Nandipati Giridhar, Shim Yunsic, Amar Jacques G, Karim Altaf, Kara Abdelkader, Rahman Talat S, Trushin Oleg
Department of Physics and Astronomy, University of Toledo, Toledo, OH 43606, USA.
J Phys Condens Matter. 2009 Feb 25;21(8):084214. doi: 10.1088/0953-8984/21/8/084214. Epub 2009 Jan 30.
The results of parallel kinetic Monte Carlo (KMC) simulations of the room-temperature coarsening of Ag(111) islands carried out using a very large database obtained via self-learning KMC simulations are presented. Our results indicate that, while cluster diffusion and coalescence play an important role for small clusters and at very early times, at late time the coarsening proceeds via Ostwald ripening, i.e. large clusters grow while small clusters evaporate. In addition, an asymptotic analysis of our results for the average island size S(t) as a function of time t leads to a coarsening exponent n = 1/3 (where S(t)∼t(2n)), in good agreement with theoretical predictions. However, by comparing with simulations without concerted (multi-atom) moves, we also find that the inclusion of such moves significantly increases the average island size. Somewhat surprisingly we also find that, while the average island size increases during coarsening, the scaled island-size distribution does not change significantly. Our simulations were carried out both as a test of, and as an application of, a variety of different algorithms for parallel kinetic Monte Carlo including the recently developed optimistic synchronous relaxation (OSR) algorithm as well as the semi-rigorous synchronous sublattice (SL) algorithm. A variation of the OSR algorithm corresponding to optimistic synchronous relaxation with pseudo-rollback (OSRPR) is also proposed along with a method for improving the parallel efficiency and reducing the number of boundary events via dynamic boundary allocation (DBA). A variety of other methods for enhancing the efficiency of our simulations are also discussed. We note that, because of the relatively high temperature of our simulations, as well as the large range of energy barriers (ranging from 0.05 to 0.8 eV), developing an efficient algorithm for parallel KMC and/or SLKMC simulations is particularly challenging. However, by using DBA to minimize the number of boundary events, we have achieved significantly improved parallel efficiencies for the OSRPR and SL algorithms. Finally, we note that, among the three parallel algorithms which we have tested here, the semi-rigorous SL algorithm with DBA led to the highest parallel efficiencies. As a result, we have obtained reasonable parallel efficiencies in our simulations of room-temperature Ag(111) island coarsening for a small number of processors (e.g. N(p) = 2 and 4). Since the SL algorithm scales with system size for fixed processor size, we expect that comparable and/or even larger parallel efficiencies should be possible for parallel KMC and/or SLKMC simulations of larger systems with larger numbers of processors.
本文展示了使用通过自学习动力学蒙特卡罗（KMC）模拟获得的非常大的数据库，对Ag(111)岛在室温下粗化过程进行的并行KMC模拟结果。我们的结果表明，虽然团簇扩散和合并在小团簇以及非常早期阶段起着重要作用，但在后期粗化过程是通过奥斯特瓦尔德熟化进行的，即大团簇生长而小团簇蒸发。此外，对平均岛尺寸S(t)作为时间t的函数进行渐近分析，得出粗化指数n = 1/3（其中S(t)∼t(2n)），这与理论预测吻合良好。然而，通过与不包含协同（多原子）移动的模拟进行比较，我们还发现包含此类移动会显著增加平均岛尺寸。有点令人惊讶的是，我们还发现，虽然在粗化过程中平均岛尺寸增加，但缩放后的岛尺寸分布变化并不显著。我们的模拟既是对多种不同的并行KMC算法的测试，也是其应用，这些算法包括最近开发的乐观同步弛豫（OSR）算法以及半严格同步子晶格（SL）算法。还提出了一种与带伪回滚的乐观同步弛豫（OSRPR）相对应的OSR算法变体，以及一种通过动态边界分配（DBA）提高并行效率和减少边界事件数量的方法。还讨论了多种其他提高模拟效率的方法。我们注意到，由于我们模拟的温度相对较高，以及能量势垒范围较大（从0.05到0.8 eV），开发一种用于并行KMC和/或SLKMC模拟的高效算法特别具有挑战性。然而，通过使用DBA将边界事件数量减至最少，我们在OSRPR和SL算法中实现了显著提高的并行效率。最后，我们注意到，在我们在此测试的三种并行算法中，带有DBA的半严格SL算法实现了最高的并行效率。因此，在对少量处理器（例如N(p) = 2和4）进行的室温Ag(111)岛粗化模拟中，我们获得了合理的并行效率。由于SL算法在固定处理器尺寸下与系统大小成比例，我们预计对于具有更多处理器的更大系统进行并行KMC和/或SLKMC模拟时，应能实现相当甚至更高的并行效率。
