Bowick Mark, Shin Homin, Travesset Alex
Department of Physics, Syracuse University, Syracuse, New York 13244-1130, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Feb;75(2 Pt 1):021404. doi: 10.1103/PhysRevE.75.021404. Epub 2007 Feb 22.
Point defects are ubiquitous in two-dimensional crystals and play a fundamental role in determining their mechanical and thermodynamical properties. When crystals are formed on a curved background, finite-length grain boundaries (scars) are generally needed to stabilize the crystal. We provide a continuum elasticity analysis of defect dynamics in curved crystals. By exploiting the fact that any point defect can be obtained as an appropriate combination of disclinations, we provide an analytical determination of the elastic spring constants of dislocations within scars and compare them with existing experimental measurements from optical microscopy. We further show that vacancies and interstitials, which are stable defects in flat crystals, are generally unstable in curved geometries. This observation explains why vacancies or interstitials are never found in equilibrium spherical crystals. We finish with some further implications for experiments and future theoretical work.
点缺陷在二维晶体中普遍存在，并且在决定其力学和热力学性质方面起着基础性作用。当晶体在弯曲背景上形成时，通常需要有限长度的晶界（疤痕）来使晶体稳定。我们提供了弯曲晶体中缺陷动力学的连续弹性分析。通过利用任何点缺陷都可以通过位错的适当组合得到这一事实，我们对疤痕内位错的弹性弹簧常数进行了解析确定，并将其与光学显微镜现有的实验测量结果进行比较。我们进一步表明，在平面晶体中稳定的空位和间隙原子，在弯曲几何结构中通常是不稳定的。这一观察结果解释了为什么在平衡球形晶体中从未发现空位或间隙原子。我们最后对实验和未来的理论工作提出了一些进一步的启示。
