def graphene_nanoribbon(n,
m,
side='zigzag',
saturated="no",
C_H=1.09,
C_C=1.42,
vacc=5.,
magnetic=None,
initial_mag=1.12,
sheet=False,
main_element='C',
satur_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: The width of the nanoribbon
m: The length of the nanoribbon.
side ('zigzag'): The orientation of the ribbon. Must be either 'zigzag'
or 'armchair'.
saturated (no/yes/side): If yes, hydrogen atoms are placed along the edges. If side, then only 2 sides are saturated.
C_H: Carbon-hydrogen bond length. Default: 1.09 Angstrom
C_C: Carbon-carbon bond length. Default: 1.42 Angstrom.
vacc: Amount of vacuum. Default 5 Angstrom.
magnetic: Make the edges magnetic.
initial_mag: Magnitude of magnetic moment if magnetic=True.
sheet: If true, make an infinite sheet instead of a ribbon.
"""
#This function creates the coordinates for a graphene nanoribbon,
#n is width, m is length
b = sqrt(3) * C_C / 4
arm_unit = Atoms(main_element + '4',
pbc=(1, 0, 1),
cell=[4 * b, vacc, 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]]
zz_unit = Atoms(main_element + '2',
pbc=(1, 0, 1),
cell=[3 * C_C / 2., vacc, b * 4])
zz_unit.positions = [[0, 0, 0], [C_C / 2., 0, b * 2]]
atoms = Atoms()
tol = 1e-4
if sheet:
vacc2 = 0.0
else:
vacc2 = vacc
if side == 'zigzag':
edge_index0 = np.arange(m) * 2 + 1
edge_index1 = (n - 1) * m * 2 + np.arange(m) * 2
edge_index2 = []
edge_index3 = []
for i in range(0, n, 2):
edge_index2.append(i * m * 2)
edge_index3.append((i + 1) * m * 2 - 1)
if i > 1:
edge_index2.append(i * m * 2 - 1)
edge_index3.append(i * m * 2 - 2)
edge_index2 = np.array(edge_index2)
edge_index3 = np.array(edge_index3)
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
if magnetic:
atoms.set_initial_magnetic_moments(mms)
if saturated != "no":
H_atoms0 = Atoms(satur_element + str(m))
H_atoms0.positions = atoms[edge_index0].positions
H_atoms0.positions[:, 0] += C_H
H_atoms1 = Atoms(satur_element + str(m))
H_atoms1.positions = atoms[edge_index1].positions
H_atoms1.positions[:, 0] -= C_H
H_atoms2 = Atoms(satur_element + str(n))
H_atoms2.positions = atoms[edge_index2].positions
H_atoms2.positions[:, 2] -= C_H
H_atoms3 = Atoms(satur_element + str(n))
H_atoms3.positions = atoms[edge_index3].positions
H_atoms3.positions[:, 2] += C_H
if saturated == "yes":
atoms += H_atoms0 + H_atoms1 + H_atoms2 + H_atoms3
if saturated == "side":
atoms += H_atoms0 + H_atoms1
atoms.cell = [n * 3 * C_C / 2 + vacc2, vacc + 5.0, m * 4 * b]
elif side == 'armchair':
for i in range(n):
layer = arm_unit.repeat((1, 1, m))
layer.positions[:, 0] -= 4 * b * i
atoms += layer
atoms.cell = [b * 4 * n + vacc2, vacc, 3 * C_C * m]
atoms.center()
atoms.set_pbc([sheet, False, True])
return atoms
def nanotube(n, m, length=1, bond=1.42, symbol='C', verbose=False):
if n < m:
m, n = n, m
nk = 6000
sq3 = sqrt(3.0)
a = sq3 * bond
l2 = n * n + m * m + n * m
l = sqrt(l2)
dt = a * l / np.pi
nd = gcd(n, m)
if (n - m) % (3 * nd) == 0:
ndr = 3 * nd
else:
ndr = nd
nr = (2 * m + n) / ndr
ns = -(2 * n + m) / ndr
nt2 = 3 * l2 / ndr / ndr
nt = np.floor(sqrt(nt2))
nn = 2 * l2 / ndr
ichk = 0
if nr == 0:
n60 = 1
else:
n60 = nr * 4
absn = abs(n60)
nnp = []
nnq = []
for i in range(-absn, absn + 1):
for j in range(-absn, absn + 1):
j2 = nr * j - ns * i
if j2 == 1:
j1 = m * i - n * j
if j1 > 0 and j1 < nn:
ichk += 1
nnp.append(i)
nnq.append(j)
if ichk == 0:
raise RuntimeError('not found p, q strange!!')
