Centrosymmetry parameter#

Centrosymmetry parameter (CSP) was introduced by Kelchner et al. [1] to identify defects in crystals. The parameter measures the loss of local symmetry. For an atom with \(N\) nearest neighbors, the parameter is given by,

\[ \mathrm{CSP} = \sum_{i=1}^{N/2} \big | \textbf{r}_i + \textbf{r}_{i+N/2} \big |^2 \]

\(\textbf{r}_i\) and \(\textbf{r}_{i+N/2}\) are vectors from the central atom to two opposite pairs of neighbors. There are two main methods to identify the opposite pairs of neighbors as described in this publication. The first of the approaches is called Greedy Edge Selection (GES) [2] and is implemented in LAMMPS and Ovito. GES algorithm calculates a weight \(w_{ij} = |\textbf{r}_i + \textbf{r}_j|\) for all combinations of neighbors around an atom and calculates CSP over the smallest \(N/2\) weights.

A centrosymmetry parameter calculation using GES algorithm can be carried out as follows-

from pyscal3 import System
sys = System('conf.dump')
csm = sys.calculate.centrosymmetry(nmax = 12)

nmax parameter specifies the number of nearest neighbors to be considered for the calculation of CSP.

References#

  1. Kelchner, C. L., Plimpton, S. J. & Hamilton, J. C. Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085–11088 (1998).

  2. Stukowski, A. Structure identification methods for atomistic simulations of crystalline materials. Modelling and Simulation in Materials Science and Engineering 20, (2012).