def hcp_edge_dislocation(self):
sz = (40, 40, 10)
atoms = othoHCP(latticeconstant=(self.pot['ahcp'], self.pot['chcp'],
self.pot['ahcp'] * sqrt(3.)),
size=sz,
symbol=self.pot['element'])
# let the axes consistent with the elastic constants
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
# the lattice constant has conventional direction as
# x - [1 -2 1 0] y[1, 0, -1, 0] z [0, 0, 0, 1]
c.hexagonal(C11=61.8, C33=67.5, C12=25.9, C13=21.9, C44=18.2) # kim
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cx = 20 * self.pot["ahcp"] + 0.01
cy = 20 * self.pot["chcp"] + 0.01
s1 = np.ones(pos.shape) * np.array([cx, cy, 0.0])
d1 = stroh.displacement(pos - s1)
# cy = 60 * self.pot["chcp"] - 0.01
# s2 = np.ones(pos.shape) * np.array([cx, cy, 0.0])
# d2 = stroh.displacement(pos - s2)
atoms.set_positions(pos + np.real(d1))
# cut a layer normal the burger direction
# atoms = self.cut_x_normal_atoms(atoms, lata, 1, sqrt(3) / 4.0)
# atoms = self.cut_x_normal_atoms(atoms)
atoms = self.cut_y_normal_atoms(atoms)
atoms = self.cut_x_normal_atoms(atoms)
self.write_lmp_config_data(atoms)
def build_screw_basal_hcp_atoms(self, atoms):
axes = np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
# the lattice constant has conventional direction as
# x - [1 -2 1 0] y[1, 0, -1, 0] z [0, 0, 0, 1]
# c.hexagonal(C11=61.8, C33=67.5, C12=25.9, C13=21.9, C44=18.2) # kim
c.hexagonal(C11=64.3218889159844,
C33=70.9452244231304,
C12=25.4175328222502,
C13=20.306421440903,
C44=18.0690056385527) # curtin
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
cell = atoms.get_cell()
cx = 0.25 * cell[0, 0] + 0.01
cy = 0.50 * cell[1, 1] + 0.01
pos = atoms.get_positions()
shift = np.ones(pos.shape) * np.array([cx, cy, 0.0])
disp = stroh.displacement(pos - shift)
atoms.set_positions(pos + np.real(disp))
# pos = atoms.get_positions()
# shiftN = np.ones(pos.shape) * np.array([cx + 0.5 * cell[0, 0],
# cy, 0.0])
# dispN = stroh.displacement(pos - shiftN)
# atoms.set_positions(pos + np.real(dispN))
return atoms
def build_screw_basal_hcp_atoms_dipole(self, atoms):
axes = np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
c.hexagonal(C11=64.3218889159844,
C33=70.9452244231304,
C12=25.4175328222502,
C13=20.306421440903,
C44=18.0690056385527) # curtin
stroh1 = stroh_solve.Stroh(c, burgers, axes=axes)
# stroh2 = stroh_solve.Stroh(c, -burgers, axes=axes)
cell = atoms.get_cell()
pos = atoms.get_positions()
cx = 0.25 * cell[0, 0] + 0.01
cy1 = 0.25 * cell[1, 1] + 0.01
cy2 = 0.75 * cell[1, 1] + 0.01
pos = atoms.get_positions()
print(cy1, cy2)
shift1 = np.ones(pos.shape) * np.array([cx, cy1, 0.0])
shift2 = np.ones(pos.shape) * np.array([cx, cy2, 0.0])
disp1 = stroh1.displacement(pos - shift1)
disp2 = stroh1.displacement(pos - shift2)
# atoms.set_positions(pos + np.real(disp1))
atoms.set_positions(pos + np.real(disp1) - np.real(disp2))
return atoms
def intro_edge(self):
self.find_angles_1100(il=[[1], [1]], jl=[1]) # 58.361
ux = self.pot['ahcp']
uy = self.pot['chcp']
uz = self.pot['ahcp'] * sqrt(3.)
