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.

The input file is included below:

[options]
name = "2000.0eV_0.0001deg_He_H_TiO2_Al_Si"
track_trajectories = true
track_recoils = true
track_recoil_trajectories = true
stream_size = 8000
weak_collision_order = 0
suppress_deep_recoils = false
high_energy_free_flight_paths = false
electronic_stopping_mode = "LOW_ENERGY_NONLOCAL"
mean_free_path_model = "LIQUID"
interaction_potential = [
  ["KR_C", {"LENNARD_JONES_65_6"={sigma = 0.8E-10, epsilon = 5E-19}}],
  [{"LENNARD_JONES_65_6"={sigma = 0.8E-10, epsilon = 5E-19}}, "KR_C"]
]
scattering_integral = [
  ["MENDENHALL_WELLER", {"GAUSS_MEHLER"={n_points = 100}}],
  [{"GAUSS_MEHLER"={n_points = 100}}, "MENDENHALL_WELLER"]
]
root_finder = [
  [{"NEWTON"={max_iterations=100, tolerance=1E-6}}, {"POLYNOMIAL"={complex_threshold=1E-12}}],
  [{"POLYNOMIAL"={complex_threshold=1E-12}}, {"NEWTON"={max_iterations=100, tolerance=1E-6}}]
]
use_hdf5 = false
num_threads = 4
num_chunks = 10

[particle_parameters]
length_unit = "MICRON"
energy_unit = "EV"
mass_unit = "AMU"
N = [ 10, 10]
m = [ 4.002602, 1.008]
Z = [ 2, 1]
E = [ 2000.0, 2000.0]
Ec = [ 0.1, 0.1]
Es = [ 0.0, 1.0]
interaction_index = [0, 1]
pos = [ [ -1.7453292519934434e-8, 0.0, 0.0,], [ -1.7453292519934434e-8, 0.0, 0.0,],]
dir = [ [ 0.9999999999984769, 1.7453292519934434e-6, 0.0,], [ 0.9999999999984769, 1.7453292519934434e-6, 0.0,],]
particle_input_filename = ""

[mesh_2d_input]
length_unit = "MICRON"
coordinate_sets = [ [ 0.0, 0.01, 0.0, 0.5, 0.5, -0.5,], [ 0.0, 0.01, 0.01, -0.5, 0.5, -0.5,], [ 0.01, 0.01, 0.04, -0.5, 0.5, -0.5,], [ 0.01, 0.04, 0.04, 0.5, 0.5, -0.5,], [ 0.04, 0.5, 0.04, 0.5, 0.5, -0.5,], [ 0.04, 0.5, 0.5, -0.5, 0.5, -0.5,],]
densities = [ [ 3.0e+28, 6.0e+28, 0.0, 0.0,], [ 3.0e+28, 6.0e+28, 0.0, 0.0,], [ 0.0, 0.0, 6.026e+28, 0.0,], [ 0.0, 0.0, 6.026e+28, 0.0,], [ 0.0, 0.0, 0.0, 4.996e+28,], [ 0.0, 0.0, 0.0, 4.996e+28,],]
boundary_points = [ [ 0.0, 0.5,], [ 0.5, 0.5,], [ 0.5, -0.5,], [ 0.0, -0.5,],]
simulation_boundary_points = [ [ 0.6, -0.6,], [ -0.1, -0.6,], [ -0.1, 0.6,], [ 0.6, 0.6,], [ 0.6, -0.6,],]

[material_parameters]
energy_unit = "EV"
mass_unit = "AMU"
Eb = [ 3.0, 2.58, 3.0, 0.0,]
Es = [ 4.84, 2.58, 3.39, 4.72,]
Ec = [ 3.5, 2.0, 3.0, 1.5,]
n = [ 5.67e+28, 4.291e+28, 6.026e+28, 4.996e+28,]
Z = [ 22, 8, 13, 14,]
m = [ 47.867, 15.9994, 26.98, 28.08553,]
interaction_index = [0, 0, 0, 0]
electronic_stopping_correction_factor = 1.0
energy_barrier_thickness = 6.71e-5