oldr = a[0].position.copy()
a.center(vacuum=params.vacuum, axis=0)
a.center(vacuum=params.vacuum, axis=1)
tip_x0 += a[0].position[0] - oldr[0]
tip_y0 += a[0].position[1] - oldr[1]
cryst.set_cell(a.cell)
cryst.translate(a[0].position - oldr)
g = a.get_array('groups')
mask = g != 0
# Choose which bond to break.
bondlength = param('bondlength', 1.85)
bond1, bond2 = param('bond',
crack.find_tip_coordination(a, bondlength=bondlength))
logger.pr('Opening bond {0}--{1}, initial bond length {2}' \
.format(bond1, bond2, a.get_distance(bond1, bond2, mic=True)))
# centre vertically on the opening bond
a.translate([
0.,
a.cell[1, 1] / 2.0 - (a.positions[bond1, 1] + a.positions[bond2, 1]) / 2.0,
0
])
tip_x0 = (a.positions[bond1, 0] + a.positions[bond2, 0]) / 2
tip_y0 = (a.positions[bond1, 1] + a.positions[bond2, 1]) / 2
b = a.copy()
tip_y += a[0].position[1] - oldr[1]
cryst.set_cell(a.cell)
cryst.translate(a[0].position - oldr)
ase.io.write('notch.xyz', a, format='extxyz')
parprint('Initial tip position {0} {1}'.format(tip_x, tip_y))
# Groups mark the fixed region and the region use for fitting the crack tip.
g = a.get_array('groups')
# Assign calculator.
a.set_calculator(params.calc)
for j in range(params.n_bonds):
bond1, bond2 = crack.find_tip_coordination(a)
print 'Breaking tip bond {0}--{1}'.format(bond1, bond2)
# Run crack calculation.
for i, bond_length in enumerate(params.bond_lengths):
parprint('=== bond_length = {0} ==='.format(bond_length))
xyz_file = 'bond_%d_%4d.xyz' % (j+1, int(bond_length*1000))
if os.path.exists(xyz_file):
parprint('%s found, skipping' % xyz_file)
a = ase.io.read(xyz_file)
del a[np.logical_or(a.numbers == atomic_numbers[ACTUAL_CRACK_TIP],
a.numbers == atomic_numbers[FITTED_CRACK_TIP])]
a.set_calculator(params.calc)
else:
a.set_constraint(None)
a.set_distance(bond1, bond2, bond_length)
tip_x, tip_y, params.k1*k1g)
a.positions[:ncryst,0] += ux
a.positions[:ncryst,1] += uy
basename = parameter('basename', 'energy_barrier')
# Center notched configuration in simulation cell and ensure enough vacuum.
oldr = a[0].position.copy()
a.center(vacuum=params.vacuum, axis=0)
a.center(vacuum=params.vacuum, axis=1)
tip_x += a[0].position[0] - oldr[0]
tip_y += a[0].position[1] - oldr[1]
# Choose which bond to break.
bond1, bond2 = parameter('bond',
crack.find_tip_coordination(a, bondlength=bondlength))
# Hydrogenate?
if parameter('hydrogenate', False):
# Get surface atoms of cluster with crack
coord = np.bincount(neighbour_list('i', a, bondlength), minlength=len(a))
# Exclude all atoms of the crack face from hydrogenation
exclude = np.logical_and(a.get_array('groups')==1, coord!=4)
a.set_array('coord', coord)
a.set_array('exclude', exclude)
a = hydrogenate(cryst, bondlength, parameter('XH_bondlength'), b=a,
exclude=exclude)
g = a.get_array('groups')
g[np.array(a.get_chemical_symbols())=='H'] = -1
a.set_array('groups', g)
ase.io.write('{0}_hydrogenated.cfg'.format(basename), a)
def setup_crack(logger=screen):
calc = parameter('calc')
cryst = parameter('cryst').copy()
cryst.set_pbc(True)
