def gen_edge_dislocation(self):
screw_slab_unit = BodyCenteredCubic(directions = [self.x, self.y, self.z],
size = (1,1,1), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.83)
screw_slab_unit = Atoms(screw_slab_unit)
n_x = int(self.l_x/screw_slab_unit.get_cell()[0,0])
n_y = int(self.l_y/screw_slab_unit.get_cell()[1,1])
n_z = 1
screw_slab_super = supercell(screw_slab_unit, n_x, n_y, n_z)
screw_slab_unit.write('ref_slab.xyz')
b = screw_slab_unit.get_cell()[0,0]
brg_vec = b*np.array([1,0,0])
vacuum = 70.
screw_slab_super.lattice[1,1] += vacuum
disloc_l = np.array([0,0,1])
screw_slab_super.set_lattice(screw_slab_super.get_cell(), scale_positions=False)
super_slab = screw_slab_super.copy()
L_x = screw_slab_super.lattice[0,0]
L_y = screw_slab_super.lattice[1,1]
L_z = screw_slab_super.lattice[2,2]
#Maintain Periodicity along x and z for an edge dislocation:
core = np.array([(L_x)/2., (L_y-vacuum)/2., (L_z)/2.])
screw_slab_super.set_cutoff(3.0)
screw_slab_super.calc_connect()
disloc_noam(screw_slab_super, core, disloc_l, brg_vec)
screw_slab_super.info['core'] = core
screw_slab_super.write('e{0}.xyz'.format(self.name))
def gen_screw_dislocation_quad(self):
# Easy core
screw_slab_unit = BodyCenteredCubic(directions = [self.x, self.y, self.z],
size = (1,1,1), symbol='Fe', pbc=(1,1,1),
latticeconstant = alat)
screw_slab_unit = Atoms(screw_slab_unit)
# set the supercell:
n_x = int(18.0/screw_slab_unit.get_cell()[0,0])
n_y = int(18.0/screw_slab_unit.get_cell()[1,1])
n_z = 2
ref_slab = screw_slab_unit*(n_x,n_y,n_z)
ref_slab.write('ref_slab.xyz')
screw_slab_super = supercell(screw_slab_unit, n_x, n_y, n_z)
b = screw_slab_unit.get_cell()[2,2]
brg_vec = b*np.array([0,0,1])
disloc_l = np.array([0,0,1])
super_slab = screw_slab_super.copy()
L_x = screw_slab_super.lattice[0,0]
L_y = screw_slab_super.lattice[1,1]
L_z = screw_slab_super.lattice[2,2]
core = [(np.array([(L_x)/2., (L_y)/2., L_z/2.]), brg_vec),
np.array([(L_x)/2., (L_y)/2., L_z/2.]),
np.array([(L_x)/2., (L_y)/2., L_z/2.]),
np.array([(L_x)/2., (L_y)/2., L_z/2.])]
def gen_impurity(symbol='H', tetrahedral=True, sup_cell=[5, 5, 5]):
"""
Add an element of type symbol to a supercell defined by the size sup_cell.
If tetrahedral is true the element is initially placed in a tetrahedral position
otherwise it is placed in an octahedral position.
"""
#Molybdenum is 42!!!
alat = 2.82893
atomic_number_dict = {'H': 1, 'B': 5, 'C': 6, 'P': 15, 'Mn': 25, 'Mo': 42}
tetra_pos = alat * np.array([0.5, 0.0, 0.75])
octa_pos = alat * np.array([0.5, 0.5, 0.0])
#Structures
ats = BodyCenteredCubic(directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
size=(sup_cell[0], sup_cell[1], sup_cell[2]),
symbol='Fe',
pbc=(1, 1, 1),
latticeconstant=alat)
mid_point = 0.5 * (np.diag(ats.get_cell()))
mid_point = [((sup_cell[0] - 1) / 2.) * alat for sp in sup_cell]
if tetrahedral:
tetra_pos += mid_point
ats.append(Atom(position=tetra_pos, symbol=symbol))
else:
octa_pos += mid_point
ats.append(Atom(position=octa_pos, symbol=symbol))
return ats
def build_tilt_sym_frac(self, bp=[-1,1,12], v=[1,1,0], c_space=None):
bpxv = [(bp[1]*v[2]-v[1]*bp[2]),(bp[2]*v[0]-bp[0]*v[2]),(bp[0]*v[1]- v[0]*bp[1])]
grain_a = BodyCenteredCubic(directions = [bpxv, bp, v],
size = (1,1,1), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.85)
n_grain_unit = len(grain_a)
