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

Abstract

When a material is subjected to irradiation, many primary defects are cre- ated at the atomic level by sequences of ballistic collision events to form highly disordered regions defined as displacement cascades. The long term evolution of materials under irradiation is dictated by the number and the spatial distribution of the surviving defects in the displacement cascade. The peculiar power law shape of collision cross sections is responsible for the frag- mentation of a displacement cascade into smaller subcascades. However, it remains difficult to define a subcascade. Within the fractal geometry frame- work, we demonstrate in this work that the set of atomic trajectories in a displacement cascade exhibit a fractal behavior. From this analysis, we present a new criterion to describe the fragmentation of a displacement cas- cade and to calculate the distribution and the number of defects from this fragmentation. Such an analysis provides the natural framework to estimate the number of defects created in a displacement cascade to integrate with results of MD simulations. From this defiintion of the fragmentation of a displacement cascade, this work gives some new insights to describe both the primary defects produced in a material under irradiation and then to compare different irradiations performed with different particles.