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 \(\Gamma \)-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, that is, 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.

我们研究了从原子粒子系统中出现的刚性多晶结构。原子相互作用受适当归一化的对相互作用能控制，其中“粘盘”相互作用势将原子建模为当切线时相互作用的硬球。离散能量是帧不变的，并且不假设原子结构上的基础参考晶格。通过\（\ Gamma \）-收敛，我们描述了在无限粒子限制下具有有限表面能缩放的结构的渐近行为。有效连续理论是用分段恒定场来描述的，该分段场描述了局部取向和构型的微观平移。极限能量是局部的并且集中在晶粒边界上，即，在下面的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以及界面的法线。我们进一步提供了真空-固相和固-固相变过程中晶界处表面能的精细分析。