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.

Steinhardt bond-orientational order parameters describe the angular arrangement of an atom's neighbors with rotationally invariant combinations of spherical harmonics. q_6 separates crystal-like from liquid-like environments, and q_4 with q_6 distinguishes FCC, HCP, BCC and icosahedral order. Use them to study melting, solidification and nucleation, or as features for MultiSOM. The plugin is a port of LAMMPS compute orientorder/atom.

Key	Version	Builds
`steinhardt-order-parameters`	1.0.4	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 atom i with neighbors j, the plugin averages the spherical harmonics of the bond directions, q_lm(i) = (1/Nᵢ) Σⱼ Y_lm(r̂ᵢⱼ), for each order l in the list. From them it computes:

q_l = √(4π/(2l+1) Σₘ |q_lm|²), which is invariant under rotation.
w_l, the third-order invariant built from q_lm with Wigner 3j symbols, when Compute w_l is on.
w_l_hat = w_l / q_l³, a dimensionless version of w_l, when Compute w_l_hat is on.

Neighbors are either a fixed number of nearest neighbors or all atoms within a cutoff.

Inputs

Atom positions and the simulation cell.
A Selection column, only for Only Selected Atoms.

Arguments

Argument	Type	Default	Allowed values	Description
Orders (comma-separated list of l) `qlist`	string	`4,6,8,10,12`	Comma-separated integers	The orders l to compute.
Nearest Neighbors (0 = use cutoff) `nnn`	number	`12`	0 to 64, step 1	Use this many nearest neighbors. `0` switches to all neighbors within Cutoff Radius. Use 12 for close-packed crystals and 8 or 14 for BCC.
Cutoff Radius `cutoff`	number	`0`	0 to 20, step 0.1	Neighbor cutoff. Shown and used only when Nearest Neighbors is `0`.
Compute w_l `wl`	boolean	`false`		Also compute w_l for each order.
Compute w_l_hat (normalized) `wlHat`	boolean	`false`		Also compute w_l_hat for each order.
Emit Q_l^m components for l (-1 disables) `components`	number	`-1`	−1 to 20, step 1	Write the 2l + 1 complex components q_lm / \|q_l\| for this single order l. `-1` writes none.
Only Selected Atoms `onlySelected`	boolean	`false`		Analyze only the atoms whose `Selection` column is non-zero.

Outputs

Exposure	What you get
Steinhardt Order	A listing with the parameters and the counts of liquid-like, interface and crystal-like atoms, and a `structures` sub-listing.
Steinhardt Model	A listing, and a 3D model of the atoms grouped by a heuristic label from q₆: `Liquid-like`, `Interface` or `Crystal-like`.

The workflow declares the per-atom properties q6 (q6 (bond order)), q_4, q_6, q_8, q_10 and q_12. The per-atom table also has every q_l in one q list column, w_<l> and w_hat_<l> columns when those are on, and a components list column when Emit Q_l^m components is set.

Notes

If you change Orders, the q_<l> columns follow your list, but the workflow still declares q_4 to q_12.
The Liquid-like / Interface / Crystal-like labels are a quick visual aid. For a quantitative phase assignment, color by q_6 and choose thresholds for your system.

Reference

P. J. Steinhardt, D. R. Nelson, M. Ronchetti, "Bond-orientational order in liquids and glasses", Phys. Rev. B 28, 784 (1983). W. Lechner, C. Dellago, "Accurate determination of crystal structures based on averaged local bond order parameters", J. Chem. Phys. 129, 114707 (2008).