We investigate the formation of cluster crystals with multiply occupied lattice sites on a spherical surface in systems of ultra-soft particles interacting via repulsive, bounded pair potentials. Not all interactions of this kind lead to clustering: we generalize the criterion devised in C. N. Likos et al., Phys. Rev. E, 2001, 63, 031206 to spherical systems in order to distinguish between cluster-forming systems and fluids which display reentrant melting. We use both DFT and Monte Carlo simulations to characterize the behavior of the system, and obtain semi-quantitative agreement between the two. We find that the number of clusters is determined by the ratio between the size σ of the ultra-soft particles and the radius R of the sphere in such a way that each stable configuration spans a certain interval of σ/R. Furthermore, we study the effect of topological frustration on the system due to the sphere curvature by comparing the properties of disclinations, i.e., clusters with fewer than six neighbors, and non-defective clusters. Disclinations are shown to be less stable, contain fewer particles, and be closer to their neighbors than other lattice points: these properties are explained on the basis of geometric and energetic considerations.

中文翻译：

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球形表面上超软势模型中团簇晶体的形成

我们调查通过排斥，有界对势相互作用的超软粒子系统中的球形表面上具有多个占据的晶格位点的簇状晶体的形成。并非所有此类交互都会导致聚类：我们概括了CN Likos等人设计的标准。，物理 启ê，2001，63，031206到球形系统，以便形成集群系统和流体，其显示折返熔化之间进行区分。我们使用DFT和Monte Carlo仿真来表征系统的行为，并获得两者之间的半定量一致性。我们发现簇的数量由大小σ之比决定超软粒子的半径和球半径R以这样的方式进行，使得每个稳定的构型跨越一定的σ / R间隔。此外，我们通过比较错位（即少于6个邻居的簇和无缺陷簇）的性质来研究由于球体曲率而导致的拓扑挫折对系统的影响。与其他晶格点相比，旋错显示的稳定性较差，包含的粒子更少且与邻居的距离更近：这些属性是根据几何和能量方面的考虑进行解释的。