# Double check elastic constants. We're just assuming this is really a periodic
# system. (True if it comes out of the cluster routines.)
compute_elastic_constants = parameter('compute_elastic_constants', False)
elastic_fmax = parameter('elastic_fmax', 0.01)
elastic_symmetry = parameter('elastic_symmetry', 'triclinic')
elastic_optimizer = parameter('elastic_optimizer', ase.optimize.FIRE)
if compute_elastic_constants:
cryst.set_calculator(calc)
log_file = open('elastic_constants.log', 'w')
C, C_err = fit_elastic_constants(cryst,
verbose=False,
symmetry=elastic_symmetry,
optimizer=elastic_optimizer,
logfile=log_file,
fmax=elastic_fmax)
log_file.close()
logger.pr('Measured elastic constants (in GPa):')
logger.pr(np.round(C * 10 / GPa) / 10)
crk = crack.CubicCrystalCrack(parameter('crack_surface'),
parameter('crack_front'),
Crot=C / GPa)
else:
if has_parameter('C'):
crk = crack.CubicCrystalCrack(parameter('crack_surface'),
parameter('crack_front'),
C=parameter('C'))
else:
crk = crack.CubicCrystalCrack(parameter('crack_surface'),
parameter('crack_front'),
parameter('C11'), parameter('C12'),
parameter('C44'))
logger.pr('Elastic constants used for boundary condition (in GPa):')
logger.pr(np.round(crk.C * 10) / 10)
# Get Griffith's k1.
k1g = crk.k1g(parameter('surface_energy'))
logger.pr('Griffith k1 = %f' % k1g)
# Apply initial strain field.
tip_x = parameter('tip_x', cryst.cell.diagonal()[0] / 2)
tip_y = parameter('tip_y', cryst.cell.diagonal()[1] / 2)
bondlength = parameter('bondlength', 2.7)
bulk_nn = parameter('bulk_nn', 4)
a = cryst.copy()
a.set_pbc([False, False, True])
hydrogenate_flag = parameter('hydrogenate', False)
hydrogenate_crack_face_flag = parameter('hydrogenate_crack_face', True)
if hydrogenate_flag and not hydrogenate_crack_face_flag:
# Get surface atoms of cluster with crack
a = hydrogenate(cryst, bondlength, parameter('XH_bondlength'), b=a)
g = a.get_array('groups')
g[a.numbers == 1] = -1
a.set_array('groups', g)
cryst = a.copy()
k1 = parameter('k1')
try:
k1 = k1[0]
except:
pass
ux, uy = crk.displacements(cryst.positions[:, 0], cryst.positions[:, 1],
tip_x, tip_y, k1 * k1g)
a.positions[:len(cryst), 0] += ux
a.positions[:len(cryst), 1] += uy
# Center notched configuration in simulation cell and ensure enough vacuum.
oldr = a[0].position.copy()
vacuum = parameter('vacuum')
a.center(vacuum=vacuum, axis=0)
a.center(vacuum=vacuum, axis=1)
tip_x += a[0].x - oldr[0]
tip_y += a[0].y - oldr[1]
# Choose which bond to break.
bond1, bond2 = \
parameter('bond', crack.find_tip_coordination(a, bondlength=bondlength, bulk_nn=bulk_nn))
if parameter('center_crack_tip_on_bond', False):
tip_x, tip_y, dummy = (a.positions[bond1] + a.positions[bond2]) / 2
# Hydrogenate?
coord = np.bincount(neighbour_list('i', a, bondlength), minlength=len(a))
a.set_array('coord', coord)
if parameter('optimize_full_crack_face', False):
g = a.get_array('groups')
gcryst = cryst.get_array('groups')
coord = a.get_array('coord')
g[coord != 4] = -1
gcryst[coord != 4] = -1
a.set_array('groups', g)
cryst.set_array('groups', gcryst)
if hydrogenate_flag and hydrogenate_crack_face_flag:
# Get surface atoms of cluster with crack
exclude = np.logical_and(a.get_array('groups') == 1, coord != 4)
a.set_array('exclude', exclude)
a = hydrogenate(cryst,
bondlength,
parameter('XH_bondlength'),
b=a,
exclude=exclude)
g = a.get_array('groups')
g[a.numbers == 1] = -1
a.set_array('groups', g)
basename = parameter('basename', 'energy_barrier')
ase.io.write('{0}_hydrogenated.xyz'.format(basename),
a,
format='extxyz')
# Move reference crystal by same amount
cryst.set_cell(a.cell)
cryst.set_pbc([False, False, True])
cryst.translate(a[0].position - oldr)
# Groups mark the fixed region and the region use for fitting the crack tip.
g = a.get_array('groups')
gcryst = cryst.get_array('groups')
logger.pr('Opening bond {0}--{1}, initial bond length {2}'.format(
bond1, bond2, a.get_distance(bond1, bond2, mic=True)))
# centre vertically on the opening bond
if parameter('center_cell_on_bond', True):
a.translate([
0., a.cell[1, 1] / 2.0 -
(a.positions[bond1, 1] + a.positions[bond2, 1]) / 2.0, 0.
