Coordination polyhedra¶

CoordinationPolyhedra builds the convex hull of the neighbors of some atoms, as OVITO's coordination polyhedra do: the octahedra of oxygen about the titanium of a perovskite, the tetrahedra of a silicate. The polyhedra come as one triangle mesh for render, with the volume of each.

import numpy as np
from mdapy.analysis import CoordinationPolyhedra
from mdapy.build import build_crystal
from mdapy.visualization import render

srtio3 = build_crystal(
    "perovskite", 3.905, elements=["Sr", "Ti", "O"], repeat=(3, 3, 3)
)
titanium = np.asarray(srtio3["element"]) == "Ti"
octahedra = CoordinationPolyhedra(2.2).compute(srtio3, titanium)
octahedra.volumes  # 27 octahedra of 4/3 (a/2)³ = 9.93 Å³

# the octahedra in blue, strontium and oxygen as small atoms
strontium = np.asarray(srtio3["element"]) == "Sr"
render(
    srtio3,
    "images/polyhedra.png",
    atoms=~titanium,
    radius=np.where(strontium, 0.9, 0.45),
    mesh=octahedra.mesh,
    mesh_color="#4f86c6",
    mesh_alpha=0.85,
    view=(-1.0, -0.6, -0.45),
    width=600,
    height=600,
    legend=True,
)

Octahedra of a perovskite

SrTiO₃ repeated 3 × 3 × 3 times: the TiO₆ octahedra (blue), the oxygen (red) at their corners and the strontium (green) between them. The octahedra about the atoms on the faces of the box reach out of it, whole. mesh_color also takes one color per triangle, such as that of the atom of each, colors[octahedra.atoms[octahedra.owners]].

Parameters¶

CoordinationPolyhedra(cutoff=None, *, num_neighbors=None, bonds=False)

Name	Type	Default	Unit	Meaning
`cutoff`	float64		Å	the neighbors closer than this
`num_neighbors`	int32			the nearest neighbors, this many
`bonds`	bool	`False`		the atoms bonded to each, by the bonds of the topology, as OVITO does

Give exactly one of them. compute(system, atoms=None) builds the polyhedra about the atoms of a boolean mask or of indices, all by default. Neighbors are found through the periodic boundaries with the neighbor lists of MDAPY; each polyhedron is built about its atom, whole, even where it reaches out of the box. Neighbors in one plane make one face, cut into triangles.

Results¶

A CoordinationPolyhedraResult:

Attribute	Type	Meaning
`mesh`	`TriangleMesh`	the triangles of every polyhedron, counterclockwise seen from outside; their vertices are the neighbors next to the atom
`atoms`	(M,) int64	the atom in the middle of each polyhedron
`owners`	(F,) int64	the polyhedron of each triangle, an index of `atoms`
`volumes`	(M,) float64	the volume of each polyhedron in Å³; 0 for fewer than four neighbors or neighbors in a plane

Errors¶

CoordinationPolyhedra raises InvalidParameter unless exactly one of cutoff, num_neighbors and bonds is given; compute raises InvalidParameter for atoms that are not a mask or indices of the system and as NeighborList.build does, and MissingProperty with bonds for a system without bonds.