def get_rotation_matrix_to(self, new_plane):
n1 = self.get_normal_vector()
n2 = new_plane.get_normal_vector()
length_prod = sqrt(inner(n1, n1) * inner(n2, n2))
cos_angle = dot(n1, n2) / length_prod
angle = acos(cos_angle)
p = cross(n1, n2) / length_prod
sin_angle = sqrt(inner(p, p))
assert abs(sin_angle - sin(angle)) < 1e-6
return rodrigues(p / sin_angle, angle, verbose=True)
def get_rotation_matrix_to(self, new_plane):
n1 = self.get_normal_vector()
n2 = new_plane.get_normal_vector()
length_prod = sqrt(inner(n1,n1) * inner(n2,n2))
cos_angle = dot(n1, n2) / length_prod
angle = acos(cos_angle)
p = cross(n1, n2) / length_prod
sin_angle = sqrt(inner(p,p))
assert abs(sin_angle - sin(angle)) < 1e-6
return rodrigues(p / sin_angle, angle, verbose=True)
def print_boundary_type(axis, plane, theta):
if (plane == axis * sum(plane) / sum(axis)).all():
bt = "twist"
elif inner(plane, axis) == 0:
R = rodrigues(axis, theta, verbose=False)
p2 = dot(linalg.inv(R), plane)
plane2 = csl.scale_to_integers(p2)
bt = "tilt (%i %i %i) (%i %i %i)" % (tuple(plane) + tuple(plane2))
else:
bt = "mixed"
return bt
def print_boundary_type(axis, plane, theta):
if (plane == axis * sum(plane) / sum(axis)).all():
bt = "twist"
elif inner(plane, axis) == 0:
R = rodrigues(axis, theta, verbose=False)
p2 = dot(linalg.inv(R), plane)
plane2 = csl.scale_to_integers(p2)
bt = "tilt (%i %i %i) (%i %i %i)" % (tuple(plane) + tuple(plane2))
else:
bt = "mixed"
return bt
def print_details(hkl, m, n):
sigma = get_cubic_sigma(hkl, m, n)
theta = get_cubic_theta(hkl, m, n)
print "sigma=%d, theta=%.3f, m=%d, n=%d, axis=[%d,%d,%d]" % (
sigma, degrees(theta), m, n, hkl[0], hkl[1], hkl[2])
R = rodrigues(hkl, theta)
print
print "R * sigma =\n%s" % (R * sigma)
C = find_csl_matrix(sigma, R)
print "CSL primitive cell (det=%s):\n%s" % (det(C), C)
## optional, for FCC
#C = pc2fcc(C)
#C = beautify_matrix(C)
#print_matrix("CSL cell for fcc:", C)
Cp = make_parallel_to_axis(C, col=2, axis=hkl)
if (Cp != C).any():
print "after making z || %s:\n%s" % (hkl, Cp)
pbc = find_orthorhombic_pbc(Cp)
print_matrix("Minimal(?) orthorhombic PBC", pbc)
def test_rotmono_adjust():
lattice = make_zincblende_lattice(symbols=("Si", "C"), a=4.36)
a = lattice.unit_cell.a
dimensions = [10 * a, 10 * a, 10 * a]
theta = radians(float(sys.argv[1]))
d = dimensions[0]
n_ = d * sin(theta) / a
m_ = d / (a * cos(theta))
n = round(n_)
m = round(m_)
new_th = 0.5 * asin(2. * n / m)
new_d = m * a * cos(new_th)
print "theta =", degrees(new_th), " d =", new_d
dimensions[0] = new_d
dimensions[1] = round(dimensions[1] / a) * a
theta = new_th
rot_mat = rotmat.rodrigues((0, 1, 0), theta, verbose=False)
config = RotatedMonocrystal(lattice, dimensions, rot_mat)
config.generate_atoms()
config.export_atoms("monotest.cfg", format="atomeye")
def _get_orthorhombic_pbc(m):
"""\
the input is matrix 3x3, the output is diagonal.
Distorts the input matrix such that the output
is orthorhombic with the same volume as the
space defined by the input matrix.
