Example: Multiple Interaction Potentials

Trajectories of hydrogen and helium ions at 2 keV on a layered TiO2-Al-Si target.

This example demonstrates the ability of rustbca to include multiple interaction potentials. In particular, this example shows 2 keV hydrogen (red) and helium (fuchsia) incident on a layered TiO2-Al-Si target. Hydrogen interacts with all target species with a Lennard-Jones 6.5-6 potential. Helium interacts with all target species with a Kr-C screened potential. All target species interact with each other through Kr-C potentials.

This is handled in the input file through interaction matrices. The interaction matrix for this rather artificial system is:

[[other-other: Kr-C, other-H: LJ-6.5-6],
[H-other: LJ-6.5-6, other-other: Kr-C]]

Since the interaction index of H is 1 and the interaction indices of all other species are 0. Other is one of: He, Ti, O, Al, Si. RustBCA can handle an arbitrary number of distinct interactions, but only two are used for this example. Since the LJ-6.5-6 potential requires the use of a non-Newton rootfinder, the rootfinder field of the input file is:

[[Newton, Polynomial],
[Polynomial, Newton]]

and the scattering integral field is:

[[Mendenhall-Weller, Gauss-Mehler],
[Gauss-Mehler, Mendenhall-Weller]]

It is apparent that the LJ potential results in many more large-angle scattering events than the Kr-C, especially for energies that exhibit the orbiting condition, where theta -> -infinity (see figures below).

Scattering angles through a Lennard-Jones 6.5-6 potential. Epsilon is the Lindhard reduced energy, p the impact parameter, and a the scattering length.

Distances of closest approach through a Lennard-Jones 6.5-6 potential. Epsilon is the Lindhard reduced energy, p the impact parameter, and a the scattering length.