Vacancy elastodiffusion around cavities in aluminium: Fast first passage algorithms based on Krylov subspace projection techniques

The Kinetic Monte Carlo method is widely used in material science to simulate the microstructural evolution of alloys under irradiation. This approach is based on a master equation and a transition rate matrix. The KMC method is inefficient when the transition rate matrix exhibits a wide spectrum of frequencies. Defects perform a huge number of transitions between atomic configurations which are connected by small energy barriers. They form trapping basins; the system remains trapped in metastable thermodynamic states. Acceleration methods based on the theory of absorbing Markov Chains are available to overcome this issue in the KMC method. The escaping events are characterized by their first passage and no-passage distributions. Assuming the diffusion processes are reversible, a property satisfied by the dynamics of defects in metals and alloys, we show that the involved eigenvalue problems to be solved can be symmetrized. We illustrate the performance of a tool based on Krylov subspace by computing sink strengths for the emission and absorption of vacancies from and to cavities in aluminium^1,2.
¹M. Athènes, S. Kaur, G. Adjanor, T. Vanacker, and T. Jourdan, Phys. Rev. Materials 3, 103802 (2019)
²D. Carpentier, T. Jourdan, Y. Le Bouar, M. C. Marinica, Acta Mater. 136 323-334 (2017)