Calculation of migration rates of vacancies and divacancies in a-Iron using transition path sampling biased with a Lyapu
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Calculation of migration rates of vacancies and divacancies in α-Iron using transition path sampling biased with a Lyapunov indicator Massimiliano Picciani, Manuel Athènes and Mihai-Cosmin Marinica CEA, DEN, Service de Recherches de Métallurgie Physique, F-91191 Gif-sur-Yvette, France ABSTRACT Predicting the microstructural evolution of radiation damage in materials requires handling the physics of infrequent-events, in which several time scales are involved. The reactions rates characterizing these events are the main ingredient for simulating the kinetics of materials under irradiation over large time scales and high irradiation doses. We propose here an efficient, finite temperature method to compute reaction rate constants of thermally activated processes. The method consists of two steps. Firstly, rare reactive trajectories in phase-space are sampled using a transition path sampling (TPS) algorithm supplemented with a local Lyapunov bias favoring diverging trajectories. This enables the system to visit transition regions separating stable configurations more often, and thus enhances the probability of observing transitions between stable states during relatively short simulations. Secondly, reaction constants are estimated from the unbiased fraction of reactive trajectories, yielded by an appropriate statistical data analysis tool, the multistate Bennett acceptance ratio (MBAR) package. We apply our method to the calculation of reaction rates for vacancy and di-vacancy migration in α-Iron crystal, using an Embedded Atom Model potential, for temperatures ranging from 300 K to 800 K. INTRODUCTION Physical events occurring with a very low probability on the simulation and experimental time scale in condensed matter physics are described as “rare events”: they involve thermally activated processes, i.e. passages between two stable configurations of the system that are separated by free energy barriers. Evaluating the frequency of these rare events from numerical simulations demands a large amount of CPU time, as the probability of observing one of these passages is very low: for example, the migration of a vacancy in α-Iron at 500K typically happens every microsecond, while usual durations for molecular dynamics simulations are of the order of a few picoseconds. In the last 15 years, several methods have been elaborated in order to accelerate the dynamics, and enhance the probability of observing infrequent events during short simulations [1]. Among these methods, transition path sampling [2] (TPS) consists of generating dynamical trajectories in phase space, and implementing a biased Metropolis algorithm to favor the sampling of reactive trajectories linking two free energy basins A and B. Resorting to a BennetChandler approach [2], TPS also allows to estimate reaction rates as the ratio of the number of reactive trajectories to the total amount of sampled paths. However, a sufficient number of reactive paths has to be harvested, in order to achieve reliable statistics. Herein, we present a variant of the TPS meth
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