Whereas disclination defects are energetically prohibitive in two-dimensional flat crystals, their existence is necessary in crystals with spherical topology, such as viral capsids, colloidosomes, or fullerenes. Such a geometrical frustration gives rise to large elastic stresses, which render the crystal unstable when its size is significantly larger than the typical lattice spacing. Depending on the compliance of the crystal with respect to stretching and bending deformations, these stresses are alleviated either by a local increase of the intrinsic curvature in proximity of the disclinations or by the proliferation of excess dislocations, often organized in the form of one-dimensional chains known as “scars.” The associated strain field of the scars is such as to counterbalance the one resulting from the isolated disclinations. Here we develop a continuum theory of dislocation screening in two-dimensional closed crystals with genus one. Upon modeling the flux of scars emanating from a given disclination as an independent scalar field, we demonstrate that the elastic energy of closed two-dimensional crystals with various degrees of asphericity can be expressed as a simple quadratic function of the screened topological charge of the disclinations, at both zero and finite temperature. This allows us to predict the optimal density of the excess dislocations as well as the minimal stretching energy attained by the crystal.

中文翻译：

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具有球形拓扑结构的晶体中的位错筛选。

尽管向错缺陷在二维平面晶体中在能量上是禁止的，但在具有球形拓扑的晶体（例如病毒衣壳，胶体或富勒烯）中，存在缺陷是必不可少的。这种几何上的挫折会产生很大的弹性应力，当晶体的尺寸明显大于典型的晶格间距时，就会使晶体不稳定。根据晶体相对于拉伸和弯曲变形的顺应性，这些应力可以通过向错附近的固有曲率局部增大，或者通过通常以一维形式组织的过量位错的扩散来缓解。连锁店被称为“疤痕”。疤痕的相关应变场可以抵消由于孤立的向错所引起的应变场。在这里，我们发展了一种连续的位错筛查理论，该筛查是一类二维封闭晶体的结果。通过将给定旋错产生的疤痕通量建模为独立的标量场，我们证明了具有不同非球面度的闭合二维晶体的弹性能可以表示为旋错的筛选拓扑电荷的简单二次函数，在零温度和有限温度下均如此。这使我们能够预测过量位错的最佳密度以及晶体获得的最小拉伸能。我们证明了具有不同非球面度的闭合二维晶体的弹性能可以表示为零和有限温度下向错的屏蔽拓扑电荷的简单二次函数。这使我们能够预测过量位错的最佳密度以及晶体获得的最小拉伸能。我们证明了具有不同非球面度的闭合二维晶体的弹性能可以表示为零和有限温度下向错的屏蔽拓扑电荷的简单二次函数。这使我们能够预测过量位错的最佳密度以及晶体获得的最小拉伸能。