g3 Explorer

After measuring the g3 distribution, view it interactively:

cell.measure_g3()
cell.plot_g3()

Returns a Jupyter widget (anywidget) with:

  • Heatmap: 2D slice of the g3 distribution (\(r\) vs \(\phi\)) for a selected radial shell.

  • Radial profile: pair correlation function with drag-to-select shell range.

  • Channel selector: switch between triplet types (e.g. Si | Si Si, C | C Si).

  • Normalize toggle: show raw counts or density-normalized values approaching 1.0 in the random limit.

  • Auto-shell toggle: when unchecked, the shell selection stays fixed while switching channels.

What is a rooted three-body distribution?

For every atom \(i\) and every pair of neighbours \((j, k)\) the code records the three scalars

  • \(r_{ij}\), the distance from \(i\) to the “root” neighbour \(j\),

  • \(r_{ik}\), the distance from \(i\) to the “partner” neighbour \(k\),

  • \(\phi_{jik}\), the angle at the central atom \(i\).

Accumulated over all central atoms of the relevant species, this gives a four-index histogram \(g_3^{t}(r_j, r_k, \phi)\) for every triplet type \(t\) (e.g. Si | Si Si). “Rooted” means the distribution is conditioned on one of the two bonds (the root bond) sitting in a specific radial shell.

The 2D viewer shows a slice of the full distribution: the root-bond length \(r_j\) is integrated over a user-chosen shell window (usually the first neighbour peak), leaving a 2D map of \((r_k, \phi)\). This is the quantity plotted in the heatmap.

How to read the static viewer embedded in the case studies

  • Upper panel: the 2D slice \(g_3(r, \phi)\) for a fixed root-bond shell. Axes are partner-bond distance \(r\) (horizontal) and angle \(\phi\) (vertical, 0-180 degrees). The diverging RdBu_r colormap has white at \(g = 1\) (uniform random reference), blue for depleted, red for enhanced.

  • Lower panel: the pair profile \(g(r)\), i.e. the full two-body correlation function for the same triplet channel.

    • The amber band labelled “root bond” is the radial shell that was integrated over to produce the slice above. Any peak that falls inside this band is “the root bond”; peaks outside it appear as vertical stripes in the 2D slice at the corresponding partner-bond distance.

    • The dashed line at \(g = 1\) marks the uniform density reference.

  • The static viewer displays the distribution measured after relaxation; the interactive Jupyter widget can be invoked at any point in the workflow.

Parameters

cell.plot_g3(pair=0, normalize=True)

  • pair: triplet channel index or label (e.g. "Si | Si Si").

  • normalize: if True, divides out the ideal density factor so the plot shows deviation from random.

Requirements

measure_g3() must be called first:

cell.generate(shell_target, ...)
cell.measure_g3()       # required
cell.plot_g3()