具有Heitmann-Radin粘盘能的原子系统中刚性多晶体的涌现
Emergence of rigid Polycrystals from atomistic Systems with Heitmann-Radin sticky disk energy
摘要：
我们研究刚性多晶结构的原子粒子系统的出现。原子的相互作用是由一个适当的归一化对相互作用能，其中的“粘盘”相互作用势模型的硬球时，他们是切向相互作用的原子。离散的能量是框架不变的，没有潜在的参考晶格上的原子配置被假定。利用$Γ$ -收敛性，我们刻画了有限表面能标度组态在无限粒子极限下的渐近行为。有效的连续介质理论描述在一个分段恒定的字段划定的局部取向和微平移的配置。限制能量是局部的并且集中在晶界上，即，在底层微观结构具有恒定参数的区域的边界上。相应的表面能密度取决于两个晶粒的相对取向、它们的微观平移失配和界面的法线。我们进一步提供了一个精细的分析，在真空-固体和固体-固体相变的晶界表面能。后者基本上依赖于晶界的结构结果，表明由于裂纹附近的内插边界层的极脆设置，在能量上是不利的。
英文摘要：
We investigate the emergence of rigid polycrystalline structures from atomistic particle systems. The atomic interaction is governed by a suitably normalized pair interaction energy, where the `sticky disk' interaction potential models the atoms as hard spheres that interact when they are tangential. The discrete energy is frame invariant and no underlying reference lattice on the atomistic configurations is assumed. By means of $Γ$-convergence, we characterize the asymptotic behavior of configurations with finite surface energy scaling in the infinite particle limit. The effective continuum theory is described in terms of a piecewise constant field delineating the local orientation and micro-translation of the configuration. The limiting energy is local and concentrated on the grain boundaries, i.e., on the boundaries of the zones where the underlying microscopic configuration has constant parameters. The corresponding surface energy density depends on the relative orientation of the two grains, their microscopic translation misfit, and the normal to the interface. We further provide a fine analysis of the surface energies at grain boundaries both for vacuum-solid and solid-solid phase transitions. The latter relies fundamentally on a structure result for grain boundaries showing that due to the extremely brittle setup interpolating boundary layers near cracks are energetically not favorable.
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