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from math import sqrt
import numpy as np
from ase.atoms import Atoms
def graphene_nanoribbon(n, m, type='zigzag', saturated=False, C_H=1.09,
C_C=1.42, vacuum=None, magnetic=False, initial_mag=1.12,
sheet=False, main_element='C', saturate_element='H'):
"""Create a graphene nanoribbon.
Creates a graphene nanoribbon in the x-z plane, with the nanoribbon
running along the z axis.
Parameters:
n: int
The width of the nanoribbon. For armchair nanoribbons, this
n may be half-integer to repeat by half a cell.
m: int
The length of the nanoribbon.
type: str
The orientation of the ribbon. Must be either 'zigzag'
or 'armchair'.
saturated: bool
If true, hydrogen atoms are placed along the edge.
C_H: float
Carbon-hydrogen bond length. Default: 1.09 Angstrom.
C_C: float
Carbon-carbon bond length. Default: 1.42 Angstrom.
vacuum: None (default) or float
Amount of vacuum added to non-periodic directions, if present.
magnetic: bool
Make the edges magnetic.
initial_mag: float
Magnitude of magnetic moment if magnetic.
sheet: bool
If true, make an infinite sheet instead of a ribbon (default: False)
"""
if m % 1 != 0:
raise ValueError('m must be integer')
if type == 'zigzag' and n % 1 != 0:
raise ValueError('n must be an integer for zigzag ribbons')
b = sqrt(3) * C_C / 4
arm_unit = Atoms(main_element + '4',
pbc=(1, 0, 1),
cell=[4 * b, 0, 3 * C_C])
arm_unit.positions = [[0, 0, 0],
[b * 2, 0, C_C / 2.],
[b * 2, 0, 3 * C_C / 2.],
[0, 0, 2 * C_C]]
arm_unit_half = Atoms(main_element + '2',
pbc=(1, 0, 1),
cell=[2 * b, 0, 3 * C_C])
arm_unit_half.positions = [[b * 2, 0, C_C / 2.],
[b * 2, 0, 3 * C_C / 2.]]
zz_unit = Atoms(main_element + '2',
pbc=(1, 0, 1),
cell=[3 * C_C / 2.0, 0, b * 4])
zz_unit.positions = [[0, 0, 0],
[C_C / 2.0, 0, b * 2]]
atoms = Atoms()
if type == 'zigzag':
edge_index0 = np.arange(m) * 2
edge_index1 = (n - 1) * m * 2 + np.arange(m) * 2 + 1
if magnetic:
mms = np.zeros(m * n * 2)
for i in edge_index0:
mms[i] = initial_mag
for i in edge_index1:
mms[i] = -initial_mag
for i in range(n):
layer = zz_unit.repeat((1, 1, m))
layer.positions[:, 0] += 3 * C_C / 2 * i
if i % 2 == 1:
layer.positions[:, 2] += 2 * b
layer[-1].position[2] -= b * 4 * m
atoms += layer
xmin = atoms.positions[0, 0]
if magnetic:
atoms.set_initial_magnetic_moments(mms)
if saturated:
H_atoms0 = Atoms(saturate_element + str(m))
H_atoms0.positions = atoms[edge_index0].positions
H_atoms0.positions[:, 0] -= C_H
H_atoms1 = Atoms(saturate_element + str(m))
H_atoms1.positions = atoms[edge_index1].positions
H_atoms1.positions[:, 0] += C_H
atoms += H_atoms0 + H_atoms1
atoms.cell = [n * 3 * C_C / 2, 0, m * 4 * b]
elif type == 'armchair':
n *= 2
n_int = int(round(n))
if abs(n_int - n) > 1e-10:
raise ValueError(
'The argument n has to be half-integer for armchair ribbons.')
n = n_int
for i in range(n // 2):
layer = arm_unit.repeat((1, 1, m))
layer.positions[:, 0] -= 4 * b * i
atoms += layer
if n % 2:
layer = arm_unit_half.repeat((1, 1, m))
layer.positions[:, 0] -= 4 * b * (n // 2)
atoms += layer
xmin = atoms.positions[-1, 0]
if saturated:
if n % 2:
arm_right_saturation = Atoms(saturate_element + '2',
pbc=(1, 0, 1),
cell=[2 * b, 0, 3 * C_C])
arm_right_saturation.positions = [
[- sqrt(3) / 2 * C_H, 0, C_C / 2 - C_H * 0.5],
[- sqrt(3) / 2 * C_H, 0, 3 * C_C / 2.0 + C_H * 0.5]]
else:
arm_right_saturation = Atoms(saturate_element + '2',
pbc=(1, 0, 1),
cell=[4 * b, 0, 3 * C_C])
arm_right_saturation.positions = [
[- sqrt(3) / 2 * C_H, 0, C_H * 0.5],
[- sqrt(3) / 2 * C_H, 0, 2 * C_C - C_H * 0.5]]
arm_left_saturation = Atoms(saturate_element + '2', pbc=(1, 0, 1),
cell=[4 * b, 0, 3 * C_C])
arm_left_saturation.positions = [
[b * 2 + sqrt(3) / 2 * C_H, 0, C_C / 2 - C_H * 0.5],
[b * 2 + sqrt(3) / 2 * C_H, 0, 3 * C_C / 2.0 + C_H * 0.5]]
arm_right_saturation.positions[:, 0] -= 4 * b * (n / 2.0 - 1)
atoms += arm_right_saturation.repeat((1, 1, m))
atoms += arm_left_saturation.repeat((1, 1, m))
atoms.cell = [b * 4 * n / 2.0, 0, 3 * C_C * m]
atoms.set_pbc([sheet, False, True])
# The ribbon was 'built' from x=0 towards negative x.
# Move the ribbon to positive x:
atoms.positions[:, 0] -= xmin
if not sheet:
atoms.cell[0] = 0.0
if vacuum is not None:
atoms.center(vacuum, axis=1)
if not sheet:
atoms.center(vacuum, axis=0)
return atoms
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