Levy flight of atoms in collision cascades

Abstract

In this work we analyze the ballistic phase of displacement cascades. Monte Carlo simulations performed with realistic cross-sections were used to calculate the probability density function, pL(l), describing the length traveled by a particle between two successive collisions within the binary collision approximation framework. From the analysis of pL(l), this work shows that the trajectories set displays a bifractal behavior. The comparison of different MC simulations clearly shows that this bifractality is only due to the long tail of pL(l). The unusual form of pL(l) implies that atoms displaced in the collision cascade during irradiation follow a Levy flight. Since the Levy law is scale invariant, an anomalous diffusion of atoms at large distances is then expected under irradiation and may explain experimental results.

Study of the fragmentation of a displacement cascade into subcascades within the Binary Collision Approximation framework

“…As the kinetic energy of knocked-on particles remains large, most of the collisions occurring in the target can then be treated as [14][15][16]. The Binary Collision Approximation (BCA) can then be applied to describe the numerous collisions in the target.…”

“…The collisions acquire then a more collective behavior with many atoms suffering small random displacements in a limited volume called a subcascade [17,9]. Even though the Molecular Dynamics (MD) method is now more extensively used to describe the slowing down of particles in subcascades, the BCA gives helpful information on the geometric spreading of displacement cascades [16,18,19] and includes the correct partitioning of energy into nuclear and electronic energy loss, which is often missing in MD simulations.…”

“…From this analysis, it is then possible to introduce the characteristic length of the problem L ¼ 1 NrðxÞ , where x is the kinetic energy of the particle that initiates the displacement cascade, N the number of atoms per unit volume (equal to 1 A À3 in all our MC simulations) and r(x) is the Ziegler Biersack Littmark (ZBL) cross section of the atom that generates the displacement cascade. Since realistic ZBL cross sections derived from the universal ZBL interatomic potential [20], extensively used in MD simulations, exhibit a power law shape, the set of atomic trajectories in the displacement cascade within the BCA exhibit a fractal feature [16,18,19]. After the seminal work of Cheng who was the first to point out this fractality of trajectories set [19], many attempts were devoted to handle the fractal feature of a displacement cascade [15,18,19,3,21,22].…”

“…After the seminal work of Cheng who was the first to point out this fractality of trajectories set [19], many attempts were devoted to handle the fractal feature of a displacement cascade [15,18,19,3,21,22]. The nature of the fractality associated with the atomic trajectories set was clearly achieved only recently [16]. The fractal property of the trajectories set is pointed out computing the normalized moments [16,18,23] Z(q, L):…”

“…The nature of the fractality associated with the atomic trajectories set was clearly achieved only recently [16]. The fractal property of the trajectories set is pointed out computing the normalized moments [16,18,23] Z(q, L):…”