# $$\chi$$ 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.calculate_chiparams()


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

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

Note

Associated methods