半共格界面 Peierls-Nabarro 模型中位错的均匀分布
Uniform distribution of dislocations in Peierls-Nabarro models for semi-coherent interfaces
AI总结：
该研究建立半共格界面刃位错的 Peierls-Nabarro 型模型，通过弹性能 Γ-收敛证明一维圆周上等间距均匀位错分布达到最小界面能量。
摘要：
本文介绍了用于两种异质晶体间半共格界面处刃位错的 Peierls-Nabarro 型模型，并证明了均匀分布刃位错的最优性。具体而言，作者表明弹性能以 Γ-收敛趋于一个由两部分组成的极限泛函：其一为常数 c_∞>0，用于衡量界面处位错诱导的最小能量，并对应于刃位错的均匀分布；另一部分计入由额外的、可能并非均匀分布的位错存在所诱导的远场弹性能。在假设周期边界条件并形式上考虑从半共格界面到共格界面的极限后，研究表明，当位错在一维圆周上等间距分布时达到 c_∞。
英文摘要：
In this paper we introduce Peierls-Nabarro type models for edge dislocations at semi-coherent interfaces between two heterogeneous crystals, and prove the optimality of uniformly distributed edge dislocations. Specifically, we show that the elastic energy $Γ$-converges to a limit functional comprised of two contributions: one is given by a constant $c_\infty>0$ gauging the minimal energy induced by dislocations at the interface, and corresponding to a uniform distribution of edge dislocations; the other one accounts for the far field elastic energy induced by the presence of further, possibly not uniformly distributed, dislocations. After assuming periodic boundary conditions and formally considering the limit from semi-coherent to coherent interfaces, we show that $c_\infty$ is reached when dislocations are evenly-spaced on the one dimensional circle.
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