This modifier calculates the centrosymmetry parameter (CSP) for particles [Kelchner, Plimpton, Hamilton, Phys. Rev. B, 58, 11085 (1998)]. In solid-state systems the centrosymmetry parameter is a useful measure of the local lattice disorder around an atom and can be used to characterize whether the atom is part of a perfect lattice, a local defect (e.g. a dislocation or stacking fault), or at a surface.
The CSP value pCSP of an atom having N nearest neighbors (N = 12 for fcc, N = 8 for bcc) is given by
where ri and ri+N/2 are vectors pointing from the central atom to a pair of opposite neighbors. OVITO uses the same algorithm as LAMMPS to calculate the centrosymmetry parameter. For lattice sites in an ideal centrosymmetric crystal, the contributions of all neighbor pairs in this formula will cancel, and hence the resulting CSP value will be zero. Atomic sites within a defective crystal region, in contrast, typically have a disturbed, non-centrosymmetric neighborhood. In this case the CSP becomes positive. Using an appropriate threshold, to tolerate small perturbations due to thermal displacements and elastic strains, the CSP can be used as an order parameter to extract crystal defect atoms.
One input parameter of the modifier is the number of neighbors that should be taken into account when computing the centrosymmetry value for an atom. This parameter value should match the ideal number of nearest neighbors in the crystal lattice at hand (12 in fcc crystals; 8 in bcc).
Note that the modifier needs to see the complete set of particles to perform the computation. It should therefore be placed at the beginning of the data pipeline, preceding any modifiers that delete particles.
The calculated CSP values are stored in the
Centrosymmetry output particle property by the modifier.
Subsequently, you can use the
Color Coding modifier to color atoms based on their CSP value
or use the Expression Selection modifier to select atoms
having a CSP value below some threshold.
These undisturbed atoms can then be hidden to reveal crystal defect atoms by using the Delete Selected
modifier. Furthermore, the Histogram modifier may be used to study the distribution
of CSP values in a system.