atoms = ase.io.read("dump/dump.00017", format='lammps-dump')
atoms.rotate(self.ag[0][0], 'z') # rotate
atoms.translate(np.array([80 * ux, 0.0, 0]))
# # introduce dislocation
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
c.hexagonal(C11=self.pot['C11'], C12=self.pot['C12'],
C33=self.pot['C33'], C13=self.pot['C13'], C44=self.pot['C44'])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cx = 60 * ux + 0.01
cy = 60 * uy + 0.01
shift = np.ones(pos.shape) * np.array([cx, cy, 0.0])
disp = stroh.displacement(pos - shift)
atoms.set_positions(pos + np.real(disp))
atoms.translate(np.array([-80 * ux, 0.0, 0]))
atoms.rotate(-self.ag[0][0], 'z') # rotate back
# try with non periodict boundary conditions
cell = atoms.get_cell()
cell[0, 0] += 30
cell[1, 1] += 30
atoms.translate(np.array([15, 15, 0.0]))
atoms.set_cell(cell)
# ase.io.write("pos02", images=atoms, format='cfg')
self.write_lmp_config_data(atoms, "pos02")
def aniso_211(self):
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
e1 = [1, 0, 0]
e2 = [0, 1, -1]
e3 = [0, 1, 1]
# axes = np.array([e2, e1, e3])
axes = np.array([e1, e2, e3])
burgers = self.pot["lattice"] / 2. * np.array([1., 1., -1.])
burgers = axes_check.axes_check(axes).dot(burgers)
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
self.ckcoeff.K1 = sqrt(2 * self.pot["surf110"] /
abs(Gamma[1, 1] * 1e3))
# theta = np.deg2rad(54.735610317245346)
theta = np.deg2rad(35.2643896828)
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = omega * Gamma * omega.transpose() #
Gamma = np.abs(np.linalg.inv(Gamma))
Gamma = Gamma * 1e9 # Pa
print(self.ckcoeff.K1)
if axes is not None:
burgers = axes_check.axes_check(axes).dot(burgers)
c = c.transform(axes)
G00 = Gamma[0, 0]
usf = 0.57405172613
k1e = np.sqrt(G00 * usf) * 1e-6
print(Gamma)
print(self.ckcoeff.K1, k1e)
self.set_plane_strain_bij(c.Sij)
# self.get_scalarB(self.pot["surf110"]) get the same k1c
self.get_coeffs()
atoms = self.intro_crack_k1(atoms=self.gn_perf_plate())
self.write_lmp_config_data(atoms, 'crack.txt')
def bcc_screw_dipole_alongz_atoms(self, atoms, c1, c2):
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
atoms = self.bcc_screw_dipole_tools(stroh, pos, atoms, c1, 1)
atoms = self.bcc_screw_dipole_tools(stroh, pos, atoms, c2, -1)
return atoms
def get_bcc_w_result211(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
e1 = [1, 0, 0]
e2 = [0, 1, -1]
e3 = [0, 1, 1]
# glide plane [2, 1, -1]
axes = np.array([e1, e2, e3])
# x [1, 0, 0], y[0, 1, -1], z[0, 1, 1]
burgers = param['lat'] / 2. * np.array([1., 1., -1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
surf = param['surf']
k1c = sqrt(2 * surf / abs(Gamma[1, 1] * 1e3))
theta = np.deg2rad(54.735610317245346)
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = omega * Gamma * omega.transpose()
Gamma = np.abs(np.linalg.inv(Gamma))
Gamma = Gamma * 1e9 # Pa
# K1c
# G11 = Gamma[1, 1]
# k1c = sqrt(2 * surf / G11) * 1e6
# Ke
if axes is not None:
T = axes_check.axes_check(axes)
burgers = T.dot(burgers)
c = c.transform(axes)
(coeff, Kg) = self.cal_crack(param, c, theta=theta)
print(Kg)
usf = param['ugsf1'] # J/m^2
G00 = Gamma[0, 0]
k1e = np.sqrt(G00 * usf) * 1e-6
k1e = k1e / coeff
print(k1e, k1c, Kg, k1e / k1c)
return (k1e, k1c, k1e / k1c)
def build_hcp_ase_1100_with_edge(self):
self.find_angles_1100(il=[[1], [1]], jl=[1]) # 58.361
ux = self.pot['ahcp']
uy = self.pot['chcp']
uz = self.pot['ahcp'] * sqrt(3.)
