# Example B1: Computing Voronoi indices¶

This script demonstrates the use of the VoronoiAnalysisModifier. The script calculates the distribution of Voronoi coordination polyhedra in an amorphous structure.

A Voronoi polyhedron is expressed in terms of the Schlaefli notation, which is a vector of indices (n1, n2, n3, n4, n5, n6, …), where ni is the number of polyhedron faces with i edges/vertices.

The script computes the distribution of these Voronoi index vectors and lists the 10 most frequent polyhedron types in the dataset. In the case of a Cu64%-Zr36% bulk metallic glass, the most frequent polyhedron type is the icosahedron. It has 12 faces with five edges each. Thus, the corresponding Voronoi index vector is:

(0, 0, 0, 0, 12, 0, …)

Python script:

# Import OVITO modules.
from ovito.io import *
from ovito.modifiers import *

# Import NumPy module.
import numpy

# Load a simulation snapshot of a Cu-Zr metallic glass.
pipeline = import_file("input/simulation.0.dump")

# The LAMMPS dump file imported above contains only numeric atom type IDs but
# no chemical element names or atom radius information. That's why we explicitly set the
# atomic radii of Cu & Zr atoms now (required for polydisperse Voronoi tessellation).
atom_types = data.particles_.particle_types_
atom_types.type_by_id_(1).radius = 1.35   # Cu atomic radius assigned to atom type 1
atom_types.type_by_id_(2).radius = 1.55   # Zr atomic radius assigned to atom type 2

# Set up the Voronoi analysis modifier.
voro = VoronoiAnalysisModifier(
compute_indices = True,
edge_threshold = 0.1
)
pipeline.modifiers.append(voro)

# Let OVITO compute the results.
data = pipeline.compute()

# Access computed Voronoi indices.
# This is an (N) x (M) array, where M is the maximum face order.
voro_indices = data.particles['Voronoi Index']

# This helper function takes a two-dimensional array and computes a frequency
# histogram of the data rows using some NumPy magic.
# It returns two arrays (of equal length):
#    1. The list of unique data rows from the input array
#    2. The number of occurences of each unique row
# Both arrays are sorted in descending order such that the most frequent rows
# are listed first.
def row_histogram(a):
ca = numpy.ascontiguousarray(a).view([('', a.dtype)] * a.shape[1])
unique, indices, inverse = numpy.unique(ca, return_index=True, return_inverse=True)
counts = numpy.bincount(inverse)
sort_indices = numpy.argsort(counts)[::-1]
return (a[indices[sort_indices]], counts[sort_indices])

# Compute frequency histogram.
unique_indices, counts = row_histogram(voro_indices)

# Print the ten most frequent histogram entries.
for i in range(10):
print("%s\t%i\t(%.1f %%)" % (tuple(unique_indices[i]),
counts[i],
100.0*float(counts[i])/len(voro_indices)))


Program output:

(0, 0, 0, 0, 12, 0)     12274   (11.4 %)
(0, 0, 0, 2, 8, 2)      7485    (6.9 %)
(0, 0, 0, 3, 6, 4)      5637    (5.2 %)
(0, 0, 0, 1, 10, 2)     4857    (4.5 %)
(0, 0, 0, 3, 6, 3)      3415    (3.2 %)
(0, 0, 0, 2, 8, 1)      2927    (2.7 %)
(0, 0, 0, 1, 10, 5)     2900    (2.7 %)
(0, 0, 0, 1, 10, 4)     2068    (1.9 %)
(0, 0, 0, 2, 8, 6)      2063    (1.9 %)
(0, 0, 0, 2, 8, 5)      1662    (1.5 %)