n = 2
# Slightly different from slabmaker since in the fracture
# Simulations we want the grainboundary plane to be normal to y.
while(grain_a.get_cell()[1,1] < 120.0):
grain_a = BodyCenteredCubic(directions = [bpxv, bp, v],
size = (1,n,2), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.85)
n += 1
print '\t {0} repeats in z direction'.format(n)
grain_b = grain_a.copy()
grain_c = grain_a.copy()
print '\t', '{0} {1} {2}'.format(v[0],v[1],v[2])
print '\t', '{0} {1} {2}'.format(bpxv[0],bpxv[1],bpxv[2])
print '\t', '{0} {1} {2}'.format(bp[0], bp[1], bp[2])
if c_space==None:
s1 = surface('Fe', (map(int, bp)), n)
c_space = s1.get_cell()[2,2]/float(n) #-s1.positions[:,2].max()
s2 = surface('Fe', (map(int, v)), 1)
x_space = s2.get_cell()[0,0] #-s1.positions[:,2].max()
s3 = surface('Fe', (map(int, bpxv)), 1)
y_space = s3.get_cell()[1,1] #-s1.positions[:,2].max()
print '\t Interplanar spacing: ', x_space.round(2), y_space.round(2), c_space.round(2), 'A'
# Reflect grain b in z-axis (across mirror plane):
print grain_a.get_cell()[1,1]-grain_a.positions[:,1].max()
grain_b.positions[:,1] = -1.0*grain_b.positions[:,1]
grain_c.extend(grain_b)
grain_c.set_cell([grain_c.get_cell()[0,0], 2*grain_c.get_cell()[1,1], grain_c.get_cell()[2,2]])
grain_c.positions[:,1] += abs(grain_c.positions[:,1].min())
pos = [grain.position for grain in grain_c]
pos = sorted(pos, key= lambda x: x[2])
dups = get_duplicate_atoms(grain_c)
# now center fracture cell with plenty of vacuum
grain_c.center(vacuum=10.0,axis=1)
return grain_c
def gen_screw_dislocation(self):
screw_slab_unit = BodyCenteredCubic(directions = [self.x, self.y, self.z],
size = (1,1,1), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.83)
screw_slab_unit = Atoms(screw_slab_unit)
# set the supercell:
n_x = int(self.l_x/screw_slab_unit.get_cell()[0,0])
n_y = int(self.l_y/screw_slab_unit.get_cell()[1,1])
n_z = 2
screw_slab_super = supercell(screw_slab_unit, n_x, n_y, n_z)
ref_slab = screw_slab_unit*(n_x,n_y,n_z)
ref_slab.write('ref_slab.xyz')
#Burgers vector modulus:
b = screw_slab_unit.get_cell()[2,2]
brg_vec = b*np.array([0,0,1])
print b
vacuum = 70.
screw_slab_super.lattice[0,0] += vacuum
screw_slab_super.lattice[1,1] += vacuum
disloc_l = np.array([0,0,1])
screw_slab_super.set_lattice(screw_slab_super.get_cell(), scale_positions=False)
super_slab = screw_slab_super.copy()
L_x = screw_slab_super.lattice[0,0]
L_y = screw_slab_super.lattice[1,1]
L_z = screw_slab_super.lattice[2,2]
core = np.array([(L_x-vacuum)/2., (L_y-vacuum)/2., L_z/2.])
screw_slab_super.set_cutoff(3.0)
screw_slab_super.calc_connect()
disloc_noam(screw_slab_super, core, disloc_l, brg_vec)
screw_slab_super.info['core'] = core
screw_slab_super.write('s{0}.xyz'.format(self.name))
def build_surface(self, bp=[-1,1,12], v=[1,1,0]):
'''
Build Surface unit cell
'''
bpxv = [(bp[1]*v[2]-v[1]*bp[2]), (bp[2]*v[0]-bp[0]*v[2]), (bp[0]*v[1]- v[0]*bp[1])]
surf_cell = BodyCenteredCubic(directions = [v, bpxv, bp],
size = (1,1,1), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.85)
n = 2
while(surf_cell.get_cell()[2,2]< 20.0 ):
surf_cell = BodyCenteredCubic(directions = [v, bpxv, bp],
size = (1,1,n), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.85)
n += 1
surf_cell.center(vacuum=20.0, axis=2)
return surf_cell
# use one of the routines from utilities module to relax the initial
# unit cell and atomic positions
bulk = relax_atoms_cell(bulk, tol=fmax, traj_file=None)
else:
bulk = model.bulk_reference.copy()
bulk.set_calculator(model.calculator)
a0 = bulk.cell[0,0] # get lattice constant from relaxed bulk
bulk = Diamond(symbol="Si", latticeconstant=a0, directions=[[1,-1,0],[0,0,1],[1,1,0]])
bulk.set_calculator(model.calculator)
# set up supercell
bulk *= (1, 1, 10)
# flip coord system for ASE (precon minim?)
c = bulk.get_cell()
t_v = c[0,:].copy()
c[0,:] = c[1,:]
c[1,:] = t_v
bulk.set_cell(c)
ase.io.write(sys.stdout, bulk, format='extxyz')
def surface_energy(bulk, z_offset):
Nat = bulk.get_number_of_atoms()
# shift so cut is through shuffle plane
bulk.positions[:,2] += z_offset
bulk.wrap()
# relax atom positions, holding cell fixed
POT_DIR = os.environ['POTDIR']
eam_pot = os.path.join(POT_DIR, 'PotBH.xml')
r_scale = 1.00894848312
pot = Potential('IP EAM_ErcolAd do_rescale_r=T r_scale={0}'.format(r_scale), param_filename=eam_pot)
#alat = 2.82893
#could just use the proper one as well....