print(self.ag)
atoms = othoHCP(latticeconstant=(ux, uy, uz),
size=(80, 80, 2),
symbol=self.pot['element'])
# introduce dislocation
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
c.hexagonal(C11=self.pot['C11'],
C12=self.pot['C12'],
C33=self.pot['C33'],
C13=self.pot['C13'],
C44=self.pot['C44'])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cell = atoms.get_cell()
cell[0, 0], cell[1, 1] = 8 * self.ag[0][1], 300
cx = 30 * ux + 0.01
cy = 30 * uy + 0.01
shift = np.ones(pos.shape) * np.array([cx, cy, 0.0])
disp = stroh.displacement(pos - shift)
atoms.set_positions(pos + np.real(disp))
atoms.rotate(self.ag[0][0], 'z')
atoms.translate(np.array([cell[0, 0], -100, 0]))
lob = np.array([0.0, 10, 0.0])
hib = np.array([cell[0, 0], 0.5 * cell[1, 1] + 0.3, cell[2, 2]])
atoms = self.make_cubic('out', atoms, lob, hib)
atoms2 = othoHCP(latticeconstant=(ux, uy, uz),
size=(80, 80, 2),
symbol=self.pot['element'])
lob = np.array([0.0, 0.5 * cell[1, 1], 0.0])
hib = np.array([cell[0, 0], cell[1, 1] - 10, cell[2, 2]])
atoms2.rotate(-self.ag[0][0], 'z')
atoms2.translate(np.array([-90, cell[1, 1], 0])) # for 72.877
atoms2 = self.make_cubic('out', atoms2, lob, hib)
atoms.extend(atoms2)
# try with non periodict boundary conditions
atoms.set_cell(cell)
self.write_lmp_config_data(atoms, "lmp_init.txt")
def get_cutin_result_mat_k2e(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
# A
axes = np.array([[1, 1, 2], [1, 1, -1], [-1, 1, 0]])
burgers = param['lat'] / np.sqrt(6.) * np.array([1., 1., 2.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
# print A * B.transpose() + B * A.transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
theta = np.deg2rad(0.0)
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = np.abs(omega * Gamma * omega)
# phi = 0
# svect = np.mat(np.array([cos(phi), 0.0, sin(phi)]))
Gamma = np.linalg.inv(Gamma)
Gamma00 = Gamma[0, 0] # in GPa
Gamma11 = Gamma[1, 1]
Gamma00 *= 1e9
Gamma11 *= 1e9
# cal F(theta)
soltrace = np.mat([[stroh.p[0], 0.0, 0.0], [0.0, stroh.p[2], 0.0],
[0.0, 0.0, stroh.p[4]]],
dtype='complex')
Fmat1 = soltrace / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat1 = np.real(B * Fmat1 * np.linalg.inv(B))
Fmat2 = 1.0 / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat2 = np.real(B * Fmat2 * np.linalg.inv(B))
print(Fmat1[0, 1])
# print Gamma
k2e = np.sqrt(Gamma00 * param['ugsf']) * 1e-6 # Mpa
print('k2e', k2e / abs(Fmat1[0, 1]))
def build_screw_basal_hcp(self):
sz = (100, 100, 5)
ux = self.pot["ahcp"] * sqrt(3)
uy = self.pot["chcp"]
uz = self.pot['ahcp']
atoms = othoHCPB(latticeconstant=(ux, uy, uz),
size=sz,
symbol=self.pot['element'])
# let the axes consistent with the elastic constants
axes = np.array([[0, 1, 0], [0, 0, 1], [1, 0, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
# the lattice constant has conventional direction as
# x - [1 -2 1 0] y[1, 0, -1, 0] z [0, 0, 0, 1]
# c.hexagonal(C11=61.8, C33=67.5, C12=25.9, C13=21.9, C44=18.2)
# c.hexagonal(C11=62.807, C33=69.615, C12=25.974,
# C13=21.184, C44=17.138) # Kim
c.hexagonal(C11=64.3218889159844,
C33=70.9452244231304,
C12=25.4175328222502,
C13=20.306421440903,
C44=18.0690056385527) # curtin
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cx = 0.5 * sz[0] * ux + 0.01
