import numpy as np
from ase import Atoms
from ase.cluster.util import get_element_info
[docs]def Decahedron(symbol, p, q, r, latticeconstant=None):
"""
Return a decahedral cluster.
Parameters
----------
symbol: Chemical symbol (or atomic number) of the element.
p: Number of atoms on the (100) facets perpendicular to the five
fold axis.
q: Number of atoms on the (100) facets parallel to the five fold
axis. q = 1 corresponds to no visible (100) facets.
r: Depth of the Marks re-entrence at the pentagon corners. r = 0
corresponds to no re-entrence.
latticeconstant (optional): The lattice constant. If not given,
then it is extracted form ase.data.
"""
symbol, atomic_number, latticeconstant = get_element_info(
symbol, latticeconstant)
# Check values of p, q, r
if p < 1 or q < 1:
raise ValueError("p and q must be greater than 0.")
if r < 0:
raise ValueError("r must be greater than or equal to 0.")
# Defining constants
t = 2.0 * np.pi / 5.0
b = latticeconstant / np.sqrt(2.0)
a = b * np.sqrt(3.0) / 2.0
verticies = a * np.array([[np.cos(np.pi / 2.), np.sin(np.pi / 2.), 0.],
[np.cos(t * 1. + np.pi / 2.),
np.sin(t * 1. + np.pi / 2.), 0.],
[np.cos(t * 2. + np.pi / 2.),
np.sin(t * 2. + np.pi / 2.), 0.],
[np.cos(t * 3. + np.pi / 2.),
np.sin(t * 3. + np.pi / 2.), 0.],
[np.cos(t * 4. + np.pi / 2.), np.sin(
t * 4. + np.pi / 2.), 0.]])
# Number of atoms on the five fold axis and a nice constant
h = p + q + 2 * r - 1
g = h - q + 1 # p + 2*r
positions = []
# Make the five fold axis
for j in range(h):
pos = np.array([0.0, 0.0, j * b - (h - 1) * b / 2.0])
positions.append(pos)
# Make pentagon rings around the five fold axis
for n in range(1, h):
# Condition for (100)-planes
if n < g:
for m in range(5):
v1 = verticies[m - 1]
v2 = verticies[m]
for i in range(n):
# Condition for marks re-entrence
if n - i < g - r and i < g - r:
for j in range(h - n):
pos = (n - i) * v1 + i * v2
pos += np.array([0.0, 0.0, j * b -
(h - n - 1) * b / 2.0])
positions.append(pos)
symbols = [atomic_number] * len(positions)
return Atoms(symbols=symbols, positions=positions)