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()