cy = 0.5 * sz[1] * uy + 0.01
print(cx, cy)
self.write_lmp_config_data(atoms, "before.txt")
shift = np.ones(pos.shape) * np.array([cx, cy, 0.0])
disp = stroh.displacement(pos - shift)
atoms.set_positions(pos + np.real(disp))
self.write_lmp_config_data(atoms)
ase.io.write("SCREW.cfg", atoms, format="cfg")
return atoms
def bcc_screw_dipole_alongz_with_image(self, atoms, center):
# x direction +10.5 unitx, +21
# -10.5 unitx, -21
# y direction +(11 + 1./3.) unity + 22
# -(11 - 1./3.) unity - 22
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
px = 10.5
py = 11
# ydisp = [4 * py, 3 * py + 1. / 3., 2 * py, py + 1. / 3.,
# 0., -py + 1. / 3., -2 * py, -3 * py + 1. / 3., -4 * py]
# xdisp = [-4 * px, -3 * px, -2 * px, -1 *
# px, 0.0, px, 2 * px, 3 * px, 4 * px]
ydisp = [2 * py, py + 1. / 3., 0., -py + 1. / 3., -2 * py]
xdisp = [-2 * px, -1 * px, 0.0, px, 2 * px]
pos = atoms.get_positions()
ux = np.sqrt(6) / 3. * self.pot['lattice']
uy = np.sqrt(2) / 2. * self.pot['lattice']
sign = 1.0
for dy in ydisp:
for dx in xdisp:
ctmp = np.array([center[0] + dx * ux, center[1] + dy * uy])
atoms = self.bcc_screw_dipole_tools(stroh, pos, atoms, ctmp,
sign)
sign *= -1
atoms.wrap(pbc=[1, 1, 1])
return atoms
def build_edge_basal_hcp_atoms(self, atoms, center, sign=1):
# let the axes consistent with the elastic constants
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0]) * sign
c = am.ElasticConstants()
print("build edge basial hcp")
# x - [1 -2 1 0] y[1, 0, -1, 0] z [0, 0, 0, 1]
# c.hexagonal(C11=61.8, C33=67.5, C12=25.9, C13=21.9, C44=18.2) # kim
c.hexagonal(C11=64.3218889159844,
C33=70.9452244231304,
C12=25.4175328222502,
C13=20.306421440903,
C44=18.0690056385527) # curtin
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cx = center[0] + 0.01
cy = center[1] + 0.01
print(cx, cy)
shift = np.ones(pos.shape) * np.array([cx, cy, 0.0])
disp = stroh.displacement(pos - shift)
atoms.set_positions(pos + np.real(disp))
return atoms
def build_edge_basal_hcp(self):
sz = (200, 100, 3)
atoms = othoHCP(latticeconstant=(self.pot['ahcp'], self.pot['chcp'],
self.pot['ahcp'] * sqrt(3.)),
size=sz,
symbol=self.pot['element'])
# let the axes consistent with the elastic constants
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
# the lattice constant has conventional direction as
# x - [1 -2 1 0] y[1, 0, -1, 0] z [0, 0, 0, 1]
# c.hexagonal(C11=61.8, C33=67.5, C12=25.9, C13=21.9, C44=18.2) # kim
# c.hexagonal(C11=62.369, C33=67.788, C12=26.252,
# C13=22.113, C44=18.274) # Coco
# c.hexagonal(C11=62.807, C33=69.615, C12=25.974,
# C13=21.184, C44=17.138) # Kim
c.hexagonal(C11=64.3556,
C33=70.9849,
C12=25.460289,
C13=20.333408,
C44=18.06331) # Curtin
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cx = 0.5 * sz[0] * self.pot["ahcp"] + 0.01
cy = 0.5 * sz[1] * self.pot["chcp"] + 0.01
print(cx, cy)
shift = np.ones(pos.shape) * np.array([cx, cy, 0.0])
disp = stroh.displacement(pos - shift)
atoms.set_positions(pos + np.real(disp))
self.write_lmp_config_data(atoms)
return atoms
def formular_make_edge_large(self):
self.find_angles_1100(il=[[1], [1]], jl=[1]) # 58.361
ux = self.pot['ahcp']
uy = self.pot['chcp']
uz = self.pot['ahcp'] * np.sqrt(3.)
