Cowley short range order parameter#
The Cowley short range order parameter can be used to find if an alloy is ordered or not. The order parameter is given by,
where \(n_i\) is the number of atoms of the non reference type among the \(c_i\) atoms in the \(i\)th shell. \(m_A\) is the concentration of the non reference atom.
We can start by importing the necessary modules
from pyscal3 import System
import matplotlib.pyplot as plt
We need a binary alloy structure to calculate the order parameter. We will use the crystal structures modules to do this. Here, we will create a L12 structure.
sys = System.create.lattice.l12(lattice_constant=4.00, repetitions=[2,2,2])
To identify neighbor shell, we calculate the radial distribution function.
val, dist = sys.calculate.radial_distribution_function()
We can plot the rdf,
plt.plot(dist, val)
plt.xlabel(r"distance $\AA$")
plt.ylabel(r"$g(r)$")
plt.xlim(0, 5)
(0.0, 5.0)

In this case, we will take a cutoff of 3
sys.find.neighbors(method='cutoff', cutoff=3)
Finally we can calculate the short range order. We will use the reference type as 1 and also specify the average keyword as True. This will allow us to get an average value for the whole simulation box.
sys.chemical.short_range_order()
Value for individual atoms can be accessed by,
sys.atoms.chemical.short_range_order
array([ 1. , -0.33333333, -0.33333333, -0.33333333, 1. ,
-0.33333333, -0.33333333, -0.33333333, 1. , -0.33333333,
-0.33333333, -0.33333333, 1. , -0.33333333, -0.33333333,
-0.33333333, 1. , -0.33333333, -0.33333333, -0.33333333,
1. , -0.33333333, -0.33333333, -0.33333333, 1. ,
-0.33333333, -0.33333333, -0.33333333, 1. , -0.33333333,
-0.33333333, -0.33333333])
We can also visualise this
sys.show.continuous_property(sys.atoms.chemical.short_range_order)