Travesset Alex
Department of Physics and Astronomy, Iowa State University, Ames, Iowa 50014, USA.
Phys Rev E. 2016 Dec;94(6-1):063001. doi: 10.1103/PhysRevE.94.063001. Epub 2016 Dec 13.
The dislocation and disclination density defining the structure of a crystal constrained on a general curved background is computed analytically in the thermodynamic limit, when the number of particles is arbitrarily large. It is shown that the minimum of the elastic energy, where strains are optimally close to zero, can be formulated in terms of a connection (a rule on how to parallel transport vectors), which allows to provide an explicit solution in the thermodynamic limit that consists of disclinations surrounded by scars (grain boundaries with variable spacing). The approach allows to compute the interaction potential. For a sphere, a full characterization of the scars is provided, and it is shown that the potential of interaction among disclinations "dressed" by scars is inversely proportional to the sinus of the geodesic distance and that the ground state consists of 12 dressed disclinations that display icosahedral symmetry. The case of a torus is also considered. More generally, the thermodynamic solution implements a "perfect screening" condition, where defects completely screen the Gaussian curvature. Implications for the problem of melting are discussed.
在热力学极限下，即粒子数任意大时，解析计算了定义在一般弯曲背景上的晶体结构的位错和向错密度。结果表明，在应变最优地接近零的情况下，弹性能的最小值可以用一个联络（一种平行移动矢量的规则）来表述，这使得在热力学极限下能够得到一个显式解，该解由被疤痕（间距可变的晶界）包围的向错组成。该方法能够计算相互作用势。对于球体，给出了疤痕的完整特征描述，并表明被疤痕“修饰”的向错之间的相互作用势与测地距离的正弦成反比，且基态由12个具有二十面体对称性的修饰向错组成。还考虑了环面的情况。更一般地，热力学解实现了一个“完美屏蔽”条件，即缺陷完全屏蔽高斯曲率。讨论了对熔化问题的影响。
