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arXiv 2101.02596cond-mat.mtrl-sci
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晶界位错结构和能量的连续介质模型及数值方法

Continuum Model and Numerical Method for Dislocation Structure and Energy of Grain Boundaries

Xiaoxue Qin, Yejun Gu, Luchan Zhang, Yang Xiang

摘要:

我们提出了一个连续模型来确定三维小角度晶界的位错结构和能量。平衡位错结构是通过最小化晶界能量得到的,该晶界能量与受弗兰克公式约束的组分位错相关联。位错密度势函数可以方便地描述位错线在晶界上的连续分布,位错线在晶界上的轮廓线代表位错。晶界的能量是由离散位错动力学模型导出的组分位错的总能量,包括位错线能量和位错的反应。用增广拉格朗日方法和投影方法求解了约束能量最小化问题。与原子模拟结果的比较表明,我们的连续体模型是能够给平面和弯曲的小角度晶界的能量和位错密度的出色的预测。

英文摘要:

We present a continuum model to determine the dislocation structure and energy of low angle grain boundaries in three dimensions. The equilibrium dislocation structure is obtained by minimizing the grain boundary energy that is associated with the constituent dislocations subject to the constraint of Frank's formula. The orientation-dependent continuous distributions of dislocation lines on grain boundaries are described conveniently using the dislocation density potential functions, whose contour lines on the grain boundaries represent the dislocations. The energy of a grain boundary is the total energy of the constituent dislocations derived from discrete dislocation dynamics model, incorporating both the dislocation line energy and reactions of dislocations. The constrained energy minimization problem is solved by the augmented Lagrangian method and projection method. Comparisons with atomistic simulation results show that our continuum model is able to give excellent predictions of the energy and dislocation densities of both planar and curved low angle grain boundaries.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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