Absorption kinetics of vacancies by cavities in Aluminum: numerical characterization of sink strengths and first-passage statistics through Krylov subspace projection and eigenvalue deflation

TL;DR

This paper introduces a numerical method combining Krylov subspace projection and eigenvalue deflation to efficiently analyze defect absorption kinetics in aluminum, enhancing microstructural evolution modeling under irradiation.

Contribution

It presents a novel non-stochastic numerical approach for calculating first-passage times and sink strengths in defect migration, applicable to kinetic Monte Carlo and cluster dynamics simulations.

Findings

Efficient computation of first-passage time distributions and fluxes.

Small Krylov subspace with eigenvalue deflation accurately captures defect kinetics.

Method applicable to modeling defect absorption in irradiated materials.

Abstract

Modeling the microstructural evolution of metal and alloys, specifically under irradiation, is essential to predict the aging properties of materials. Many models are based on a transition rate matrix describing the jump frequencies of defects and involve a master equation governing the time evolution of a state probability vector. Here, we present non-stochastic numerical techniques to characterize the motion of individual defects migrating over long distances prior to recombining or being absorbed by another defect, resorting to the theory of absorbing Markov chains. These important events are fully determined by their first-passage time distribution to distant locations, no-passage distribution ,and walker fluxes to the sinks. We show that these functions can be efficiently computed using a method combining Krylov subspace projection and eigenvalue deflation. For a model system describing the absorption of a vacancy by a cavity in aluminum, the use of a small Krylov subspace deflated by the unique eigenmode corresponding to the quasi-stationary distribution is sufficient to capture the kinetics of the defect absorption faithfully. This method can be used in kinetic Monte Carlo simulations to perform stochastic non-local moves or in cluster dynamics simulations to compute sink strengths.