Bowick Mark J, Nelson David R, Shin Homin
Physics Department, Syracuse University, Syracuse, NY 13244-1130, USA.
Phys Chem Chem Phys. 2007 Dec 28;9(48):6304-12. doi: 10.1039/b710773k. Epub 2007 Nov 14.
Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and has a venerable history in the literature of theoretical physics and mathematics. Theory and experiment have confirmed that defects such as disclinations and dislocations are an intrinsic part of the ground state. Here we discuss the remarkable behavior of vacancies and interstitials in spherical crystals. The strain fields of isolated disclinations forced in by the spherical topology literally rip interstitials and vacancies apart, typically into dislocation fragments that combine with the disclinations to create small grain-boundary scars. The fractionalization is often into three charge-neutral dislocations, although dislocation pairs can be created as well. We use a powerful, freely-available computer program to explore interstitial fractionalization in some detail, for a variety of power-law pair potentials. We investigate the dependence on initial conditions and the final state energies, and compare the position dependence of interstitial energies with the predictions of continuum elastic theory on the sphere. The theory predicts that, before fragmentation, interstitials are repelled and vacancies are attracted from 5-fold disclinations. We also use vacancies and interstitials to study low-energy states in the vicinity of "magic numbers" that accommodate regular icosadeltahedral tessellations.
寻找堆积在球面上的相同粒子的基态对于稳定乳液具有重要意义，并且在理论物理和数学文献中有着悠久的历史。理论和实验已经证实，诸如位错和 disclinations（可译为“向错”）之类的缺陷是基态的固有组成部分。在这里，我们讨论球形晶体中空位和间隙原子的显著行为。由球形拓扑结构强制产生的孤立向错的应变场实际上会将间隙原子和空位撕裂，通常会形成与向错结合形成小晶界疤痕的位错片段。尽管也可以形成位错对，但通常会分裂成三个电荷中性的位错。我们使用一个强大的、免费的计算机程序，针对各种幂律对势，详细探讨间隙原子的分裂情况。我们研究对初始条件和最终态能量的依赖性，并将间隙原子能量的位置依赖性与球面上连续弹性理论的预测进行比较。该理论预测，在分裂之前，间隙原子会被 5 重向错排斥，空位会被吸引。我们还利用空位和间隙原子来研究容纳规则二十面体镶嵌的“幻数”附近的低能态。