"""
if is_diagonal(m):
return m
else:
# x, y, z === unit vector in orthogonal cartesian space
x, y, z = numpy.identity(3)
# xi, yi, zi === initial matrix (m)
xi, yi, zi = m
# xf, yf, zf === final matrix (orthorhombic matrix)
#
# rotate full_pbc to make xi colinear with x
angle = -1.0*numpy.sign(xi[0])*math.acos(xi[0]/linalg.norm(xi))
ortho = numpy.dot(m, rodrigues(z, angle))
# yf (zf) is the projection of the rotated yi (zi) onto y (z)
ortho = numpy.diag(numpy.diagonal(ortho))
return ortho
def _get_orthorhombic_pbc(m):
"""\
the input is matrix 3x3, the output is diagonal.
Distorts the input matrix such that the output
is orthorhombic with the same volume as the
space defined by the input matrix.
"""
if is_diagonal(m):
return m
else:
# x, y, z === unit vector in orthogonal cartesian space
x, y, z = numpy.identity(3)
# xi, yi, zi === initial matrix (m)
xi, yi, zi = m
# xf, yf, zf === final matrix (orthorhombic matrix)
#
# rotate full_pbc to make xi colinear with x
angle = -1.0 * numpy.sign(xi[0]) * math.acos(xi[0] / linalg.norm(xi))
ortho = numpy.dot(m, rodrigues(z, angle))
# yf (zf) is the projection of the rotated yi (zi) onto y (z)
ortho = numpy.diag(numpy.diagonal(ortho))
return ortho
def main():
opts = parse_args()
# R is a matrix that transforms lattice in the bottom monocrystal
# to lattice in the upper monocrystal
R = rodrigues(opts.axis, opts.theta)
if opts.sigma:
# C is CSL primitive cell
C = csl.find_csl_matrix(opts.sigma, R)
print_matrix("CSL primitive cell", C)
## and now we determine CSL for fcc lattice
#C = csl.pc2fcc(C)
#C = csl.beautify_matrix(C)
#print_matrix("CSL cell for fcc:", C)
else:
C = identity(3)
# CSL-lattice must be periodic is our system.
# * PBC box must be orthonormal
# * boundaries must be perpendicular to z axis of PBC box
print "CSL cell with z || [%s %s %s]" % tuple(opts.plane),
Cp = csl.make_parallel_to_axis(C, col=2, axis=opts.plane)
print_matrix("", Cp)
min_pbc = csl.find_orthorhombic_pbc(Cp)
print_matrix("Minimal(?) orthorhombic PBC", min_pbc)
min_dim = []
pbct = min_pbc.transpose().astype(float)
rot = zeros((3, 3))
for i in range(3):
length = sqrt(inner(pbct[i], pbct[i]))
rot[i] = pbct[i] / length
min_dim.append(length)
invrot = rot.transpose()
assert (numpy.abs(invrot - linalg.inv(rot)) < 1e-9).all(), "%s != %s" % (
invrot, linalg.inv(rot))
#print "hack warning: min_dim[1] /= 2."
#min_dim[1] /= 2.
