On the fraction-dimension migration of self-interstitials in zirconium

MD simulations were conducted to study the self-interstitial migration in zirconium. By defining the crystal lattice point, at which more than one atom fall in the Wigner-Seitz cell of the lattice point, for the location of interstitial atoms (LSIA), three types of events were identified for LSIA migration: the jump remaining in one <112_0> direction (ILJ), the jump from one <112_0> to another <112_0> direction in the same basal plane (OLJ) and the jump from one basal plane to an adjacent basal plane (OPJ). The occurrence frequencies of the three types were calculated. ILJ was found to be the dominant event in the temperature range (300K to 1200K), but the occurrence frequencies of OLJ and OPJ increased with increasing temperature. Although the three types of jumps may not follow Brownian and Arrhenius behavior, on the whole, the migration of the LSIAs tend to be Brownian-like. Moreover, the migration trajectories of LSAs in the hcp basal-plane are not what are observed if only conventional one- or two-dimensional migrations exist; rather, they exhibit the feature we call fraction-dimensional. Namely, the trajectories are composed of line segments in <112_0> directions with the average length of the line segments varying with the temperature. Using MC simulations, the potential kinetic impacts of the fraction-dimensional migration, measured by the average number of lattice sites visited per jump event n_SPE was analyzed. The significant differences between the n_SPE value of the fraction-dimensional migration and those of the conventional one- and two-dimensional migrations suggest that the conventional diffusion coefficient, which cannot reflect the feature of fraction-dimensional migration, cannot give an accurate description of the underlying kinetics of SIAs in Zr.