atoms = ase.io.read(glob.glob("dump_init_v2/dump.*")[-1],
format='lammps-dump')
atoms.rotate(180 - self.ag[0][0], 'z') # rotate
atoms.translate(np.array([80 * ux, 0, 0]))
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
c.hexagonal(C11=self.pot['C11'],
C12=self.pot['C12'],
C33=self.pot['C33'],
C13=self.pot['C13'],
C44=self.pot['C44'])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
cell = atoms.get_cell()
sh1 = np.ones(pos.shape) * \
np.array([-30 * ux + 0.1, 10 * uy, cell[2, 2]])
sh2 = np.ones(pos.shape) * \
np.array([-30 * ux + 0.1, 30 * uy, cell[2, 2]])
d1 = stroh.displacement(pos - sh1)
d2 = stroh.displacement(pos - sh2)
atoms.set_positions(pos + np.real(d1) - np.real(d2))
atoms.translate(np.array([-80 * ux, 0.0, 0]))
atoms.rotate(self.ag[0][0] - 180, 'z') # rotate back
self.write_lmp_config_data(atoms, "lmp_init02.txt")
def intro_edge_dipole(self):
ux = self.pot['ahcp']
uy = self.pot['chcp']
uz = self.pot['ahcp'] * sqrt(3.)
angle = 67.66901744178166
atoms = ase.io.read("dump.save", format='lammps-dump')
cell = atoms.get_cell()
# before rotate, mark the center
upper = cell[1, 1] * 0.5 + 2
lower = cell[1, 1] * 0.5 - 2
left = cell[0, 0] * 0.3
right = cell[0, 0] * 0.3 + 4
for atm in atoms:
if (atm.position[1] > lower and atm.position[1] < upper
and atm.position[0] >= left and atm.position[0] <= right):
print(atm.position)
atm.symbol = 'Nb'
atoms.rotate(angle, 'z') # rotate
shift = cell[1, 1] * np.sin(np.deg2rad(angle))
atoms.translate(np.array([shift, 0.0, 0]))
# check line after rotation
for atm in atoms:
if (atm.symbol == 'Nb'):
print(atm.position)
dis_core_pos = atm.position
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
c.hexagonal(C11=self.pot['C11'],
C12=self.pot['C12'],
C33=self.pot['C33'],
C13=self.pot['C13'],
C44=self.pot['C44'])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
dis_core_pos[2] = 0
sh1 = dis_core_pos
sh2 = np.copy(dis_core_pos)
sh2[0] = sh2[0] - 80
sh1[1] += 0.01
sh2[1] += 0.01
print(sh1, sh2)
sh1 = np.ones(pos.shape) * sh1
sh2 = np.ones(pos.shape) * sh2
org_sh1 = np.ones(pos.shape) * \
np.array([50 * ux + 0.01, 40 * uy + 0.01, 0.0])
org_sh2 = np.ones(pos.shape) * \
np.array([50 * ux + 0.01, 50 * uy + 0.01, 0.0])
# print(sh1, org_sh1)
d1 = stroh.displacement(pos - sh1)
d2 = stroh.displacement(pos - sh2)
atoms.set_positions(pos + np.real(d1) - np.real(d2))
atoms.translate(np.array([-shift, 0.0, 0]))
atoms.rotate(-angle, 'z') # rotate back
self.write_lmp_config_data(atoms, "lmp_init.txt")
def get_cutin_result_mat_k1e(self, param):
c = tool_elastic_constants.elastic_constants(C11=param['c11'],
C12=param['c12'],
C44=param['c44'])
axes = np.array([[-1, -1, 2], [1, 1, 1], [-1, 1, 0]])
burgers = param['lat'] / np.sqrt(6.) * np.array([-1., -1., 2.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
A = np.mat(np.zeros([3, 3]), dtype='complex')
A[:, 0] = np.mat(stroh.A[0]).transpose()
A[:, 1] = np.mat(stroh.A[2]).transpose()
A[:, 2] = np.mat(stroh.A[4]).transpose()
B = np.mat(np.zeros([3, 3]), dtype='complex')
B[:, 0] = np.mat(stroh.L[0]).transpose()
B[:, 1] = np.mat(stroh.L[2]).transpose()
B[:, 2] = np.mat(stroh.L[4]).transpose()
Linv = np.real(np.complex(0, 1) * A * np.linalg.inv(B))
Gamma = 0.5 * Linv
v1 = np.array([-1, -1, 2])
v2 = np.array([1, 1, 2])
theta = (np.arccos(
