电荷依赖硬球模型：多晶作为低能构型

中文摘要 AI 辅助

我们研究了原子离子粒子系统中刚性多晶结构作为低能构型的涌现。相反电荷粒子之间的相互作用通过硬球建模，当它们相切时发生相互作用。同种电荷粒子之间的相互作用建模为硬排斥，迫使它们之间保持最小距离。原子能量是框架不变的，并且对离子构型不假设任何底层参考晶格。通过Γ-收敛，我们识别了具有有限表面能标度的构型的渐近行为。相关的连续介质理论由分段常数场描述，这些场编码了构型的局部取向。极限能量是局部的，并集中在晶界处，晶界对应于底层构型具有恒定取向的区域的边界。极限能量密度是各向异性的，取决于两个晶粒的相对错向、它们的平移失配以及它们界面的法线。此外，我们对固-固和固-真空相变的表面能进行了精细分析，并确定了能量上有利的取向失配。这依赖于我们晶界的一个结构结果，该结果表明，由于刚性设置，晶界界面附近的插值层在能量上是不利的。

英文摘要

We investigate the emergence of rigid polycrystalline structures in atomistic ionic particle systems as low-energy configurations. The interaction between particles of opposite charge is modeled by hard spheres that interact when they are tangential. The interaction between particles of same charge is modeled as a hard repulsion that forces a minimal distance between them. The atomistic energy is frame invariant, and no underlying reference lattice is assumed on the ionic configurations. The asymptotic behavior of configurations with finite surface energy scaling is identified by means of $Γ$-convergence. The related continuum theory is described by piecewise constant fields that encode the local orientation of the configuration. The limiting energy is local and concentrates at grain boundaries, which correspond to the boundaries of the regions where the underlying configuration has a constant orientation. The limiting energy density is anisotropic and depends on the relative misorientation of the two grains, their translation misfit, and the normal to their interface. Furthermore, we perform a fine analysis of surface energies for solid-solid and solid-vacuum phase transitions and determine energetically favorable orientation mismatches. This relies on a structure result for our grain boundaries, which shows that, due to the rigid setup, interpolating layers near the grain interface are energetically not favorable.

发表机构

• Technische Universität München（慕尼黑工业大学）

机构由 AI 辅助整理，请以论文原文为准。

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46 pages, 12 figures