])
a.info['bond1'] = bond1
a.info['bond2'] = bond2
return a, cryst, crk, k1g, tip_x, tip_y, bond1, bond2, g == 0, gcryst == 0, g == 1
def test_embedding_size_convergence(self):
calc = Tersoff(**Tersoff_PRB_39_5566_Si_C)
el = 'C'
a0 = 3.566
surface_energy = 2.7326 * 10
crack_surface = [1, 1, 1]
crack_front = [1, -1, 0]
skin_x, skin_y = 1, 1
cryst = bulk(el, cubic=True)
cryst.set_calculator(calc)
FIRE(UnitCellFilter(cryst), logfile=None).run(fmax=1e-6)
a0 = cryst.cell.diagonal().mean()
bondlength = cryst.get_distance(0, 1)
#print('a0 =', a0, ', bondlength =', bondlength)
cryst = diamond(el, a0, [1, 1, 1], crack_surface, crack_front)
cryst.set_pbc(True)
cryst.set_calculator(calc)
cryst.set_cell(cryst.cell.diagonal(), scale_atoms=True)
C, C_err = fit_elastic_constants(cryst,
verbose=False,
symmetry='cubic',
optimizer=FIRE,
fmax=1e-6)
#print('Measured elastic constants (in GPa):')
#print(np.round(C*10/units.GPa)/10)
bondlengths = []
refcell = None
reftip_x = None
reftip_y = None
#[41, 39, 1],
for i, n in enumerate([[21, 19, 1], [11, 9, 1], [6, 5, 1]]):
#print(n)
cryst = diamond(el, a0, n, crack_surface, crack_front)
set_groups(cryst, n, skin_x, skin_y)
cryst.set_pbc(True)
cryst.set_calculator(calc)
FIRE(UnitCellFilter(cryst), logfile=None).run(fmax=1e-6)
cryst.set_cell(cryst.cell.diagonal(), scale_atoms=True)
ase.io.write('cryst_{}.xyz'.format(i), cryst, format='extxyz')
crk = crack.CubicCrystalCrack(crack_surface,
crack_front,
Crot=C / units.GPa)
k1g = crk.k1g(surface_energy)
tip_x = cryst.cell.diagonal()[0] / 2
tip_y = cryst.cell.diagonal()[1] / 2
a = cryst.copy()
a.set_pbc([False, False, True])
k1 = 1.0
ux, uy = crk.displacements(cryst.positions[:, 0],
cryst.positions[:, 1], tip_x, tip_y,
k1 * k1g)
a.positions[:, 0] += ux
a.positions[:, 1] += uy
# Center notched configuration in simulation cell and ensure enough vacuum.
oldr = a[0].position.copy()
if refcell is None:
a.center(vacuum=10.0, axis=0)
a.center(vacuum=10.0, axis=1)
refcell = a.cell.copy()
tip_x += a[0].x - oldr[0]
tip_y += a[0].y - oldr[1]
reftip_x = tip_x
reftip_y = tip_y
else:
a.set_cell(refcell)
# Shift tip position so all systems are exactly centered at the same spot
a.positions[:, 0] += reftip_x - tip_x
a.positions[:, 1] += reftip_y - tip_y
refpositions = a.positions.copy()
# Move reference crystal by same amount
cryst.set_cell(a.cell)
cryst.set_pbc([False, False, True])
cryst.translate(a[0].position - oldr)
bond1, bond2 = crack.find_tip_coordination(
a, bondlength=bondlength * 1.2)
