间隙分形与球形晶体学
Interstitial Fractionalization and Spherical Crystallography
摘要：
寻找堆积在球体上的相同粒子的基态与稳定乳状液有关，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，诸如向错和位错的缺陷是基态的固有部分。本文讨论球形晶体中空位和杂质的显著行为。由球形拓扑结构强制进入的孤立的向错的应变场实际上将晶体和空位撕裂开，通常为位错碎片，其与向错结合以产生小的晶界疤痕。分馏通常分为三个电荷中性位错，尽管也可以产生位错对。我们使用一个功能强大的，免费提供的计算机程序，探索间隙细分的一些细节，各种幂律对电位。我们调查的初始条件和最终状态的能量的依赖性，并比较的位置依赖性的间隙能量与连续弹性理论的预测球。该理论预测，在碎裂之前，间隙原子被5倍向错排斥，空位被吸引。我们还使用空位和光子来研究低能态附近的“幻数”，以适应定期二十面体镶嵌。
英文摘要：
Finding the ground states of identical particles packed on spheres has relevance for stabilizing emulsions and 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 fractionation 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 from 5-fold disclinations and vacancies are attracted. We also use vacancies and interstitials to study low energy states in the vicinity of "magic numbers" that accommodate regular icosadeltahedral tessellations.
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