if ichk >= 2:
raise RuntimeError('more than 1 pair p, q strange!!')
nnnp = nnp[0]
nnnq = nnq[0]
if verbose:
print('the symmetry vector is', nnnp, nnnq)
lp = nnnp * nnnp + nnnq * nnnq + nnnp * nnnq
r = a * sqrt(lp)
c = a * l
t = sq3 * c / ndr
if 2 * nn > nk:
raise RuntimeError('parameter nk is too small!')
rs = c / (2.0 * np.pi)
if verbose:
print('radius=', rs, t)
q1 = np.arctan((sq3 * m) / (2 * n + m))
q2 = np.arctan((sq3 * nnnq) / (2 * nnnp + nnnq))
q3 = q1 - q2
q4 = 2.0 * np.pi / nn
q5 = bond * np.cos((np.pi / 6.0) - q1) / c * 2.0 * np.pi
h1 = abs(t) / abs(np.sin(q3))
h2 = bond * np.sin((np.pi / 6.0) - q1)
ii = 0
x, y, z = [], [], []
for i in range(nn):
x1, y1, z1 = 0, 0, 0
k = np.floor(i * abs(r) / h1)
x1 = rs * np.cos(i * q4)
y1 = rs * np.sin(i * q4)
z1 = (i * abs(r) - k * h1) * np.sin(q3)
kk2 = abs(np.floor((z1 + 0.0001) / t))
if z1 >= t - 0.0001:
z1 -= t * kk2
elif z1 < 0:
z1 += t * kk2
ii += 1
x.append(x1)
y.append(y1)
z.append(z1)
z3 = (i * abs(r) - k * h1) * np.sin(q3) - h2
ii += 1
if z3 >= 0 and z3 < t:
x2 = rs * np.cos(i * q4 + q5)
y2 = rs * np.sin(i * q4 + q5)
z2 = (i * abs(r) - k * h1) * np.sin(q3) - h2
x.append(x2)
y.append(y2)
z.append(z2)
else:
x2 = rs * np.cos(i * q4 + q5)
y2 = rs * np.sin(i * q4 + q5)
z2 = (i * abs(r) - (k + 1) * h1) * np.sin(q3) - h2
kk = abs(np.floor(z2 / t))
if z2 >= t - 0.0001:
z2 -= t * kk
elif z2 < 0:
z2 += t * kk
x.append(x2)
y.append(y2)
z.append(z2)
ntotal = 2 * nn
X = []
for i in range(ntotal):
X.append([x[i], y[i], z[i]])
if length > 1:
xx = X[:]
for mnp in range(2, length + 1):
for i in range(len(xx)):
X.append(xx[i][:2] + [xx[i][2] + (mnp - 1) * t])
TransVec = t
NumAtom = ntotal * length
Diameter = rs * 2
ChiralAngle = np.arctan((sq3 * n) / (2 * m + n)) / (np.pi * 180)
cell = [Diameter * 2, Diameter * 2, length * t]
atoms = Atoms(symbol + str(NumAtom),
positions=X,
cell=cell,
pbc=[False, False, True])
atoms.center()
if verbose:
print('translation vector =', TransVec)
print('diameter = ', Diameter)
print('chiral angle = ', ChiralAngle)
return atoms
def surface(symbol, structure, face, size, a, c, vacuum, orthogonal=True):
"""Function to build often used surfaces.
Don't call this function directly - use fcc100, fcc110, bcc111, ..."""