alat = 2.837666
sup_cell = args.supercellsize
tetra_pos = alat*np.array([0.5, 0.0, 0.75])
octa_pos = alat*np.array([0.5, 0.5, 0.0])
#Structures
gb = BodyCenteredCubic(directions = [[1,0,0], [0,1,0], [0,0,1]],
size = (sup_cell[0],sup_cell[1],sup_cell[2]), symbol='Fe', pbc=(1,1,1),
latticeconstant = alat)
mid_point = 0.5*(np.diag(gb.get_cell()))
mid_point = [((sup_cell[0]-1)/2.)*alat for sp in sup_cell]
gb = Atoms(gb)
if args.tetra:
print 'Tetrahedral Defect'
tetra_pos += mid_point
gb.add_atoms(tetra_pos, 1)
gb.write('bcc_h.xyz')
elif args.octa:
print 'Octahedral Defect'
octa_pos += mid_point
gb.add_atoms(octa_pos, 1)
gb.write('bcc_h.xyz')
else:
gb.write('bcc.xyz')
print '\tDislocation Type: ', dis_type, ' dislocation.'
print '\tCalculate Dynamics: ', run_dyn
print '\tCalculate Nye Tensor: ', calc_nye
print '\tInput File: ', input_file
print '\tPotential: ', pot_type
if pot_type == 'EAM':
global potdir
potdir = os.environ['POTDIR']
eam_pot = os.path.join(potdir, 'PotBH.xml')
r_scale = 1.00894848312
pot = Potential('IP EAM_ErcolAd do_rescale_r=T r_scale={0}'.format(r_scale), param_filename=eam_pot)
elif pot_type == 'TB':
tb = TightBindingPot(alat= 1.00, nk=12)
screw_slab_unit = Atoms(screw_slab_unit)
center_cell = np.diag(screw_slab_unit.get_cell())/2.
screw_slab_unit.add_atoms(center_cell,1)
#screw_slab_unit.add_atoms(center_cell*0.76, 6)
screw_slab_unit.set_atoms(screw_slab_unit.Z)
print len(screw_slab_unit)
tb.write_control_file('ctrl.fe', screw_slab_unit)
pot = Potential('IP LMTO_TBE', param_str="""
<params>
<LMTO_TBE_params n_types="2" control_file="ctrl.fe">
<per_type_data type="1" atomic_num="26"/>
<per_type_data type="2" atomic_num="1"/>
</LMTO_TBE_params>
</params>""")
#If there is an initial strain energy increment that here:
pot.print_()
print '\tCalculate Nye Tensor: ', calc_nye
print '\tInput File: ', input_file
print '\tPotential: ', pot_type
if pot_type == 'EAM':
global potdir
potdir = os.environ['POTDIR']
eam_pot = os.path.join(potdir, 'PotBH.xml')
r_scale = 1.00894848312
pot = Potential(
'IP EAM_ErcolAd do_rescale_r=T r_scale={0}'.format(r_scale),
param_filename=eam_pot)
elif pot_type == 'TB':
tb = TightBindingPot(alat=1.00, nk=12)
screw_slab_unit = Atoms(screw_slab_unit)
center_cell = np.diag(screw_slab_unit.get_cell()) / 2.
screw_slab_unit.add_atoms(center_cell, 1)
#screw_slab_unit.add_atoms(center_cell*0.76, 6)
screw_slab_unit.set_atoms(screw_slab_unit.Z)
print len(screw_slab_unit)
tb.write_control_file('ctrl.fe', screw_slab_unit)
pot = Potential('IP LMTO_TBE',
param_str="""
<params>
<LMTO_TBE_params n_types="2" control_file="ctrl.fe">
<per_type_data type="1" atomic_num="26"/>
<per_type_data type="2" atomic_num="1"/>
</LMTO_TBE_params>
</params>""")
#If there is an initial strain energy increment that here:
from ase.utils.eos import EquationOfState
from ase.lattice.cubic import BodyCenteredCubic
from ase import Atom
a = 2.87
cell = [[1,0,0],[0,1,0],[0,0,1]]
bcc = BodyCenteredCubic('Fe', directions=cell)
bcc.set_initial_magnetic_moments([5,5])
carbon = Atom('C', position=(0,0.5*a,0.5*a), charge=0.4)
bcc = bcc*(2,2,2) + carbon
#atoms = atoms*(2,2,2)
constraint = FixAtoms(indices=[5,7,8,10,12,13,14,15,16])
bcc.set_constraint(constraint)
view(bcc)
def save( filename, arg ):
f = open(filename, 'a+t')
f.write('{0} \n'.format(arg))
f.close()
os.system('mkdir result')
print bcc.get_cell()
def screw_cyl_octahedral(alat, C11, C12, C44,
scan_r=15,
symbol="W",
imp_symbol='H',
hard_core=False,
center=(0., 0., 0.)):
"""Generates a set of octahedral positions with `scan_r` radius.
Applies the screw dislocation displacement for creating an initial guess
for the H positions at dislocation core.
Parameters
----------
alat : float
Lattice constant of the material.
C11 : float
C11 elastic constant of the material.
C12 : float
C12 elastic constant of the material.
C44 : float
C44 elastic constant of the material.
symbol : string
Symbol of the element to pass to ase.lattuce.cubic.SimpleCubicFactory
default is "W" for tungsten
imp_symbol : string
Symbol of the elemnt to pass creat Atoms object
default is "H" for hydrogen
symbol : string
Symbol of the elemnt to pass creat Atoms object
hard_core : float
Type of the dislocatino core if True then -u
(sign of displacement is flipped) is applied.
Default is False i.e. soft core is created.
center : tuple of floats
Coordinates of dislocation core (center) (x, y, z).
Default is (0., 0., 0.)
Returns
-------
ase.Atoms object
Atoms object with predicted tetrahedral
positions around dislocation core.
