The influence of the interaction potential on the fractal dimension of the collision cascade

Abstract

The structure of the collision cascade created by an ion moving in the solid state resembles the fractal tree, hence has a fractal nature. The fractal dimension D of such a tree is D=ln2/ln(1/γ) where γ is the ratio of the successive branches of the fractal tree. To describe the properties of the collision cascade, knowledge of the interaction potential between the moving ion and the target atoms is necessary. This paper presents the influence of the interaction potential on the fractal dimension of the collision cascade. It is shown that Moliere potential generates the cascade with a higher fractal dimension than the fractal dimension of the cascade generated by BZ and ZBL potentials. This means that in the first case the collision cascade is more space filling (“richer”). The calculations were performed for some typical potentials: inverse power potential, BZ potential, ZBL potential and Moliere potential, for homogeneous systems such as Fe–Fe, Ag–Ag and Au–Au. The weighted fractal dimension was introduced and the values of this parameter obtained by the Monte Carlo computations and the theoretical calculations for the Au–Au system were compared, showing a good agreement.