np.dot(v1, v2) / (np.linalg.norm(v1) * np.linalg.norm(v2))))
omega = np.mat([[cos(theta), sin(theta), 0.0],
[-sin(theta), cos(theta), 0.0], [0.0, 0.0, 1.0]])
Gamma = omega * Gamma * omega.transpose()
# phi = 0
# svect = np.mat(np.array([cos(phi), 0.0, sin(phi)]))
Gamma = np.linalg.inv(Gamma)
Gamma = np.abs(Gamma)
Gamma00 = Gamma[0, 0] # in GPa
Gamma11 = Gamma[1, 1]
Gamma00 *= 1e9
Gamma11 *= 1e9
if axes is not None:
T = axes_check.axes_check(axes)
burgers = T.dot(burgers)
c = c.transform(axes)
(coeff, Kg) = self.cal_crack(param, c, theta)
# print((cos(0.5 * theta))**2 * sin(0.5 * theta))
# cal F(theta)
soltrace = np.mat([[stroh.p[0], 0.0, 0.0], [0.0, stroh.p[2], 0.0],
[0.0, 0.0, stroh.p[4]]],
dtype='complex')
Fmat1 = soltrace / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat1 = np.real(B * Fmat1 * np.linalg.inv(B))
Fmat2 = 1.0 / np.sqrt(np.cos(theta) + soltrace * np.sin(theta))
Fmat2 = np.real(B * Fmat2 * np.linalg.inv(B))
# print(((Fmat1 + Fmat2) * Gamma) * 1e-3 * param["ugsf"])
k1e = sqrt(Gamma00 * param['ugsf']) * 1e-6 # Mpa
print('k1e', k1e)
print('k1e / coeff', k1e / coeff)
def formular_make_edge(self):
self.find_angles_1100(il=[[1], [1]], jl=[1]) # 58.361
ux = self.pot['ahcp']
uy = self.pot['chcp']
uz = self.pot['ahcp'] * np.sqrt(3.)
atoms = ase.io.read(glob.glob("dump_init/dump.*")[-1],
format='lammps-dump')
print(len(atoms))
cell = atoms.get_cell()
atoms.rotate(self.ag[0][0], 'z') # rotate
atoms.translate(np.array([83.5 * ux, -80 * uy, 0]))
axes = np.array([[1, 0, 0], [0, 0, 1], [0, -1, 0]])
burgers = self.pot['lattice'] * np.array([1, 0, 0])
c = am.ElasticConstants()
c.hexagonal(C11=self.pot['C11'],
C12=self.pot['C12'],
C33=self.pot['C33'],
C13=self.pot['C13'],
C44=self.pot['C44'])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
pos = atoms.get_positions()
# sh1 = np.ones(pos.shape) * \
# np.array([30 * ux + 0.1, 0.5 * uy, cell[2, 2]])
sh1 = np.ones(pos.shape) * \
np.array([34.5 * ux + 0.1, 0.5 * uy, cell[2, 2]])
sh2 = np.ones(pos.shape) * \
np.array([-20 * ux + 0.1, 0.5 * uy, cell[2, 2]])
d1 = stroh.displacement(pos - sh1)
d2 = stroh.displacement(pos - sh2)
atoms.set_positions(pos + np.real(d1) - np.real(d2))
# lob = np.array([0.0, 0.0, 0.0])
# hib = np.array([29.5 * ux, 0.5 * uy, cell[2, 2]])
# for i in range(len(atoms)):
# if all(((atoms[i].position - lob) * (atoms[i].position - hib)) <= 0.0):
# atoms[i].symbol = 'Mg'
# lob2 = np.array([0.0, 0.5 * uy, 0.0])
# hib2 = np.array([30 * ux, 1.0 * uy, cell[2, 2]])
# for i in range(len(atoms)):
# if all(((atoms[i].position - lob2) * (atoms[i].position - hib2)) <= 0.0):
# atoms[i].symbol = 'Cr'
atoms.translate(np.array([-83.5 * ux, 80 * uy, 0]))
atoms.rotate(-self.ag[0][0], 'z') # rotate back
self.write_lmp_config_data(atoms, "lmp_init01.txt")
# add shear
strain = np.mat([[1.0, 0.0, 0.0], [-0.015, 1.0, 0.0], [0.0, 0.0, 1.0]])
pos = atoms.get_positions() * strain
cell = strain * atoms.get_cell()
atoms.set_cell(cell)
atoms.set_positions(pos)
self.write_lmp_config_data(atoms, "lmp_init02.txt")
self.write_lmp_config_data(atoms, "lmp_init.txt")
def bcc_screw_dipole_configs_alongz(self, sizen=1):
c = tool_elastic_constants.elastic_constants(C11=self.pot['c11'],
C12=self.pot['c12'],
C44=self.pot['c44'])
burgers = self.pot['lattice'] / 2 * np.array([1., 1., 1.])
