Microscopic Rate Constants of Crystal Growth from Molecular Dynamic Simulations Combined with Metadynamics

Atomistic simulation of crystal growth can be decomposed into two steps: the determination of the microscopic rate constants and a mesoscopic kinetic Monte Carlo simulation. We proposed a method to determine kinetic rate constants of crystal growth. We performed classical molecular dynamics on the equilibrium liquid/crystal interface of argon. Metadynamics was used to explore the free energy surface of crystal growth. A crystalline atom was selected at the interface, and it was displaced to the liquid phase by adding repulsive Gaussian potentials. The activation free energy of this process was calculated as the maximal potential energy density of the Gaussian potentials. We calculated the rate constants at different interfacial structures using the transition state theory. In order to mimic real crystallization, we applied a temperature difference in the calculations of the two opposite rate constants, and they were applied in kinetic Monte Carlo simulation. The novelty of our technique is that it can be used for slow crystallization processes, while the simple following of trajectories can be applied only for fast reactions. Our method is a possibility for determination of elementary rate constants of crystal growth that seems to be necessary for the long-time goal of computer-aided crystal design. 1. Introduction The macroscopic shape of a crystal reflects the net effect of complex processes. The number of the important processes and the dependence of the results on many factors mean a large task for theoretical description and computational modelling. The most important factors are the properties of the solute and the solvent, the temperature, the pressure, the impurities, and the form of the possible seeds. Crystallization is usually divided into two steps, the formation of the seeds and the growth of the crystal [1]. There are numerous ways to model both steps. A possible grouping of the methods is according to the size scale of the methods terming as microscopic, mesoscopic, and macroscopic ones. In detailed modelling, we can use quantum mechanics where the electrons of the system are explicitly included. If the effect of the electrons is averaged in classical mechanical interaction potentials among the atoms or molecules, we can use atomic/molecular modelling with classical mechanics. We can use mesoscopic lattice models, where the atoms or molecules occupy lattice points defined in advance. We may even simplify the model up to limit, where the model includes only the information, that a lattice point is occupied or it is vacant. If the basics of