if "," in opts.lattice_name:
name1, name2 = opts.lattice_name.split(",")
lattice1 = get_named_lattice(name1)
lattice2 = get_named_lattice(name2)
else:
lattice1 = get_named_lattice(opts.lattice_name)
lattice2 = deepcopy(lattice1)
if opts.lattice_shift:
lattice1.shift_nodes(opts.lattice_shift)
lattice2.shift_nodes(opts.lattice_shift)
# the anti-phase GB can be made by swapping two species in one grain
if opts.antiphase:
assert lattice2.count_species() == 2
lattice2.swap_node_atoms_names()
a = lattice1.unit_cell.a
opts.find_dim([i * a for i in min_dim])
#rot_mat1 = rodrigues(opts.axis, rot1)
#rot_mat2 = rodrigues(opts.axis, rot2)
rot_mat1 = dot(linalg.inv(R), invrot)
rot_mat2 = invrot
#print "rot1", "det=%g" % linalg.det(rot_mat1), rot_mat1
#print "rot2", "det=%g" % linalg.det(rot_mat2), rot_mat2
title = get_command_line()
if opts.mono1:
config = RotatedMonocrystal(lattice1, opts.dim, rot_mat1,
title=title)
elif opts.mono2:
config = RotatedMonocrystal(lattice2, opts.dim, rot_mat2,
title=title)
else:
config = Bicrystal(lattice1, lattice2, opts.dim, rot_mat1, rot_mat2,
title=title)
config.generate_atoms(z_margin=opts.vacuum)
if not opts.mono1 and not opts.mono2 and opts.remove_dist > 0:
print "Removing atoms in distance < %s ..." % opts.remove_dist
config.remove_close_neighbours(opts.remove_dist)
if opts.remove_dist2:
a_atoms = []
b_atoms = []
a_name = config.atoms[0].name
for i in config.atoms:
if i.name == a_name:
a_atoms.append(i)
else:
b_atoms.append(i)
config.atoms = []
for aa in a_atoms, b_atoms:
print "Removing atoms where %s-%s distance is < %s ..." % (
aa[0].name, aa[0].name, opts.remove_dist2)
config.remove_close_neighbours(distance=opts.remove_dist2, atoms=aa)
config.atoms += aa
if opts.edge:
z1, z2 = opts.edge
sel = [n for n, a in enumerate(config.atoms)
if 0 < a.pos[1] <= config.pbc[1][1] / 2. and z1 < a.pos[2] < z2]
print "edge: %d atoms is removed" % len(sel)
for i in reversed(sel):
del config.atoms[i]
if opts.all:
#config.output_all_removal_possibilities(opts.output_filename)
config.apply_all_possible_cutoffs_to_stgb(opts.output_filename,
single_cutoff=True)
return
if opts.allall:
config.apply_all_possible_cutoffs_to_stgb(opts.output_filename,
single_cutoff=False)
return
config.export_atoms(opts.output_filename)
def parse_args():
if len(sys.argv) < 7:
print usage
sys.exit()
opts = BicrystalOptions()
opts.axis = csl.parse_miller(sys.argv[1])
print "-------> rotation axis: [%i %i %i]" % tuple(opts.axis)
opts.parse_sigma_and_find_theta(sys.argv[3])
plane = sys.argv[2]
if plane == "twist":
opts.plane = opts.axis.copy()
elif plane.startswith("m"):
m_plane = csl.parse_miller(plane[1:])
if inner(m_plane, opts.axis) != 0:
raise ValueError("Axis must be contained in median plane.")
R = rodrigues(opts.axis, opts.theta / 2., verbose=False)
plane_ = dot(R, m_plane)
opts.plane = csl.scale_to_integers(plane_)
else:
opts.plane = csl.parse_miller(plane)
print "-------> boundary plane: (%i %i %i)" % tuple(opts.plane)
bt = print_boundary_type(opts.axis, opts.plane, opts.theta)
print " boundary type:", bt
opts.req_dim = [float(eval(i, math.__dict__)) for i in sys.argv[4:7]]
options = sys.argv[7:-1]
for i in options:
if i == "nofit":
assert opts.fit is None
opts.fit = False
if i == "nozfit":
assert opts.zfit is None
opts.zfit = False
elif i == "mono1":
assert opts.mono1 is None
opts.mono1 = True
elif i == "mono2":
assert opts.mono2 is None
opts.mono2 = True
elif i == "all":
assert opts.all is None and opts.allall is None