Z = atomic_numbers[symbol]
if a is None:
sym = reference_states[Z]['symmetry'].lower()
if sym != structure:
raise ValueError("Can't guess lattice constant for %s-%s!" %
(structure, symbol))
a = reference_states[Z]['a']
if structure == 'hcp' and c is None:
if reference_states[Z]['symmetry'].lower() == 'hcp':
c = reference_states[Z]['c/a'] * a
else:
c = sqrt(8 / 3.0) * a
positions = np.empty((size[2], size[1], size[0], 3))
positions[..., 0] = np.arange(size[0]).reshape((1, 1, -1))
positions[..., 1] = np.arange(size[1]).reshape((1, -1, 1))
positions[..., 2] = np.arange(size[2]).reshape((-1, 1, 1))
numbers = np.ones(size[0] * size[1] * size[2], int) * Z
tags = np.empty((size[2], size[1], size[0]), int)
tags[:] = np.arange(size[2], 0, -1).reshape((-1, 1, 1))
slab = Atoms(numbers,
tags=tags.ravel(),
pbc=(True, True, False),
cell=size)
surface_cell = None
sites = {'ontop': (0, 0)}
surf = structure + face
if surf == 'fcc100':
cell = (sqrt(0.5), sqrt(0.5), 0.5)
positions[-2::-2, ..., :2] += 0.5
sites.update({'hollow': (0.5, 0.5), 'bridge': (0.5, 0)})
elif surf == 'fcc110':
cell = (1.0, sqrt(0.5), sqrt(0.125))
positions[-2::-2, ..., :2] += 0.5
sites.update({'hollow': (0.5, 0.5), 'longbridge': (0.5, 0),
'shortbridge': (0, 0.5)})
elif surf == 'bcc100':
cell = (1.0, 1.0, 0.5)
positions[-2::-2, ..., :2] += 0.5
sites.update({'hollow': (0.5, 0.5), 'bridge': (0.5, 0)})
else:
if orthogonal and size[1] % 2 == 1:
raise ValueError(("Can't make orthorhombic cell with size=%r. " %
(tuple(size),)) +
'Second number in size must be even.')
if surf == 'fcc111':
cell = (sqrt(0.5), sqrt(0.375), 1 / sqrt(3))
if orthogonal:
positions[-1::-3, 1::2, :, 0] += 0.5
positions[-2::-3, 1::2, :, 0] += 0.5
positions[-3::-3, 1::2, :, 0] -= 0.5
positions[-2::-3, ..., :2] += (0.0, 2.0 / 3)
positions[-3::-3, ..., :2] += (0.5, 1.0 / 3)
else:
positions[-2::-3, ..., :2] += (-1.0 / 3, 2.0 / 3)
positions[-3::-3, ..., :2] += (1.0 / 3, 1.0 / 3)
sites.update({'bridge': (0.5, 0), 'fcc': (1.0 / 3, 1.0 / 3),
'hcp': (2.0 / 3, 2.0 / 3)})
elif surf == 'hcp0001':
cell = (1.0, sqrt(0.75), 0.5 * c / a)
if orthogonal:
positions[:, 1::2, :, 0] += 0.5
positions[-2::-2, ..., :2] += (0.0, 2.0 / 3)
else:
positions[-2::-2, ..., :2] += (-1.0 / 3, 2.0 / 3)
sites.update({'bridge': (0.5, 0), 'fcc': (1.0 / 3, 1.0 / 3),
'hcp': (2.0 / 3, 2.0 / 3)})
elif surf == 'bcc110':
cell = (1.0, sqrt(0.5), sqrt(0.5))
if orthogonal:
positions[:, 1::2, :, 0] += 0.5
positions[-2::-2, ..., :2] += (0.0, 1.0)
else:
positions[-2::-2, ..., :2] += (-0.5, 1.0)
sites.update({'shortbridge': (0, 0.5),
'longbridge': (0.5, 0),
'hollow': (0.375, 0.25)})
elif surf == 'bcc111':
cell = (sqrt(2), sqrt(1.5), sqrt(3) / 6)
if orthogonal:
positions[-1::-3, 1::2, :, 0] += 0.5
positions[-2::-3, 1::2, :, 0] += 0.5
positions[-3::-3, 1::2, :, 0] -= 0.5
positions[-2::-3, ..., :2] += (0.0, 2.0 / 3)
positions[-3::-3, ..., :2] += (0.5, 1.0 / 3)
else:
positions[-2::-3, ..., :2] += (-1.0 / 3, 2.0 / 3)
positions[-3::-3, ..., :2] += (1.0 / 3, 1.0 / 3)
sites.update({'hollow': (1.0 / 3, 1.0 / 3)})
surface_cell = a * np.array([(cell[0], 0),
(cell[0] / 2, cell[1])])
if not orthogonal:
cell = np.array([(cell[0], 0, 0),
(cell[0] / 2, cell[1], 0),
(0, 0, cell[2])])
if surface_cell is None:
surface_cell = a * np.diag(cell[:2])
if isinstance(cell, tuple):
cell = np.diag(cell)
slab.set_positions(positions.reshape((-1, 3)))
slab.set_cell([a * v * n for v, n in zip(cell, size)], scale_atoms=True)
if vacuum is not None:
slab.center(vacuum=vacuum, axis=2)
slab.adsorbate_info['cell'] = surface_cell
slab.adsorbate_info['sites'] = sites
return slab