Angular parameter

This illustrates the use of angular parameter to identify diamond structure. Angular parameter was introduced by Uttormark et al., and measures the tetrahedrality of the local atomic structure. An atom belonging to diamond structure has four nearest neighbors which gives rise to six three body angles around the atom. The angular parameter \(A\) is then defined as,

\(A = \sum_{i=1}^6 (\cos(\theta_i)+\frac{1}{3})^2\)

An atom belonging to diamond structure would show the value of angular params close to 0. The following example illustrates the use of this parameter.

import pyscal.core as pc
import pyscal.crystal_structures as pcs
import numpy as np
import matplotlib.pyplot as plt

Create structures

The first step is to create some structures using the crystal_structures module and assign it to a System. This can be done as follows-

atoms, box = pcs.make_crystal('diamond', lattice_constant=4, repetitions=[3,3,3])
sys = pc.System()
sys.atoms = atoms = box

Now we can find the neighbors of all atoms. In this case we will use an adaptive method using the find_neighbors() which can find an individual cutoff for each atom.

sys.find_neighbors(method='cutoff', cutoff='adaptive')

Finally, the angular criteria can be calculated by,


The above function assigns the angular value for each atom in the attribute angular which can be accessed using,

atoms = sys.atoms
angular = [atom.angular for atom in atoms]

The angular values are zero for atoms that belong to diamond structure.