Activity 4: From single scattering to multiple scattering

Activity 4: From single scattering to multiple scattering#

In the previous activity, we saw that simple single scattering calculations (SSC) can be used to simulate photodiffraction diagrams with good accuracy. The approximation works fine when the emitting atom is very close to the surface. However, the SSC approach is no longer suitable for deeper emitter atoms, where multiple scattering effects come into play. In this activity, we will focus on a major consequence of multiple scattering: the defocusing effect.

The defocusing effect is presented in the figure below for a chain of nickel atoms. Although purely illustrative, understanding multiple scattering in atomic chains is fundamental because they are found in many situations, such as in particular directions of a crystal or in molecules of various lengths.

defocusing effect

The defocusing effect dur to multiple scattering in an atomic chain of Ni atoms.#

In 1989, M.-L Xu, J.J. Barton and M.A. Van Hove studied these multiple scattering effects on atomic chains (see their paper below). In the spirit of figure 3 of their paper, we will create 3 atomic chains of Ni atoms (2, 3 and 5 atoms) tilted by 45° and we will compare the intensity of the forward scattering peak for single scattering and for full multiple scattering.

See also

based on this paper from M.-L. Xu et al. Phys. Rev. B 39 p8275 (1989)

Polar scans of Ni atomic chains#

Building a chain of atoms#

Start by creating a simple chain of 2 Ni atoms: an emitter and a scatterer in the [101] direction.

Tip

Nickel is fcc with lattice parameter \(a\)=3.499 Å. Use the Atoms class of ase like in the previous activity…

if you need help to start…

from msspec.calculator import MSSPEC
from ase  import Atoms

symbol = ...             # The kind of atom for the chain
a = ...                  # The distance bewteen 2 atoms
                         # in [101] direction

chain = Atoms(..., positions=[...])
chain.rotate(...)
chain.edit()

Create an MSSPEC calculator with expansion algortithm and set the scattering_order=1 to compute a polar scan of the Ni(3s) in single scattering. How is varying the height of the peak at 45° (along the chain) if you increase the number of atoms in the chain ?

Repeat the same experiment with inversion algorithm for having the full multiple scattering result. What do you observe ?

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