Fe团簇的吉布斯自由能可通过Tolman修正近似以精确模拟团簇形核与生长
Gibbs free energies of Fe clusters can be approximated by Tolman correction to accurately model cluster nucleation and growth
AI总结：
本文提出用MD模拟计算Fe团簇自由能的方法，并通过引入尺寸依赖的Tolman表面张力修正改进了球形团簇近似，从而能精确模拟冷却蒸气中Fe团簇的形核与生长过程。
摘要：
在冷却蒸气凝结过程中，对Fe团簇生长进行预测性建模需要精确的Fe团簇吉布斯自由能。我们提出了一种利用分子动力学（MD）模拟所提供数据来计算团簇形成自由能的直接方法。我们应用该方法计算了含有2至100个原子的Fe团簇的自由能。通过将所得自由能与MD模拟的亚饱和蒸气中的平衡团簇尺寸分布进行比较，验证了这些自由能的准确性。我们表明，这些自由能与常用的球形团簇近似所得结果存在显著差异——该近似依赖于平坦表面的表面张力系数。球形团簇近似可以通过采用依赖于团簇尺寸的表面张力Tolman修正来改进。我们推导出了Tolman长度和有效表面张力的数值，这些数值不同于常用的基于势能实验测得的表面张力。这一改进后的近似并未考虑几何幻数效应，而该效应导致了相邻团簇尺寸密度中的尖峰和低谷。尽管如此，它仍能对冷却蒸气中的团簇形成进行建模，并精确重现凝结时间线、团簇尺寸分布的整体形状、平均团簇尺寸以及分布宽度。使用恒定的表面张力系数会导致扭曲的凝结动力学和不准确的团簇尺寸分布。经典成核理论（CNT）中团簇成核速率的解析表达式已得到更新，以考虑团簇表面张力的尺寸依赖性。
英文摘要：
Accurate Gibbs free energies of Fe clusters are required for predictive modeling of Fe cluster growth during condensation of a cooling vapor. We present a straightforward method of calculating free energies of cluster formation using the data provided by molecular dynamics (MD) simulations. We apply this method to calculate free energies of Fe clusters having from 2 to 100 atoms. The free energies are verified by comparing to an MD-simulated equilibrium cluster size distribution in a sub-saturated vapor. We show that these free energies differ significantly from those obtained with a commonly used spherical cluster approximation - which relies on a surface tension coefficient of a flat surface. The spherical cluster approximation can be improved by using a cluster size-dependent Tolman correction for the surface tension. The values for the Tolman length and effective surface tension were derived, which differ from the commonly used experimentally measured surface tension based on the potential energy. This improved approximation does not account for geometric magic number effects responsible for spikes and troughs in densities of neighbor cluster sizes. Nonetheless, it allows to model cluster formation from a cooling vapor and accurately reproduce the condensation timeline, overall shape of the cluster size distribution, average cluster size, and the distribution width. Using a constant surface tension coefficient resulted in distorted condensation dynamics and inaccurate cluster size distributions. The analytical expression for cluster nucleation rate from classical nucleation theory (CNT) was updated to account for the size-dependence of cluster surface tension.
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