论文标题
来自FCC和HCP晶格上原子系统的Wulff晶体的出现
Emergence of Wulff-Crystals from atomistic systems on the FCC and HCP lattices
论文作者
论文摘要
我们考虑乘坐$ n $硬球的系统，位于$ \ mathrm {fcc} $或$ \ mathrm {hcp} $ lattice的节点上，并通过粘性磁势进行交互。由于$ n $倾向于无穷大（连续限制），假设相互作用的能量不超过$ n^{2/3} $（表面缩放），我们通过$γ$ - convergence获得了变异的粗粒模型。更确切地说，我们证明连续限制的能量是外围类型的，并且我们明确地计算其wulff形状。我们的分析表明，$ \ mathrm {fcc} $上的结晶比在$ \ mathrm {hcp} $上的$ n $最大。该方法基于积分表示和浓度 - 压缩结果，我们证明了在任何维度上的一般周期性晶格。
We consider a system of $N$ hard spheres sitting on the nodes of either the $\mathrm{FCC}$ or $\mathrm{HCP}$ lattice and interacting via a sticky-disk potential. As $N$ tends to infinity (continuum limit), assuming the interaction energy does not exceed that of the ground-state by more than $N^{2/3}$ (surface scaling), we obtain the variational coarse grained model by $Γ$-convergence. More precisely, we prove that the continuum limit energies are of perimeter type and we compute explicitly their Wulff shapes. Our analysis shows that crystallization on $\mathrm{FCC}$ is preferred to that on $\mathrm{HCP}$ for $N$ large enough. The method is based on integral representation and concentration-compactness results that we prove for general periodic lattices in any dimension.