"""
# TODO: Make one function for impurities and pass factory to it:
# TODO: i.e. octahedral or terahedral
axes = np.array([[1, 1, -2],
[-1, 1, 0],
[1, 1, 1]])
unit_cell = BodyCenteredCubic(directions=axes.tolist(),
size=(1, 1, 1), symbol=symbol,
pbc=(False, False, True),
latticeconstant=alat)
BCCOctas = BodyCenteredCubicOctahedralFactory()
impurities = BCCOctas(directions=axes.tolist(),
size=(1, 1, 1), symbol=imp_symbol,
pbc=(False, False, True),
latticeconstant=alat)
impurities = impurities[impurities.positions.T[2] < alat*1.2]
impurities.set_cell(unit_cell.get_cell())
impurities.wrap()
disloCenterY = alat * np.sqrt(2.)/6.0
disloCenterX = alat * np.sqrt(6.)/6.0
impurities.positions[:, 0] -= disloCenterX
impurities.positions[:, 1] -= disloCenterY
L = int(round(2.0*scan_r/(alat*np.sqrt(2.)))) + 1
bulk_octa = impurities * (L, L, 1)
# make 0, 0, at the center
bulk_octa.positions[:, 0] -= L * alat * np.sqrt(6.)/2. - center[0]
bulk_octa.positions[:, 1] -= L * alat * np.sqrt(2.)/2. - center[1]
x, y, z = bulk_octa.positions.T
radius_x_y_zero = np.sqrt(x**2 + y**2)
mask_zero = radius_x_y_zero < scan_r
radius_x_y_center = np.sqrt((x - center[0])**2 + (y - center[1])**2)
mask_center = radius_x_y_center < scan_r
final_mask = mask_center | mask_zero
# leave only atoms inside the cylinder
bulk_octa = bulk_octa[final_mask]
# Create a Stroh ojbect with junk data
stroh = am.defect.Stroh(am.ElasticConstants(C11=141, C12=110, C44=98),
np.array([0, 0, 1]))
c = am.ElasticConstants(C11=C11, C12=C12, C44=C44)
burgers = alat * np.array([1., 1., 1.])/2.
# Solving a new problem with Stroh.solve
stroh.solve(c, burgers, axes=axes)
dislo_octa = bulk_octa.copy()
impurities_u = stroh.displacement(bulk_octa.positions - center)
impurities_u = -impurities_u if hard_core else impurities_u
dislo_octa.positions += impurities_u
return dislo_octa
from numpy import *
from ase.utils.eos import EquationOfState
from ase.lattice.cubic import BodyCenteredCubic
from ase import Atom
a = 2.87
cell = [[1,0,0],[0,1,0],[0,0,1]]
bcc = BodyCenteredCubic('Fe', directions=cell)
bcc.set_initial_magnetic_moments([5,5])
carbon = Atom('C', position=(0,0.5*a,0.75*a), charge=0.4)
bcc = bcc*(2,2,2) + carbon
#atoms = atoms*(2,2,2)
constraint = FixAtoms(indices=[5,7,8,10,12,13,14,15,16])
bcc.set_constraint(constraint)
view(bcc)
def save( filename, arg ):
f = open(filename, 'a+t')
f.write('{0} \n'.format(arg))
f.close()
os.system('mkdir result')
print bcc.get_cell()
n_sup_z = 8
pot_file = os.path.join(pot_dir, 'PotBH.xml')
pot = Potential('IP EAM_ErcolAd', param_filename=pot_file)
#Set paths for phonon band structures:
#paths = [np.array([0,0,-0.5]), np.array([0,0,0]), np.array([0,0,0.5]), np.array([0,0.5,0.5])]
b1 = 1.0
#Nice plot for phonon:
paths = [np.array([0,0,0.0]), np.array([b1/2.0, b1/2.0, 0.0]), np.array([b1/2.0,b1/2.0,b1])]
paths = calc_band_paths(paths)
unit_cell = BodyCenteredCubic(directions = [[1,0,0], [0,1,0],[0,0,1]],
size = (1,1,1), symbol='Fe', pbc=(1,1,1),
latticeconstant = 2.83)
symbols = unit_cell.get_chemical_symbols()
cell = unit_cell.get_cell()
scaled_positions = unit_cell.get_scaled_positions()
THZ_to_mev = 4.135665538536
unit_cell = PhonopyAtoms(symbols=symbols, cell=cell, scaled_positions=scaled_positions)
phonon = Phonopy(unit_cell, [[n_sup_x,0,0],[0,n_sup_y,0],[0,0,n_sup_z]])
phonon.generate_displacements(distance=0.05)
supercells = phonon.get_supercells_with_displacements()
#We need to get the forces on these atoms...
