First-Passage-Time Kinetic Monte Carlo Simulation of Nucleation and Growth in Electrodeposition
Kinetic Monte Carlo (KMC) method is widely used to study electrodeposition and crystal growth, which are categorized as “diffusion-reaction system”. This system consists of many diffusing particles (reactants). When two (or more) particles collide with each other, some reaction occurs. In crystal growth, for example, the reactants are adatoms deposited on crystal surface and the reaction is the nucleation as a result surface diffusion. KMC method is a direct and commonly used simulation method for diffusion-reaction systems. The direct KMC method, however, becomes inefficient when the concentration of the reactants becomes low and a large number of hops have to be simulated before a reaction occurs. In order to overcome this problem, a first-passage-time KMC (FPKMC) method has been developed by Oppelstrup, et. al.  In the FPKMC method, an area is assigned to each particle which includes only one reactant, and an analytical solution is used to derive the distribution function of the first-passage time which is defined as the time when the particle reaches the boundary of the area for the first time. A particle is moved to the boundary of the area following the FPT distribution function skipping many hops. The FPKMC is an efficient and exact method to realize fast simulation of diffusion-reaction systems. In the work of Oppelstrup et. al., a continuous diffusion model is used to derive the FPT distribution function. [1, 2] Bezzola et. al. extended the FPKMC method to a discrete lattice to simulate crystal growth. [3, 4] In Bezzola’s work, solution is not explicitly included in the model.
The purpose of the present work is to study the nucleation and growth in the electrochemical systems by developing the hybrid method of FPKMC and ordinary KMC methods. The reactants are metal ions which are electrodeposited on the electrode surface. The nucleation occurs when the surface adatoms collide after surface diffusion. The mass transport of ions in solution is also taken into account. The surface diffusion and nucleation, which are the time-consuming part of the simulation, are simulated by the FPKMC method. The mass transport and reaction in solution are simulated by the ordinary KMC method. We first confirmed that the computing time is greatly reduced by applying FPKMC compared to conventional KMC method. Using the hybrid method, we study the correlation between the microscopic nucleation process and the resulting large scale crystal structure. The influence of solution structure on nucleation and growth is also discussed.
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 T. Oppelstrup, V. V. Bulatov, A. Donev, M. H. Kalos, G. H. Gilmer, and B. Sadigh, Phys. Rev. E, 80(6), 66701 (2009).
 A. Bezzola, R. C. Alkire, and L. Petzold, 221th ECS Meeting Abstract, 2012., Abstract #1031.
 A. Bezzola, B. Balesa, R. C. Alkire, and L. Petzold, Journal of Computational Physics, 256 183 (2014).