Diamond structure

DiamondStructure tells cubic diamond from hexagonal diamond (lonsdaleite) in silicon, germanium, carbon and other tetrahedrally bonded crystals, where common neighbor analysis of the four nearest neighbors says nothing.

import mdapy as mp
from mdapy.build import build_crystal
from mdapy.identify import DiamondStructure

# cubic diamond silicon of 3 x 3 x 3 cells
system = build_crystal("diamond", 5.431, elements="Si", repeat=(3, 3, 3))

result = DiamondStructure().compute(system)
result.counts()["cubic_diamond"]  # 216

In a polycrystal of silicon:

from mdapy.build import build_crystal, build_polycrystal
from mdapy.visualization import render

grains = build_polycrystal(
    build_crystal("diamond", 5.431, elements="Si"), mp.Box(60.0), 6, seed=4
)
structures = DiamondStructure().compute(grains)
render(
    grains, "images/diamond.png", color=structures, width=800, height=600, legend=True
)

Six grains of silicon as built: cubic diamond in blue, its first and second neighbors in cyan and green. An atom is cubic diamond only if its second neighbors are in order too; the atoms of the boundaries next to the grains are their neighbors, the others white.

Parameters

DiamondStructure() has no parameters. compute(system, *, neighbors=None, progress=None, cancel=None) takes the arguments of every analysis. A given neighbor list must hold the 4 nearest neighbors of every atom.

Results

A StructureResult with the types

Index	Name	Default color
0	other	light grey
1	cubic_diamond	blue
2	cubic_diamond_first_neighbor	cyan
3	cubic_diamond_second_neighbor	light green
4	hexagonal_diamond	orange
5	hexagonal_diamond_first_neighbor	yellow
6	hexagonal_diamond_second_neighbor	yellow green

The types, their numbers and their colors are those of OVITO.

Errors

compute raises InvalidParameter for a neighbor list that does not hold the 4 nearest neighbors, or a system without periodic directions of fewer than 5 atoms.

Definition

The first neighbors of an atom are its 4 nearest. Each of them has 4 nearest neighbors of its own, one of which must be the atom itself; otherwise the atom is other. The other three of each give the 12 second neighbors of the atom, which form an fcc shell in cubic diamond and an hcp shell in hexagonal diamond. Common neighbor analysis of these 12, with the cutoff \(\frac{1+\sqrt 2}{2}\) times their mean distance, decides: fcc is cubic_diamond and hcp hexagonal_diamond. Then, atom by atom in the order of the system, an atom that is still other and among the 4 nearest of a diamond atom becomes its first neighbor (of cubic or hexagonal diamond, as that atom); after all first neighbors, an atom that is still other and among the 4 nearest of a first neighbor becomes a second neighbor of the same kind. The first atom in order to reach an atom decides its kind.

Please cite

Maras et al. (2016).