forces = []
print 'There are', len(supercells), 'displacement patterns'
for sc in supercells:
cell = aseAtoms(symbols=sc.get_chemical_symbols(), scaled_positions=sc.get_scaled_positions(),
cell=sc.get_cell(), pbc=(1,1,1))
cell = Atoms(cell)
from ase.lattice.cubic import BodyCenteredCubic
import numpy as np
bulk = BodyCenteredCubic(directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
size=(2, 2, 2),
latticeconstant=2.87,
symbol='Fe')
newbasis = 2.87 * np.array([[-0.5, 0.5, 0.5], [0.5, -0.5, 0.5],
[0.5, 0.5, -0.5]])
pos = bulk.get_positions()
s = np.dot(np.linalg.inv(newbasis.T), pos.T).T
print 'atom positions in primitive basis'
print s
#let us see the unit cell in terms of the primitive basis too
print 'unit cell in terms of the primitive basis'
print np.dot(np.linalg.inv(newbasis.T), bulk.get_cell().T).T
cell = [[1, 0, 0], [0, 1, 0], [0, 0, 1]]
atoms = BodyCenteredCubic('Fe', directions=cell)
atoms.set_initial_magnetic_moments([5, 5])
atoms.set_cell([a, a, a], scale_atoms=True)
carbon = Atom('C', position=(0, 0.5 * a, 0.75 * a), charge=0.4)
atoms = atoms * (2, 2, 2) + carbon
constraint = FixAtoms(indices=[8, 10, 12, 14, 16])
atoms.set_constraint(constraint)
atoms[-1].position = [0, 0.5 * a, 0.75 * a]
init = atoms.copy()
view(init)
atoms[-1].position = [0, 0.75 * a, 0.5 * a]
final = atoms.copy()
# view(final)
def save(filename, arg):
f = open(filename, 'a+t')
f.write('{0} \n'.format(arg))
f.close()
os.system('mkdir result')
print atoms.get_cell()
'forcing': 'Concentration',
'calc_method': 'LAMMPS',
'pair_style':'eam/fs',
'pot_file':'Fe_mm.eam.fs',
'lammps_thermo_steps':100,
'keep_Lammps_files': True,
'ase_min': False,
'lammps_min': mincomd,
'lammps_min_style': 'cg\nmin_modify line quadratic',
'genealogy': True,
'output_format': 'FormationEnergyPerInt',
'allenergyfile':True,
'bestindslist': True,
'finddefects':True,
'parallel' : True,
'algorithm_type' : 'lambda+mu',
'debug':['None']}
bsfe = BCC('Fe', size=parameters['supercell'])
rank = MPI.COMM_WORLD.Get_rank()
if rank==0:
write(parameters['SolidFile'],bsfe)
cell=numpy.maximum.reduce(bsfe.get_cell())
parameters['SolidCell']=cell
A = Optimizer(parameters)
A.algorithm_parallel()
if __name__ == "__main__":
main()
from ase.lattice.cubic import BodyCenteredCubic
import numpy as np
bulk = BodyCenteredCubic(directions=[[1,0,0],
[0,1,0],
[0,0,1]],
size=(2,2,2),
latticeconstant=2.87,
symbol='Fe')
newbasis = 2.87*np.array([[-0.5, 0.5, 0.5],
[0.5, -0.5, 0.5],
[0.5, 0.5, -0.5]])
pos = bulk.get_positions()
s = np.dot(np.linalg.inv(newbasis.T), pos.T).T
print('atom positions in primitive basis')
print(s)
# let us see the unit cell in terms of the primitive basis too
print('unit cell in terms of the primitive basis')
print(np.dot(np.linalg.inv(newbasis.T), bulk.get_cell().T).T)
def calc_bulk_dissolution(args):
"""Calculate the bulk dissolution energy for hydrogen
in a tetrahedral position in bcc iron.
Args:
args(list): determine applied strain to unit cell.
"""
POT_DIR = os.path.join(app.root_path, 'potentials')
eam_pot = os.path.join(POT_DIR, 'PotBH.xml')
r_scale = 1.00894848312
pot = Potential(
'IP EAM_ErcolAd do_rescale_r=T r_scale={0}'.format(r_scale),
param_filename=eam_pot)
alat = 2.83
gb = BodyCenteredCubic(directions=[[1, 0, 0], [0, 1, 0], [0, 0, 1]],
size=(6, 6, 6),
symbol='Fe',
pbc=(1, 1, 1),
latticeconstant=alat)
cell = gb.get_cell()
print 'Fe Cell', cell
e1 = np.array([1, 0, 0])
e2 = np.array([0, 1, 0])
e3 = np.array([0, 0, 1])
if args.hydrostatic != 0.0:
strain_tensor = np.eye(3) + args.hydrostatic * np.eye(3)
cell = cell * strain_tensor
gb.set_cell(cell, scale_atoms=True)
print 'Hydrostatic strain', args.hydrostatic
print 'strain tensor', strain_tensor
print gb.get_cell()
elif args.stretch != 0.0:
strain_tensor = np.tensordot(e2, e2, axes=0)
strain_tensor = np.eye(3) + args.stretch * strain_tensor
cell = strain_tensor * cell
print 'Stretch strain'
print 'Cell:', cell
gb.set_cell(cell, scale_atoms=True)
elif args.shear != 0.0:
strain_tensor = np.tensordot(e1, e2, axes=0)
strain_tensor = np.eye(3) + args.shear * strain_tensor
cell = strain_tensor.dot(cell)
print 'Shear Strain', strain_tensor
print 'Cell:', cell
gb.set_cell(cell, scale_atoms=True)
gb.write('sheared.xyz')
else:
print 'No strain applied.'