# Groups mark the fixed region and the region use for fitting the crack tip.
g = a.get_array('groups')
gcryst = cryst.get_array('groups')
ase.io.write('cryst_{}.xyz'.format(i), cryst)
a.set_calculator(calc)
a.set_constraint(FixAtoms(mask=g == 0))
FIRE(a, logfile=None).run(fmax=1e-6)
dpos = np.sqrt((
(a.positions[:, 0] - refpositions[:, 0]) / ux)**2 + (
(a.positions[:, 1] - refpositions[:, 1]) / uy)**2)
a.set_array('dpos', dpos)
distance_from_tip = np.sqrt((a.positions[:, 0] - reftip_x)**2 +
(a.positions[:, 1] - reftip_y)**2)
ase.io.write('crack_{}.xyz'.format(i), a)
# Compute average bond length per atom
neighi, neighj, neighd = neighbour_list('ijd',
a,
cutoff=bondlength *
1.2)
coord = np.bincount(neighi)
assert coord.max() == 4
np.savetxt(
'dpos_{}.out'.format(i),
np.transpose(
[distance_from_tip[coord == 4], dpos[coord == 4]]))
# Compute distances from tipcenter
neighdist = np.sqrt((
(a.positions[neighi, 0] + a.positions[neighj, 0]) / 2 -
reftip_x)**2 + (
(a.positions[neighi, 1] + a.positions[neighj, 1]) / 2 -
reftip_y)**2)
np.savetxt('bl_{}.out'.format(i),
np.transpose([neighdist, neighd]))
bondlengths += [a.get_distance(bond1, bond2)]
print(bondlengths, np.diff(bondlengths),
bondlengths / bondlengths[-1] - 1)
assert np.all(np.diff(bondlengths) > 0)
assert np.max(bondlengths / bondlengths[0] - 1) < 0.01
def test_embedding_size_convergence(self):
calc = Tersoff(**Tersoff_PRB_39_5566_Si_C)
el = 'C'
a0 = 3.566
surface_energy = 2.7326 * 10
crack_surface = [1, 1, 1]
crack_front = [1, -1, 0]
skin_x, skin_y = 1, 1
cryst = bulk(el, cubic=True)
cryst.set_calculator(calc)
FIRE(UnitCellFilter(cryst), logfile=None).run(fmax=1e-6)
a0 = cryst.cell.diagonal().mean()
bondlength = cryst.get_distance(0, 1)
#print('a0 =', a0, ', bondlength =', bondlength)
cryst = diamond(el, a0, [1,1,1], crack_surface, crack_front)
cryst.set_pbc(True)
cryst.set_calculator(calc)
cryst.set_cell(cryst.cell.diagonal(), scale_atoms=True)
C, C_err = fit_elastic_constants(cryst, verbose=False,
symmetry='cubic',
optimizer=FIRE,
fmax=1e-6)
#print('Measured elastic constants (in GPa):')
#print(np.round(C*10/units.GPa)/10)
bondlengths = []
refcell = None
reftip_x = None
reftip_y = None
#[41, 39, 1],
for i, n in enumerate([[21, 19, 1], [11, 9, 1], [6, 5, 1]]):
#print(n)
cryst = diamond(el, a0, n, crack_surface, crack_front)
set_groups(cryst, n, skin_x, skin_y)
cryst.set_pbc(True)
cryst.set_calculator(calc)
FIRE(UnitCellFilter(cryst), logfile=None).run(fmax=1e-6)
cryst.set_cell(cryst.cell.diagonal(), scale_atoms=True)
ase.io.write('cryst_{}.xyz'.format(i), cryst, format='extxyz')
crk = crack.CubicCrystalCrack(crack_surface,
crack_front,
Crot=C/units.GPa)
k1g = crk.k1g(surface_energy)
tip_x = cryst.cell.diagonal()[0]/2
tip_y = cryst.cell.diagonal()[1]/2
a = cryst.copy()
a.set_pbc([False, False, True])
k1 = 1.0
ux, uy = crk.displacements(cryst.positions[:,0], cryst.positions[:,1],
tip_x, tip_y, k1*k1g)
a.positions[:, 0] += ux
a.positions[:, 1] += uy
# Center notched configuration in simulation cell and ensure enough vacuum.
oldr = a[0].position.copy()
if refcell is None:
a.center(vacuum=10.0, axis=0)
a.center(vacuum=10.0, axis=1)
refcell = a.cell.copy()
tip_x += a[0].x - oldr[0]
tip_y += a[0].y - oldr[1]
reftip_x = tip_x
reftip_y = tip_y
else:
a.set_cell(refcell)
# Shift tip position so all systems are exactly centered at the same spot
a.positions[:, 0] += reftip_x - tip_x
a.positions[:, 1] += reftip_y - tip_y
refpositions = a.positions.copy()
# Move reference crystal by same amount
cryst.set_cell(a.cell)
cryst.set_pbc([False, False, True])
cryst.translate(a[0].position - oldr)
bond1, bond2 = crack.find_tip_coordination(a, bondlength=bondlength*1.2)
