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

Title: 位错线运动和动力学的相场晶体理论

Abstract: We present a general method to compute the dislocation density tensor and its evolution from the configuration of a spatially periodic order parameter associated with a given crystal symmetry. The method is applied to a phase field crystal model (PFC) of a bcc lattice, and used to investigate the shrinkage of a dislocation loop. The dislocation velocity is determined by the dynamics of the order parameter, and we have shown that the general expression predicts the overdamped motion induced by a Peach-Koehler force with mobilities determined by equilibrium properties. We introduce an additional, configuration dependent, lattice distortion, defined such that the configurational stress is maintained in elastic equilibrium at all times. The resulting far-field stress field agrees very well with predictions from continuum elasticity, while the near-field to defect core is regularized by lattice discreteness. For the shrinkage of a dislocation loop, we find that the classical PFC model captures its evolution only qualitatively, while the process happens on a much faster time scale when the system is constrained to remain in mechanical equilibrium. The formulation provides a robust and accurate tracking of defect motion in a deformed crystalline lattice. Show Chinese abstract

Abstract: 我们提出一种通用方法，从与给定晶体对称性相关的空间周期性序参数的构型计算位错密度张量及其演化。 该方法应用于体心立方晶格的相场晶体模型（PFC），并用于研究位错环的收缩。 位错速度由序参数的动力学决定，我们证明通用表达式预测了由Peach-Koehler力引起的过阻尼运动，其迁移率由平衡性质确定。 我们引入一个额外的、依赖于构型的晶格畸变，使得构型应力始终维持在弹性平衡状态。 结果的远场应力场与连续弹性理论的预测非常吻合，而缺陷核心附近的近场则通过晶格离散性得到正则化。 对于位错环的收缩，我们发现经典PFC模型仅能定性地捕捉其演化，而当系统被约束保持机械平衡时，该过程发生在更快的时间尺度上。 该公式提供了在变形晶体晶格中缺陷运动的稳健且精确的跟踪方法。