tetra_pos = alat * np.array([0.25, 0.0, 0.5])
h2 = aseAtoms('H2', positions=[[0, 0, 0], [0, 0, 0.7]])
h2 = Atoms(h2)
gb = Atoms(gb)
gb_h = gb.copy()
gb_h.add_atoms(tetra_pos, 1)
#caclulators
gb.set_calculator(pot)
h2.set_calculator(pot)
gb_h.set_calculator(pot)
gb_h.write('hydrogen_bcc.xyz')
#Calc Hydrogen molecule energy
opt = BFGS(h2)
opt.run(fmax=0.0001)
E_h2 = h2.get_potential_energy()
h2.write('h2mol.xyz')
#strain_mask = [1,1,1,0,0,0]
strain_mask = [0, 0, 0, 0, 0, 0]
ucf = UnitCellFilter(gb_h, strain_mask)
#opt = BFGS(gb_h)
opt = FIRE(ucf)
opt.run(fmax=0.0001)
E_gb = gb.get_potential_energy()
E_gbh = gb_h.get_potential_energy()
E_dis = E_gbh - E_gb - 0.5 * E_h2
print 'E_gb', E_gb
print 'E_gbh', E_gbh
print 'H2 Formation Energy', E_h2
print 'Dissolution Energy', E_dis
def make_screw_quadrupole(alat,
left_shift=0,
right_shift=0,
n1u=5,
symbol="W"):
"""Generates a screw dislocation dipole configuration
for effective quadrupole arrangement. Works for BCC systems.
Parameters
----------
alat : float
Lattice parameter of the system in Angstrom.
left_shift : float, optional
Shift of the left dislocation core in number of dsitances to next
equivalent disocation core positions needed for creation for final
configuration for NEB. Default is 0.
right_shift : float, optional
shift of the right dislocation core in number of dsitances to next
equivalent disocation core positions needed for creation for final
configuration for NEB. Default is 0.
n1u : int, odd number
odd number! length of the cell a doubled distance between core along x.
Main parameter to calculate cell vectors
symbol : string
Symbol of the element to pass to ase.lattuce.cubic.SimpleCubicFactory
default is "W" for tungsten
Returns
-------
disloc_quadrupole : ase.Atoms
Resulting quadrupole configuration.
W_bulk : ase.Atoms
Perfect system.
dislo_coord_left : list of float
Coodrinates of left dislocation core [x, y]
dislo_coord_right : list of float
Coodrinates of right dislocation core [x, y]
Notes
-----
Calculation of cell vectors
+++++++++++++++++++++++++++
From [1]_ we take:
- Unit vectors for the cell are:
.. math::
u = \frac{1}{3}[1 \bar{2} 1];
.. math::
v = \frac{1}{3}[2 \bar{1} \bar{1}];
.. math::
z = b = \frac{1}{2}[1 1 1];
- Cell vectors are:
.. math::
C_1 = n^u_1 u + n^v_1 v + C^z_1 z;
.. math::
C_2 = n^u_2 u + n^v_2 v + C^z_2 z;
.. math::
C_3 = z
- For quadrupole arrangement n1u needs to be odd number,
for 135 atoms cell we take n1u=5
- To have quadrupole as as close as possible to a square one has to take:
.. math::
2 n^u_2 + n^v_2 = n^u_1
.. math::
n^v_2 \approx \frac{n^u_1}{\sqrt{3}}
- for n1u = 5:
.. math::
n^v_2 \approx \frac{n^u_1}{\sqrt{3}} = 2.89 \approx 3.0
.. math::
n^u_2 = \frac{1}{2} (n^u_1 - n^v_2) \approx \frac{1}{2} (5-3)=1
- Following [2]_ cell geometry is optimized by ading tilt compomemts
Cz1 and Cz2 for our case of n1u = 3n - 1:
Easy core
.. math::
C^z_1 = + \frac{1}{3}
.. math::
C^z_2 = + \frac{1}{6}
Hard core
.. math::
C^z_1 = + \frac{1}{3}
.. math::
C^z_2 = + \frac{1}{6}
may be typo in the paper check the original!
References:
+++++++++++
.. [1] Ventelon, L. & Willaime, F. J 'Core structure and Peierls potential
of screw dislocations in alpha-Fe from first principles: cluster versus
dipole approaches' Computer-Aided Mater Des (2007) 14(Suppl 1): 85.
https://doi.org/10.1007/s10820-007-9064-y
.. [2] Cai W. (2005) Modeling Dislocations Using a Periodic Cell.
In: Yip S. (eds) Handbook of Materials Modeling. Springer, Dordrecht
https://link.springer.com/chapter/10.1007/978-1-4020-3286-8_42
"""
unit_cell = BodyCenteredCubic(directions=[[1, -2, 1],
[2, -1, -1],
[1, 1, 1]],
symbol=symbol,
pbc=(True, True, True),
latticeconstant=alat, debug=0)
unit_cell_u, unit_cell_v, unit_cell_z = unit_cell.get_cell()
# calculate the cell vectors according to the Ventelon paper
# the real configrution depends on rounding check it here
n2v = int(np.rint(n1u/np.sqrt(3.0)))
# when the n1u - n2v difference is odd it is impossible to have
# perfect arrangemt of translation along x with C2 equal to 0.5*n1u
# choice of rounding between np.ceil() and np.trunc() makes a different
# configuration but of same quality of arrangement of quadrupoles (test)
n2u = np.ceil((n1u - n2v) / 2.)