# Groups mark the fixed region and the region use for fitting the crack tip.
g = a.get_array('groups')
gcryst = cryst.get_array('groups')
ase.io.write('cryst_{}.xyz'.format(i), cryst)
a.set_calculator(calc)
a.set_constraint(FixAtoms(mask=g==0))
FIRE(a, logfile=None).run(fmax=1e-6)
dpos = np.sqrt(((a.positions[:, 0]-refpositions[:, 0])/ux)**2 + ((a.positions[:, 1]-refpositions[:, 1])/uy)**2)
a.set_array('dpos', dpos)
distance_from_tip = np.sqrt((a.positions[:, 0]-reftip_x)**2 + (a.positions[:, 1]-reftip_y)**2)
ase.io.write('crack_{}.xyz'.format(i), a)
# Compute average bond length per atom
neighi, neighj, neighd = neighbour_list('ijd', a, cutoff=bondlength*1.2)
coord = np.bincount(neighi)
assert coord.max() == 4
np.savetxt('dpos_{}.out'.format(i), np.transpose([distance_from_tip[coord==4], dpos[coord==4]]))
# Compute distances from tipcenter
neighdist = np.sqrt(((a.positions[neighi,0]+a.positions[neighj,0])/2-reftip_x)**2 +
((a.positions[neighi,1]+a.positions[neighj,1])/2-reftip_y)**2)
np.savetxt('bl_{}.out'.format(i), np.transpose([neighdist, neighd]))
bondlengths += [a.get_distance(bond1, bond2)]
print(bondlengths, np.diff(bondlengths), bondlengths/bondlengths[-1]-1)
assert np.all(np.diff(bondlengths) > 0)
assert np.max(bondlengths/bondlengths[0]-1) < 0.01
def setup_crack(logger=screen):
calc = parameter('calc')
cryst = parameter('cryst').copy()
cryst.set_pbc(True)
# Double check elastic constants. We're just assuming this is really a periodic
# system. (True if it comes out of the cluster routines.)
compute_elastic_constants = parameter('compute_elastic_constants', False)
elastic_fmax = parameter('elastic_fmax', 0.01)
elastic_symmetry = parameter('elastic_symmetry', 'triclinic')
elastic_optimizer = parameter('elastic_optimizer', ase.optimize.FIRE)
if compute_elastic_constants:
cryst.set_calculator(calc)
log_file = open('elastic_constants.log', 'w')
C, C_err = fit_elastic_constants(cryst, verbose=False,
symmetry=elastic_symmetry,
optimizer=elastic_optimizer,
logfile=log_file,
fmax=elastic_fmax)
log_file.close()
logger.pr('Measured elastic constants (in GPa):')
logger.pr(np.round(C*10/GPa)/10)
crk = crack.CubicCrystalCrack(parameter('crack_surface'),
parameter('crack_front'),
Crot=C/GPa)
else:
if has_parameter('C'):
crk = crack.CubicCrystalCrack(parameter('crack_surface'),
parameter('crack_front'),
C=parameter('C'))
else:
crk = crack.CubicCrystalCrack(parameter('crack_surface'),
parameter('crack_front'),
parameter('C11'), parameter('C12'),
parameter('C44'))
logger.pr('Elastic constants used for boundary condition (in GPa):')
logger.pr(np.round(crk.C*10)/10)
# Get Griffith's k1.
k1g = crk.k1g(parameter('surface_energy'))
logger.pr('Griffith k1 = %f' % k1g)
# Apply initial strain field.
tip_x = parameter('tip_x', cryst.cell.diagonal()[0]/2)
tip_y = parameter('tip_y', cryst.cell.diagonal()[1]/2)
bondlength = parameter('bondlength', 2.7)
bulk_nn = parameter('bulk_nn', 4)
a = cryst.copy()
a.set_pbc([False, False, True])
hydrogenate_flag = parameter('hydrogenate', False)
hydrogenate_crack_face_flag = parameter('hydrogenate_crack_face', True)
if hydrogenate_flag and not hydrogenate_crack_face_flag:
# Get surface atoms of cluster with crack
a = hydrogenate(cryst, bondlength, parameter('XH_bondlength'), b=a)
g = a.get_array('groups')
g[a.numbers==1] = -1
a.set_array('groups', g)
cryst = a.copy()
k1 = parameter('k1')
try:
k1 = k1[0]
except:
pass
ux, uy = crk.displacements(cryst.positions[:,0], cryst.positions[:,1],
tip_x, tip_y, k1*k1g)
