Centrosymmetry Parameter
Measure how far each atom's neighbor shell is from centrosymmetric, to find dislocation cores, stacking faults and surfaces in centrosymmetric crystals.
The centrosymmetry parameter (CSP) measures how much an atom's neighbor shell departs from inversion symmetry. In a perfect centrosymmetric lattice such as FCC or BCC each neighbor has an opposite partner and the CSP is close to zero; at dislocation cores, stacking faults, surfaces and vacancies it grows. Use it to highlight defects in FCC and BCC metals, or as a feature for MultiSOM. It is not meaningful for lattices without inversion symmetry at the atom, such as HCP or diamond.
| Key | Version | Builds |
|---|---|---|
centrosymmetry-parameter | 2.0.3 | Linux, macOS, Windows |
This plugin has no browser build, so it can't be installed on a machine that runs in the browser or the desktop app.
How it works
For each atom, the plugin takes its N nearest neighbors and pairs them up into N/2 pairs of opposite neighbors. The CSP is the sum over those pairs of |rᵢ + rⱼ|², where rᵢ and rⱼ are the bond vectors to the two neighbors of a pair. The two modes differ in how they pick the pairs:
- Conventional follows the original definition: it takes the N/2 smallest values of |rᵢ + rⱼ|² over all neighbor pairs.
- Matching finds the pairing (a minimum-weight perfect matching) that minimizes the sum, so each neighbor is used exactly once.
Inputs
- Atom positions and the simulation cell.
Arguments
| Argument | Type | Default | Allowed values | Description |
|---|---|---|---|---|
Num Neighbors num_neighbors | number | 12 | ≥ 2, step 1 | Number of nearest neighbors N. Use 12 for FCC and 8 for BCC. It must be even, and at most 32. |
Mode mode | select | conventional | conventional (Conventional), matching (Matching) | How neighbors are paired; see above. |
Outputs
| Exposure | What you get |
|---|---|
| Centrosymmetry | A listing with the frame's summary. |
| Centrosymmetry Model | A listing, and a 3D model of the atoms. |
The workflow declares the per-atom properties csp (Centrosymmetry (CSP)) and coordination (Coordination number).
Notes
- The CSP has units of length squared and scales with the square of the lattice constant, so a threshold that separates defects from crystal in one material doesn't carry over to another.
- Thermal vibrations raise the CSP of crystalline atoms; compare frames at the same temperature.
Reference
C. L. Kelchner, S. J. Plimpton, J. C. Hamilton, "Dislocation nucleation and defect structure during surface indentation", Phys. Rev. B 58, 11085 (1998). Matching mode: P. M. Larsen, "Revisiting the common neighbour analysis and the centrosymmetry parameter", arXiv:2003.08879 (2020).
Coordination Analysis
Count each atom's neighbors within a cutoff and compute the radial distribution function of the frame, with partial histograms per type pair.
Steinhardt Order Parameters
Compute the bond-orientational order parameters q_l, w_l and w_l_hat of each atom, to tell crystal from liquid and follow nucleation.