# \(\chi\) parameters for structural identification¶

\(\chi\) parameters introduced by Ackland and Jones [1] measures all local angles created by an atom with its neighbors and creates a histogram of these angles to produce vector which can be used to identify structures. After finding the neighbors of an atom, \(\cos \theta_{ijk}\) for atoms j and k which are neighbors of i is calculated for all combinations of i, j and k. The set of all calculated cosine values are then added to a histogram with the following bins - [-1.0, -0.945, -0.915, -0.755, -0.705, -0.195, 0.195, 0.245, 0.795, 1.0]. Compared to \(\chi\) parameters from \(\chi_0\) to \(\chi_7\) in the associated publication, the vector calculated in pyscal contains values from \(\chi_0\) to \(\chi_8\) which is due to an additional \(\chi\) parameter which measures the number of neighbors between cosines -0.705 to -0.195. The \(\chi\) vector is characteristic of the local atomic environment and can be used to identify crystal structures, details of which can be found in the publication [1].

\(\chi\) parameters can be calculated in pyscal using,

```
import pyscal.core as pc
sys = pc.System()
sys.read_inputfile('conf.dump')
sys.find_neighbors(method='cutoff', cutoff='adaptive')
sys.calculate_chiparams()
```

The calculated values for each atom can be accessed using `chiparams`

.

[1] | (1, 2) Ackland, Jones, Phys. Rev. B 73, 2006 |