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首页> 外文期刊>Discrete and continuous dynamical systems >RIGIDITY OF THREE-DIMENSIONAL LATTICES AND DIMENSION REDUCTION IN HETEROGENEOUS NANOWIRES
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RIGIDITY OF THREE-DIMENSIONAL LATTICES AND DIMENSION REDUCTION IN HETEROGENEOUS NANOWIRES

机译：异质纳米线的三维晶格刚度和维数减少

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摘要

In the context of nanowire heterostructures we perform a discrete to continuum limit of the corresponding free energy by means of Γ-convergence techniques. Nearest neighbours are identified by employing the notions of Voronoi diagrams and Delaunay triangulations. The scaling of the nanowire is done in such a way that we perform not only a continuum limit but a dimension reduction simultaneously. The main part of the proof is a discrete geometric rigidity result that we announced in an earlier work and show here in detail for a variety of three-dimensional lattices. We perform the passage from discrete to continuum twice: once for a system that compensates a lattice mismatch between two parts of the heterogeneous nanowire without defects and once for a system that creates dislocations. It turns out that we can verify the experimentally observed fact that the nanowires show dislocations when the radius of the specimen is large.
机译：在纳米线异质结构的背景下，我们通过Γ收敛技术对相应自由能进行了离散到连续的极限。通过使用Voronoi图和Delaunay三角剖分的概念来识别最近的邻居。纳米线的缩放以这样的方式完成：我们不仅执行连续极限，而且同时执行尺寸减小。证明的主要部分是离散的几何刚度结果，我们在较早的工作中宣布了结果，并在此详细显示了各种三维晶格。我们执行从离散到连续的两次转换：一次用于补偿无缺陷的异质纳米线两部分之间晶格失配的系统，一次用于产生位错的系统。事实证明，我们可以验证实验观察到的事实，即当样品的半径较大时，纳米线会显示出位错。

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