate of shrinkage of an dislocation loop seeded in its glide plane. Show Chinese abstract

Abstract: 我们引入了一种位错密度张量，并从三维晶体变形的相场描述中推导出其运动学演化定律。 相场晶体（PFC）模型用于定义晶格畸变，包括拓扑奇点以及相关的构型应力。 我们推导出由相场演化决定的位错线速度的精确表达式，并表明PFC中的位错运动是由Peach-Koehler力驱动的。 正如早期的PFC模型研究中所熟知的，对于一般的场配置，构型应力不是散度为零的。 因此，我们还提出了一种方法（PFCMEq），通过添加一个独立且可积的畸变来约束扩散动力学以达到力学平衡，从而使总应力散度为零。 在PFCMEq模型中，远场应力与连续弹性理论的预测非常吻合，而位错核心周围的近场应力则由于相场的平滑特性而被正则化。 我们将这个框架应用于研究在滑移面上生成的位错环的收缩速率。