A First-Passage Kinetic Monte Carlo Algorithm for Complex Diffusion-Reaction Systems

TL;DR

This paper introduces an efficient First-Passage Kinetic Monte Carlo algorithm for simulating complex diffusion-reaction systems, particularly effective at low densities, and demonstrates its application to long-term metal irradiation simulations.

Contribution

The paper presents a novel asynchronous event-driven FPKMC algorithm that improves efficiency and accuracy for simulating diffusion-reaction systems over long timescales.

Findings

Efficient simulation of long-term metal irradiation damage.

Ability to simulate durations orders of magnitude longer than previous methods.

Accurate modeling of diffusion and reactions at low particle densities.

Abstract

We develop an asynchronous event-driven First-Passage Kinetic Monte Carlo (FPKMC) algorithm for continuous time and space systems involving multiple diffusing and reacting species of spherical particles in two and three dimensions. The FPKMC algorithm presented here is based on the method introduced in [Phys. Rev. Lett., 97:230602, 2006] and is implemented in a robust and flexible framework. Unlike standard KMC algorithms such as the n-fold algorithm, FPKMC is most efficient at low densities where it replaces the many small hops needed for reactants to find each other with large first-passage hops sampled from exact time-dependent Green's functions, without sacrificing accuracy. We describe in detail the key components of the algorithm, including the event-loop and the sampling of first-passage probability distributions, and demonstrate the accuracy of the new method. We apply the FPKMC algorithm to the challenging problem of simulation of long-term irradiation of metals, relevant to the performance and aging of nuclear materials in current and future nuclear power plants. The problem of radiation damage spans many decades of time-scales, from picosecond spikes caused by primary cascades, to years of slow damage annealing and microstructure evolution. Our implementation of the FPKMC algorithm has been able to simulate the irradiation of a metal sample for durations that are orders of magnitude longer than any previous simulations using the standard Object KMC or more recent asynchronous algorithms.