Nucleation rate in the two dimensional Ising model in the presence of random impurities,Soft Matter

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Nucleation rate in the two dimensional Ising model in the presence of random impurities
Soft Matter ( IF 2.9 ) Pub Date : 2021-09-13 , DOI: 10.1039/d1sm01172c
Dipanjan Mandal ₁ , David Quigley ₁

Affiliation

Nucleation phenomena are ubiquitous in nature and the presence of impurities in every real and experimental system is unavoidable. Yet numerical studies of nucleation are nearly always conducted for entirely pure systems. We have studied the behaviour of the droplet free energy in two dimensional Ising model in the presence of randomly positioned static and dynamic impurities. We have shown that both the free energy barrier height and critical nucleus size monotonically decreases with increasing the impurity density for the static case. We have compared the nucleation rates obtained from the Classical Nucleation Theory and the Forward Flux Sampling method for different densities of the static impurities. The results show good agreement. In the case of dynamic impurities, we observe preferential occupancy of the impurities at the boundary positions of the nucleus when the temperature is low. This further boosts enhancement of the nucleation rate due to lowering of the effective interfacial free energy.

中文翻译：

存在随机杂质时二维 Ising 模型中的成核率

成核现象在自然界中无处不在，在每个真实和实验系统中都不可避免地存在杂质。然而，对成核的数值研究几乎总是针对完全纯系统进行的。我们研究了在随机定位的静态和动态杂质存在的情况下，二维 Ising 模型中液滴自由能的行为。我们已经表明，在静态情况下，自由能垒高度和临界核尺寸都随着杂质密度的增加而单调减小。我们比较了从经典成核理论和正向通量采样方法获得的不同密度静态杂质的成核率。结果显示出良好的一致性。在动态杂质的情况下，当温度较低时，我们观察到杂质优先占据原子核的边界位置。由于有效界面自由能的降低，这进一步促进了成核速率的提高。

更新日期：2021-09-17

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