# Disorder parameter¶

Kawasaki and Onuki [1] proposed a disorder variable based on Steinhardt’s order paramaters which can be used to distinguish between ordered and disordered structures

The disorder variable for an atom is defined as,

$D_j = \frac{1}{n_b^j} \sum_{k \in neighbors } [S_{jj} + S_{kk} - 2S_{jk}]$

where S is given by,

$S_{jk} = \sum_{-l \leq m \leq l} q_{lm}^j (q_{lm}^k)^*$

l = 6 was used in the original publication as it is a good indicator of crystallinity. However, l = 4 can also be used for treating bcc structures. An averaged disorder parameter for each atom can also be calculated in pyscal,

$\bar{D}_j = \frac{1}{n_b^j} \sum_{k \in neighbors } D_j$

In pyscal, disorder parameter can be calculated by the following code-block,

import pyscal.core as pc
sys = pc.System()
sys.read_inputfile('conf.dump')
sys.find_neighbors(method='cutoff', cutoff=0)
sys.calculate_q(6)
sys.calculate_disorder(averaged=True, q=6)


The value of q can be replaced with whichever is required from 2-12. The calculated values can be accessed by, Atom.disorder and Atom.avg_disorder attributes.

## References¶

1

Takeshi Kawasaki and Akira Onuki. Construction of a disorder variable from Steinhardt order parameters in binary mixtures at high densities in three dimensions. Journal of Chemical Physics, 2011. doi:10.1063/1.3656762.