Weatherspoon Howard, Peters Baron
Chemical and Biomolecular Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
J Chem Phys. 2023 Mar 21;158(11):114306. doi: 10.1063/5.0132601.
Magic clusters are metastable faceted nanoparticles that are thought to be important and, sometimes, observable intermediates in the nucleation of certain faceted crystallites. This work develops a broken bond model for spheres with a face-centered-cubic packing that form tetrahedral magic clusters. With just one bond strength parameter, statistical thermodynamics yield a chemical potential driving force, an interfacial free energy, and free energy vs magic cluster size. These properties exactly correspond to those from a previous model by Mule et al. [J. Am. Chem. Soc. 143, 2037 (2021)]. Interestingly, a Tolman length emerges (for both models) when the interfacial area, density, and volume are treated consistently. To describe the kinetic barriers between magic cluster sizes, Mule et al. invoked an energy parameter to penalize the two-dimensional nucleation and growth of new layers in each facet of the tetrahedra. According to the broken bond model, barriers between magic clusters are insignificant without the additional edge energy penalty. We estimate the overall nucleation rate without predicting the rates of formation for intermediate magic clusters by using the Becker-Döring equations. Our results provide a blueprint for constructing free energy models and rate theories for nucleation via magic clusters starting from only atomic-scale interactions and geometric considerations.
魔数团簇是亚稳态的多面体纳米颗粒，被认为在某些多面体微晶的成核过程中起着重要作用，有时还是可观察到的中间体。这项工作为具有面心立方堆积的球体建立了一个断键模型，这些球体形成四面体魔数团簇。仅用一个键强参数，统计热力学就能得出化学势驱动力、界面自由能以及自由能与魔数团簇尺寸的关系。这些性质与Mule等人之前的模型[《美国化学会志》143, 2037 (2021)]中的性质完全一致。有趣的是，当一致地处理界面面积、密度和体积时，（两个模型都）出现了托尔曼长度。为了描述魔数团簇尺寸之间的动力学势垒，Mule等人引入了一个能量参数来惩罚四面体每个面中新层的二维成核和生长。根据断键模型，在没有额外边缘能量惩罚的情况下，魔数团簇之间的势垒微不足道。我们通过使用贝克尔 - 多林方程来估计整体成核速率，而不预测中间魔数团簇的形成速率。我们的结果为仅从原子尺度相互作用和几何考虑出发，构建通过魔数团簇进行成核的自由能模型和速率理论提供了蓝图。