a.positions[:len(cryst),0] += ux
a.positions[:len(cryst),1] += uy
# Center notched configuration in simulation cell and ensure enough vacuum.
oldr = a[0].position.copy()
vacuum = parameter('vacuum')
a.center(vacuum=vacuum, axis=0)
a.center(vacuum=vacuum, axis=1)
tip_x += a[0].x - oldr[0]
tip_y += a[0].y - oldr[1]
# Choose which bond to break.
bond1, bond2 = \
parameter('bond', crack.find_tip_coordination(a, bondlength=bondlength, bulk_nn=bulk_nn))
if parameter('center_crack_tip_on_bond', False):
tip_x, tip_y, dummy = (a.positions[bond1]+a.positions[bond2])/2
# Hydrogenate?
coord = np.bincount(neighbour_list('i', a, bondlength), minlength=len(a))
a.set_array('coord', coord)
if parameter('optimize_full_crack_face', False):
g = a.get_array('groups')
gcryst = cryst.get_array('groups')
coord = a.get_array('coord')
g[coord!=4] = -1
gcryst[coord!=4] = -1
a.set_array('groups', g)
cryst.set_array('groups', gcryst)
if hydrogenate_flag and hydrogenate_crack_face_flag:
# Get surface atoms of cluster with crack
exclude = np.logical_and(a.get_array('groups')==1, coord!=4)
a.set_array('exclude', exclude)
a = hydrogenate(cryst, bondlength, parameter('XH_bondlength'), b=a,
exclude=exclude)
g = a.get_array('groups')
g[a.numbers==1] = -1
a.set_array('groups', g)
basename = parameter('basename', 'energy_barrier')
ase.io.write('{0}_hydrogenated.xyz'.format(basename), a,
format='extxyz')
# Move reference crystal by same amount
cryst.set_cell(a.cell)
cryst.set_pbc([False, False, True])
cryst.translate(a[0].position - oldr)
# Groups mark the fixed region and the region use for fitting the crack tip.
g = a.get_array('groups')
gcryst = cryst.get_array('groups')
logger.pr('Opening bond {0}--{1}, initial bond length {2}'.
format(bond1, bond2, a.get_distance(bond1, bond2, mic=True)))
# centre vertically on the opening bond
if parameter('center_cell_on_bond', True):
a.translate([0., a.cell[1,1]/2.0 -
(a.positions[bond1, 1] +
a.positions[bond2, 1])/2.0, 0.])
a.info['bond1'] = bond1
a.info['bond2'] = bond2
return a, cryst, crk, k1g, tip_x, tip_y, bond1, bond2, g==0, gcryst==0, g==1
a.positions[:,1] += uy
oldr = a[0].position.copy()
a.center(vacuum=params.vacuum, axis=0)
a.center(vacuum=params.vacuum, axis=1)
tip_x0 += a[0].position[0] - oldr[0]
tip_y0 += a[0].position[1] - oldr[1]
cryst.set_cell(a.cell)
cryst.translate(a[0].position - oldr)
g = a.get_array('groups')
mask = g!=0
# Choose which bond to break.
bondlength = param('bondlength', 1.85)
bond1, bond2 = param('bond', crack.find_tip_coordination(a, bondlength=bondlength))
logger.pr('Opening bond {0}--{1}, initial bond length {2}' \
.format(bond1, bond2, a.get_distance(bond1, bond2, mic=True)))
# centre vertically on the opening bond
a.translate([0., a.cell[1,1]/2.0 -
(a.positions[bond1, 1] +
a.positions[bond2, 1])/2.0, 0])
tip_x0 = (a.positions[bond1, 0] + a.positions[bond2, 0])/2
tip_y0 = (a.positions[bond1, 1] + a.positions[bond2, 1])/2
b = a.copy()
b += ase.Atom('H', (tip_x0, tip_y0, b.cell[2, 2]/2))
ase.io.write('notch.xyz', b, format='extxyz')