stroh = stroh_solve.Stroh(c, burgers, axes=axes)
atoms = self.set_dipole_box()
atoms_perf = atoms.copy()
pos = atoms.get_positions()
ux = sqrt(6) / 3. * self.pot['lattice']
uy = sqrt(2) / 2. * self.pot['lattice']
uz = sqrt(3) / 2. * self.pot['lattice']
sx = 10.0 * sizen
sy = 5 * sizen
ix = 10.5 * sizen
# c1 = 1. / 3. * np.sum(self.pot['core1'], axis=0)
# c2 = 1. / 3. * np.sum(self.pot['core2'], axis=0)
# shiftc1 = \
# np.ones(np.shape(pos)) * np.array([c1[0, 0], c1[0, 1], 0.0])
# shiftc2 = \
# np.ones(np.shape(pos)) * np.array([c2[0, 0], c2[0, 1], 0.0])
opt = 'original'
if opt in ['split']:
c1 = self.pot['posleft'] + \
np.array([0.0, 0.21 * self.pot['yunit']])
c2 = self.pot['posrigh'] + \
np.array([0.0, -0.21 * self.pot['yunit']])
elif opt in ['move']:
c1 = [(sx + 0.5) * ux, (sy + 1. / 3. - 0.95 * 1. / 3.) * uy]
c2 = [(sx + ix + 0.5) * ux, (sy + 2. / 3. + 0.95 * 1. / 3.) * uy]
else:
c1 = [(sx) * ux, (sy + 1. / 3.) * uy]
c2 = [(sx + ix) * ux, (sy + 2. / 3.) * uy]
shiftc1 = np.ones(np.shape(pos)) * np.array([c1[0], c1[1], 0.0])
shiftc2 = np.ones(np.shape(pos)) * np.array([c2[0], c2[1], 0.0])
disp1 = stroh.displacement(pos - shiftc1)
disp2 = stroh.displacement(pos - shiftc2)
if opt in ['pull']:
radius = 2.0 # find the atoms near the center
for ps, dp in zip(pos, disp1):
dis = np.linalg.norm(ps[:2] - c1)
if (dis < radius):
dp[2] += 1. / 6. * uz
# add shirt
for ps, dp in zip(pos, disp2):
dis = np.linalg.norm(ps[:2] - c2)
if (dis < radius):
dp[2] -= 1. / 6. * uz
atoms.set_positions(pos + np.real(disp1) - np.real(disp2))
# periodic boundary conditions ???
# c2l = [(sx - ix + 0.5) * ux, (sy + 2. / 3. + 0.95 * 1. / 3.) * uy]
# shft = np.ones(np.shape(pos)) * np.array([c2l[0], c2l[1], 0.0])
# disp3 = stroh.displacement(pos - shft)
# atoms.set_positions(atoms.get_positions() - np.real(disp3))
atoms.wrap(pbc=[1, 1, 1])
ase.io.write("perf_poscar", atoms_perf, format='vasp')
ase.io.write('POSCAR', atoms, format='vasp')
return (atoms, atoms_perf)