n1v = 0
print("Not rounded values of C2 componets: ")
print("n2u: %.2f, n2v: %.2f" % ((n1u - n2v) / 2., n1u/np.sqrt(3.0)))
print("Calculated cell vectors from n1u = %i" % n1u)
print("n1v = %i" % n1v)
print("n2u = %i" % n2u)
print("n2v = %i" % n2v)
bulk = unit_cell.copy()*[n1u, n2v, 1]
# add another periodic shift in x direction to c2 vector
# for proper periodicity (n^u_2=1) of the effective quadrupole arrangement
bulk.cell[1] += n2u * unit_cell_u
C1_quadrupole, C2_quadrupole, C3_quadrupole = bulk.get_cell()
# calulation of dislocation cores positions
# distance between centers of triangles along x
# move to odd/even number -> get to upward/downward triangle
x_core_dist = alat * np.sqrt(6.)/6.0
# distance between centers of triangles along y
y_core_dist = alat * np.sqrt(2.)/6.0
# separation of the cores in a 1ux1v cell
nx_left = 2
nx_right = 5
if n2v % 2 == 0: # check if the number of cells in y direction is even
# Even: then introduce cores between two equal halfes of the cell
ny_left = -2
ny_right = -1
else: # Odd: introduce cores between two equal halfes of the cell
ny_left = 4
ny_right = 5
nx_left += 2.0 * left_shift
nx_right += 2.0 * right_shift
dislo_coord_left = np.array([nx_left * x_core_dist,
ny_left * y_core_dist,
0.0])
dislo_coord_right = np.array([nx_right * x_core_dist,
ny_right * y_core_dist,
0.0])
# caclulation of the shifts of the inital cores coordinates for the final
# quadrupole arrangements
# different x centering preferences for odd and even values
if n2v % 2 == 0: # check if the number of cells in y direction is even
# Even:
dislo_coord_left += (n2u - 1) * unit_cell_u
dislo_coord_right += (n2u - 1 + np.trunc(n1u/2.0)) * unit_cell_u
else: # Odd:
dislo_coord_left += n2u * unit_cell_u
dislo_coord_right += (n2u + np.trunc(n1u/2.0)) * unit_cell_u
dislo_coord_left += np.trunc(n2v/2.0) * unit_cell_v
dislo_coord_right += np.trunc(n2v/2.0) * unit_cell_v
u_quadrupole = dipole_displacement_angle(bulk,
dislo_coord_left,
dislo_coord_right)
# get the image contribution from the dipoles around
# (default value of N images to scan n_img=10)
u_img = get_u_img(bulk,
dislo_coord_left,
dislo_coord_right)
u_sum = u_quadrupole + u_img
# calculate the field of neghbouring cell to estimate
# linear u_err along C1 and C2 (see. Cai paper)
# u_err along C2
n1_shift = 0
n2_shift = 1
shift = n1_shift*C1_quadrupole + n2_shift*C2_quadrupole
u_quadrupole_shifted = dipole_displacement_angle(bulk,
dislo_coord_left + shift,
dislo_coord_right + shift,
shift=shift)
u_img_shifted = get_u_img(bulk,
dislo_coord_left,
dislo_coord_right,
n1_shift=n1_shift, n2_shift=n2_shift)
u_sum_shifted = u_quadrupole_shifted + u_img_shifted
delta_u = u_sum - u_sum_shifted
delta_u_C2 = delta_u.T[2].mean()
print("delta u c2: %.2f " % delta_u_C2)
# u_err along C1
n1_shift = 1
n2_shift = 0
shift = n1_shift*C1_quadrupole + n2_shift*C2_quadrupole
u_quadrupole_shifted = dipole_displacement_angle(bulk,
dislo_coord_left + shift,
dislo_coord_right + shift,
shift=shift)
u_img_shifted = get_u_img(bulk,
dislo_coord_left,
dislo_coord_right,
n1_shift=n1_shift, n2_shift=n2_shift)
u_sum_shifted = u_quadrupole_shifted + u_img_shifted
delta_u = u_sum - u_sum_shifted
delta_u_C1 = delta_u.T[2].mean()
print("delta u c1: %.3f" % delta_u_C1)
x_scaled, y_scaled, __ = bulk.get_scaled_positions(wrap=False).T
u_err_C2 = (y_scaled - 0.5)*delta_u_C2
u_err_C1 = delta_u_C1*(x_scaled - 0.5)
u_err = u_err_C1 + u_err_C2
# Calculate the u_tilt to accomodate the stress (see. Cai paper)
burgers = bulk.cell[2][2]
u_tilt = 0.5 * burgers * (y_scaled - 0.5)
final_u = u_sum
final_u.T[2] += u_err - u_tilt
disloc_quadrupole = bulk.copy()
disloc_quadrupole.positions += final_u
# tilt the cell according to the u_tilt
disloc_quadrupole.cell[1][2] -= burgers/2.0
bulk.cell[1][2] -= burgers/2.0
return disloc_quadrupole, bulk, dislo_coord_left, dislo_coord_right
cell = [[1,0,0],[0,1,0],[0,0,1]]
atoms = BodyCenteredCubic('Fe', directions=cell)
atoms.set_initial_magnetic_moments([5,5])
atoms.set_cell([a, a, a], scale_atoms=True)
carbon = Atom('C', position=(0,0.5*a,0.75*a), charge=0.4)
atoms = atoms*(2,2,2) + carbon
constraint = FixAtoms(indices=[8,10,12,14,16])
atoms.set_constraint(constraint)