opts.all = True
elif i == "allall":
assert opts.allall is None and opts.all is None
opts.allall = True
elif i.startswith("remove:"):
assert opts.remove_dist is None
opts.remove_dist = float(i[7:])
elif i.startswith("remove2:"):
assert opts.remove_dist2 is None
opts.remove_dist2 = float(i[8:])
elif i.startswith("vacuum:"):
assert opts.vacuum is None
opts.vacuum = float(i[7:]) * 10. #nm -> A
elif i.startswith("lattice:"):
opts.lattice_name = i[8:]
elif i.startswith("shift:"):
s = i[6:].split(",")
if len(s) != 3:
raise ValueError("Wrong format of shift parameter")
opts.lattice_shift = [float(i) for i in s]
elif i.startswith("edge:"):
try:
z1, z2 = i[5:].split(",")
opts.edge = (float(z1), float(z2))
except (TypeError, ValueError):
raise ValueError("Wrong format of edge parameter")
else:
raise ValueError("Unknown option: %s" % i)
# default values
if opts.fit is None:
opts.fit = True
if opts.zfit is None:
opts.zfit = True
if opts.mono1 is None:
opts.mono1 = False
if opts.mono2 is None:
opts.mono2 = False
#if opts.remove_dist is None:
# opts.remove_dist = 0.8 * opts.atom_min_dist
opts.output_filename = sys.argv[-1]
return opts
def main():
opts = parse_args()
# R is a matrix that transforms lattice in the bottom monocrystal
# to lattice in the upper monocrystal
R = rodrigues(opts.axis, opts.theta)
if opts.sigma:
# C is CSL primitive cell
C = csl.find_csl_matrix(opts.sigma, R)
print_matrix("CSL primitive cell", C)
## and now we determine CSL for fcc lattice
#C = csl.pc2fcc(C)
#C = csl.beautify_matrix(C)
#print_matrix("CSL cell for fcc:", C)
else:
C = identity(3)
# CSL-lattice must be periodic is our system.
# * PBC box must be orthonormal
# * boundaries must be perpendicular to z axis of PBC box
print "CSL cell with z || [%s %s %s]" % tuple(opts.plane),
Cp = csl.make_parallel_to_axis(C, col=2, axis=opts.plane)
print_matrix("", Cp)
min_pbc = csl.find_orthorhombic_pbc(Cp)
print_matrix("Minimal(?) orthorhombic PBC", min_pbc)
min_dim = []
pbct = min_pbc.transpose().astype(float)
rot = zeros((3, 3))
for i in range(3):
length = sqrt(inner(pbct[i], pbct[i]))
rot[i] = pbct[i] / length
min_dim.append(length)
invrot = rot.transpose()
assert (numpy.abs(invrot - linalg.inv(rot)) <
1e-9).all(), "%s != %s" % (invrot, linalg.inv(rot))
#print "hack warning: min_dim[1] /= 2."
#min_dim[1] /= 2.
if "," in opts.lattice_name:
name1, name2 = opts.lattice_name.split(",")
lattice1 = get_named_lattice(name1)
lattice2 = get_named_lattice(name2)
else:
lattice1 = get_named_lattice(opts.lattice_name)
lattice2 = deepcopy(lattice1)
if opts.lattice_shift:
lattice1.shift_nodes(opts.lattice_shift)
lattice2.shift_nodes(opts.lattice_shift)
# the anti-phase GB can be made by swapping two species in one grain
if opts.antiphase:
assert lattice2.count_species() == 2
lattice2.swap_node_atoms_names()
a = lattice1.unit_cell.a
opts.find_dim([i * a for i in min_dim])
#rot_mat1 = rodrigues(opts.axis, rot1)
#rot_mat2 = rodrigues(opts.axis, rot2)
rot_mat1 = dot(linalg.inv(R), invrot)
rot_mat2 = invrot
#print "rot1", "det=%g" % linalg.det(rot_mat1), rot_mat1
#print "rot2", "det=%g" % linalg.det(rot_mat2), rot_mat2
title = get_command_line()
if opts.mono1:
config = RotatedMonocrystal(lattice1, opts.dim, rot_mat1, title=title)
elif opts.mono2:
config = RotatedMonocrystal(lattice2, opts.dim, rot_mat2, title=title)
else:
config = Bicrystal(lattice1,
lattice2,
opts.dim,
rot_mat1,
rot_mat2,
title=title)
config.generate_atoms(z_margin=opts.vacuum)
