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

• Published in: Journal of computational physics 2022-04, Vol.454, p.110987, Article 110987
• Main Authors: Kaur, Savneet, Athènes, Manuel, Creuze, Jérôme
• Format: Article
• Language: English
• Subjects: Absorbing Markov processes; Absorption; Aging (metallurgy); Aluminum; Chemical Sciences; Computational physics; Defects; Eigenvalues; Evolution; First passage distributions; Forecasting; Holes; Kinetics; Krylov subspace projection; Markov chains; Material chemistry; Material properties; Mathematical models; Mathematical Physics; Physics; Sink strengths calculations; Subspaces; Vacancies
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2022.110987

•First-passage problem solved via Krylov subspace projection and eigenvalue deflation.•Theory of absorbing Markov chains is used to formulate sink strengths.•Dipole-dipole elastic interactions between vacancy and cavity are taken into account.•Angular anisotropy of sink strengths is investigated for cavities in aluminum. 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.