atoms[-1].position = [0, 0.5*a, 0.75*a]
init = atoms.copy()
# view(init)
atoms[-1].position = [0, 0.75*a, 0.5*a]
final = atoms.copy()
# view(final)
def save( filename, arg ):
f = open(filename, 'a+t')
f.write('{0} \n'.format(arg))
f.close()
os.system('mkdir result')
print atoms.get_cell()
class System():
def __init__(self, setting):
self.setting = setting
self.elsProps = [] # elements properties
self.setting['nAt'] = [] # number of atoms per specie
self.px = self.setting['period'][0]
self.py = self.setting['period'][1]
self.pz = self.setting['period'][2]
self.a0 = self.setting['a']
self.box =[[0, self.px*self.a0],\
[0,self.py*self.a0],\
[0,self.pz*self.a0]]
self.setElsProps()
self.setCrystal()
if self.setting['positions'] == 'rnd':
self.setRandomStructure()
self.setNumbers()
self.bulk.set_atomic_numbers(self.numbers)
def setNumbers(self):
self.numbers = []
for e in self.t1_:
self.numbers.append( self.elsProps[e - 1]['number'])
def setElsProps(self):
for e in self.setting['elements']:
a = ase.Atom(e)
mass = a.mass / _Nav
number = a.number
form = pt.formula(a.symbol)
e_ = form.structure[0][1]
crys = e_.crystal_structure['symmetry']
a_ = e_.crystal_structure['a']
self.elsProps.append({'ase':a, 'mass': mass, 'structure': crys,
'a':a_ , 'number':number})
def setCrystal(self):
crys = self.setting['structure']
if crys == 'rnd':
print 'rnd implemented'
self.genRandomPositions()
d = 1.104 # N2 bondlength
formula = 'Cu'+str(len(self.pos))
cell =[(self.px*self.a0,0,0),(0,self.py*self.a0,0),(0,0,self.pz*self.a0)]
self.bulk = ase.Atoms(formula, self.pos, pbc=True, cell=cell)
if crys == 'fcc':
print 'fcc implemented'
from ase.lattice.cubic import FaceCenteredCubic
self.bulk = FaceCenteredCubic(directions=[[1,0,0], [0,1,0], [0,0,1]],
size=(self.px,self.py,self.pz), symbol='Cu',
pbc=(1,1,1), latticeconstant=self.a0)
if crys == 'bcc':
print 'bcc implemented'
from ase.lattice.cubic import BodyCenteredCubic
self.bulk = BodyCenteredCubic(directions=[[1,0,0], [0,1,0], [0,0,1]],
size=(self.px,self.py,self.pz), symbol='Cu',
pbc=(1,1,1), latticeconstant=self.a0)
if self.setting['structure'] == 'hcp':
print 'hcp no implemented'
sys.exit(0)
self.setting['nAtoms'] = self.bulk.get_number_of_atoms()
self.calcAtoms2()
self.genStructure()
self.pos = self.bulk.get_positions()
def update (self):
cell = self.bulk.get_cell()
self.box =[[0, cell[0][0]],[0, cell[1][1]],[0, cell[2][2]]]
self.pos = self.bulk.get_positions()
def genStructure(self):
self.t1_ = []
for i,e in enumerate(self.setting['nAt']):
[self.t1_.append(i+1) for j in range(e)]
def setRandomStructure(self):
x = [int(random.random()*len(self.t1_)) for i in range(len(self.t1_))]
for i in range(len(x) - 1):
t1 = self.t1_[x[i]]
t2 = self.t1_[x[i+1]]
self.t1_[x[i]] = t2
self.t1_[x[i+1]] = t1
return self.pos, self.t1_, self.box
def genRandomPositions(self):
Lx = self.box[0][1]
Ly = self.box[1][1]
Lz = self.box[2][1]
self.pos =[]
for i in range(self.setting['nAtoms']):
x = random.random() * Lx
y = random.random() * Ly
z = random.random() * Lz
self.pos.append([x,y,z])
def getAtoms(self):
return self.elsProps
def Interaction (self):
if self.setting['pot'] == 'lj':
ljp = ljParameters.LjParameters()
str_ = ljp.lammpsInteraction(self.elsProps)
if self.setting['pot'] == 'zhou':
gz = zhou.calcPotentials(self.setting['elements'])
gz.createPot()
str_ = gz.lammpsZhouEam()
return str_
def calcAtoms2(self):
nAt = []
sum_ = 0
sumpc = 0.0000001
len_elements = len(self.setting['elements'])
len_pca = len(self.setting['pca'])
print 'calcAtom2', len_pca, len_elements
if len_elements != len_pca + 1:
print 'error len'
sys.exit(0)
for p in self.setting['pca']:
sumpc +=p
if sumpc >= 100 or sumpc <= 0:
print 'error pc'
sys.exit(0)
sumpc = 0
for i in range(len(self.setting['elements']) - 1):
p = self.setting['pca'][i]
sumpc +=p
t = int(p * self.setting['nAtoms'] / 100.0)
sum_ +=t
nAt.append(t)
nAt.append(self.setting['nAtoms'] - sum_)
self.setting['nAtoms'] = 0
for e in nAt:
self.setting['nAtoms'] +=e
print 'pca', self.setting['pca']
self.setting['nAt'] = nAt
def getMasess(self):
str_ =''
i = 1
for e in self.elsProps:
str_ += 'mass ' + str(i) + ' ' +str(e['mass']) + '\n'
i+=1
return str_