if not opts.mono1 and not opts.mono2 and opts.remove_dist > 0:
print "Removing atoms in distance < %s ..." % opts.remove_dist
config.remove_close_neighbours(opts.remove_dist)
if opts.remove_dist2:
a_atoms = []
b_atoms = []
a_name = config.atoms[0].name
for i in config.atoms:
if i.name == a_name:
a_atoms.append(i)
else:
b_atoms.append(i)
config.atoms = []
for aa in a_atoms, b_atoms:
print "Removing atoms where %s-%s distance is < %s ..." % (
aa[0].name, aa[0].name, opts.remove_dist2)
config.remove_close_neighbours(distance=opts.remove_dist2,
atoms=aa)
config.atoms += aa
if opts.edge:
z1, z2 = opts.edge
sel = [
n for n, a in enumerate(config.atoms)
if 0 < a.pos[1] <= config.pbc[1][1] / 2. and z1 < a.pos[2] < z2
]
print "edge: %d atoms is removed" % len(sel)
for i in reversed(sel):
del config.atoms[i]
if opts.all:
#config.output_all_removal_possibilities(opts.output_filename)
config.apply_all_possible_cutoffs_to_stgb(opts.output_filename,
single_cutoff=True)
return
if opts.allall:
config.apply_all_possible_cutoffs_to_stgb(opts.output_filename,
single_cutoff=False)
return
config.export_atoms(opts.output_filename)
def parse_args():
if len(sys.argv) < 7:
print usage
sys.exit()
opts = BicrystalOptions()
opts.axis = csl.parse_miller(sys.argv[1])
print "-------> rotation axis: [%i %i %i]" % tuple(opts.axis)
opts.parse_sigma_and_find_theta(sys.argv[3])
plane = sys.argv[2]
if plane == "twist":
opts.plane = opts.axis.copy()
elif plane.startswith("m"):
m_plane = csl.parse_miller(plane[1:])
if inner(m_plane, opts.axis) != 0:
raise ValueError("Axis must be contained in median plane.")
R = rodrigues(opts.axis, opts.theta / 2., verbose=False)
plane_ = dot(R, m_plane)
opts.plane = csl.scale_to_integers(plane_)
else:
opts.plane = csl.parse_miller(plane)
print "-------> boundary plane: (%i %i %i)" % tuple(opts.plane)
bt = print_boundary_type(opts.axis, opts.plane, opts.theta)
print " boundary type:", bt
opts.req_dim = [float(eval(i, math.__dict__)) for i in sys.argv[4:7]]
options = sys.argv[7:-1]
for i in options:
if i == "nofit":
assert opts.fit is None
opts.fit = False
if i == "nozfit":
assert opts.zfit is None
opts.zfit = False
elif i == "mono1":
assert opts.mono1 is None
opts.mono1 = True
elif i == "mono2":
assert opts.mono2 is None
opts.mono2 = True
elif i == "all":
assert opts.all is None and opts.allall is None
opts.all = True
elif i == "allall":
assert opts.allall is None and opts.all is None
opts.allall = True
elif i.startswith("remove:"):
assert opts.remove_dist is None
opts.remove_dist = float(i[7:])
elif i.startswith("remove2:"):
assert opts.remove_dist2 is None
opts.remove_dist2 = float(i[8:])
elif i.startswith("vacuum:"):
assert opts.vacuum is None
opts.vacuum = float(i[7:]) * 10. #nm -> A
elif i.startswith("lattice:"):
opts.lattice_name = i[8:]
elif i.startswith("shift:"):
s = i[6:].split(",")
if len(s) != 3:
raise ValueError("Wrong format of shift parameter")
opts.lattice_shift = [float(i) for i in s]
elif i.startswith("edge:"):
try:
z1, z2 = i[5:].split(",")
opts.edge = (float(z1), float(z2))
except (TypeError, ValueError):
raise ValueError("Wrong format of edge parameter")
else:
raise ValueError("Unknown option: %s" % i)
# default values
if opts.fit is None:
opts.fit = True
if opts.zfit is None:
opts.zfit = True
if opts.mono1 is None:
opts.mono1 = False
if opts.mono2 is None:
opts.mono2 = False
#if opts.remove_dist is None:
# opts.remove_dist = 0.8 * opts.atom_min_dist
opts.output_filename = sys.argv[-1]
return opts
