FIG. . a Flow chart of the kMC process. i kMC steps are repeated with each kMC simulation started from a different initial structure (i.e., j initial structures in total). b All migration events are listed on a hypothetical axis, with the solid line representing their hopping probabilities (Γ). An event no. k is then randomly proposed based on a random number ρ. Γ tot (k) is a cumulative sum of events from no. 0 to no. k (i.e., Γ tot (k) = ∑ k m=0 Γ m ). Γ tot is the sum of hopping probabilities of all migration events. and f .