The Local Compositional Dependence of Vacancy Diffusivity in 316 Stainless Steel by Gaussian Process Regression

316 stainless steel (316 SS) has a long history as a critical structural material in nuclear power plants but has a propensity for radiation swelling. Swelling can be lifetime-limiting and is attributed to vacancy diffusion within the material, meaning accurate quantification of vacancy diffusion is crucial. However, the local compositional effects on vacancy diffusion have not been studied in this material, but initial compositional heterogeneity and radiation-induced compositional segregation is common. The diffusivity of vacancies depends on their vacancy migration energy barriers (VMEB). There are several methods to calculate VMEB, such as using classical force fields or quantum mechanical calculations. Classical force fields are not sufficiently accurate to consistently match qualitative trends in experiment, necessitating the greater accuracy, and greater computational expense, of quantum mechanical calculations such as density functional theory. However, 5x10⁴ VMEB calculations are required to cover the compositional space local to a vacancy, which accordingly multiplies the already computationally expensive quantum mechanical calculations. Therefore, we implement a Gaussian process regression (GPR) trained on a subset of NEB calculations to predict VMEB values in less than one second. The GPR predicted VMEB values have greater accuracy than four molecular dynamics embedded atom potentials and are at least 10³ faster to calculate as the migration pathway does not need to be traced. To calculate diffusivity, these GPR predicted VMEB values are deployed in a kinetic Monte Carlo (KMC) simulation of a Fe-Cr-Ni solid solution near the compositional ranges of 316 SS. Incorporation of GPR predicted VMEB values into the KMC simulation shows Cr diffuses fastest opposite vacancy diffusion, followed closely by Fe, with Ni moving much slower. Despite Cr diffusing fastest opposite vacancies, the associated VMEB values vary the greatest for this element, showing the importance of other factors that influence VMEB values, such as composition local to the diffusing vacancy. Using these models, we investigate the effects of composition, defect concentration, and temperature on vacancy diffusivity of 316 SS. This methodology can be applied to any other ternary (or more complex) system for which local composition effects on vacancy diffusion are of interest, especially solid solution alloys used as fuel cladding or structural materials in nuclear power plants.