def slip_vector(system_0,
system_1,
neighbor_list=None,
neighbor_list_cutoff=None):
"""Compute the slip vectors for all atoms in system_1 relative to system_0."""
assert system_0.natoms == system_1.natoms, 'systems have different number of atoms'
#neighbor list setup
if neighbor_list is not None:
assert neighbor_list_cutoff is None, 'neighbor_list and neighbor_list_cutoff cannot both be given'
elif neighbor_list_cutoff is not None:
neighbor_list = am.nlist(system_0, neighbor_list_cutoff)
elif 'neighbors' in system_0.prop:
neighbor_list = system_0.prop['neighbors']
elif 'nlist' in system_0.prop:
neighbor_list = system_0.prop['nlist']
if isinstance(neighbor_list, am.NeighborList):
objectnlist = True
else:
objectnlist = False
#Calculate the slip vector
slip = np.zeros((system_0.natoms, 3))
for i in xrange(system_0.natoms):
if objectnlist:
js = neighbor_list[i]
else:
js = neighbor_list[i, 1:neighbor_list[i, 0] + 1]
slip[i] = -np.sum(system_1.dvect(i, js) - system_0.dvect(i, js),
axis=0)
return slip
def slip_vector(system_0, system_1, neighbor_list=None, neighbor_list_cutoff=None):
"""Compute the slip vectors for all atoms in system_1 relative to system_0."""
assert system_0.natoms == system_1.natoms, 'systems have different number of atoms'
#neighbor list setup
if neighbor_list is not None:
assert neighbor_list_cutoff is None, 'neighbor_list and neighbor_list_cutoff cannot both be given'
elif neighbor_list_cutoff is not None:
neighbor_list = am.nlist(system_0, neighbor_list_cutoff)
elif 'neighbors' in system_0.prop:
neighbor_list = system_0.prop['neighbors']
elif 'nlist' in system_0.prop:
neighbor_list = system_0.prop['nlist']
if isinstance(neighbor_list, am.NeighborList):
objectnlist = True
else:
objectnlist = False
#Calculate the slip vector
slip = np.zeros((system_0.natoms, 3))
for i in xrange(system_0.natoms):
if objectnlist:
js = neighbor_list[i]
else:
js = neighbor_list[i, 1:neighbor_list[i, 0]+1]
slip[i] = -np.sum(system_1.dvect(i, js) - system_0.dvect(i, js), axis=0)
return slip
def nlist(self, cutoff, cmult=1):
"""Build neighbor list for all atoms based on a cutoff.
Keyword Arguments:
cutoff -- radial cutoff distance for including atoms as neighbors.
cmult -- int factor that changes the underlying binning algorithm. Default is 1, which should be the fastest.
"""
self.prop['nlist'] = am.nlist(self, cutoff, cmult)
def nlist(self, cutoff, cmult=1):
"""Build neighbor list for all atoms based on a cutoff.
Keyword Arguments:
cutoff -- radial cutoff distance for including atoms as neighbors.
cmult -- int factor that changes the underlying binning algorithm. Default is 1, which should be the fastest.
"""
with warnings.catch_warnings():
warnings.simplefilter('always')
warnings.warn('nlist method is replaced with neighbors method', DeprecationWarning)
self.prop['nlist'] = am.nlist(self, cutoff, cmult=cmult)
def slip_vector(system_0, system_1, neighbor_list=None, neighbor_list_cutoff=None):
"""Compute the slip vectors for all atoms in system_1 relative to system_0."""
assert system_0.natoms == system_1.natoms, "systems have different number of atoms"
# neighbor list setup
if neighbor_list is not None:
assert neighbor_list_cutoff is None, "neighbor_list and neighbor_list_cutoff cannot both be given"
elif neighbor_list_cutoff is not None:
neighbor_list = am.nlist(system_0, neighbor_list_cutoff)
elif "nlist" in system_0.prop:
neighbor_list = system_0.prop["nlist"]
# Calculate the slip vector
slip = np.zeros((system_0.natoms, 3))
for i in xrange(system_0.natoms):
js = neighbor_list[i, 1 : neighbor_list[i, 0] + 1]
slip[i] = -np.sum(system_1.dvect(i, js) - system_0.dvect(i, js), axis=0)
return slip
def differential_displacement(base_system, disl_system, burgers_vector, plot_range,
neighbor_list = None, neighbor_list_cutoff = None, component = 'standard',
axes = None, plot_scale = 1, save_file = None, show = True):
"""
Function for generating a differential displacement plot for a
dislocation containing system.
Arguments:
base_system -- atomman.System defect-free reference system corresponding
to disl_system.
disl_system -- atomman.System system containing the defect.
burgers_vector -- 3x1 numpy array for the dislocation's Burgers vector.
plot_range -- 3x3 numpy array specifying the Cartesian space to include
atoms in the plot.
Optional Keyword Arguments:
neighbor_list -- pre-computed neighbor list for base_system.
neighbor_list_cutoff -- cutoff for computing a neighbor list for
base_system.
component -- indicates the style of the calculation to use.
axes -- 3x3 numpy array indicating the crystallographic
axes corresponding to the box's Cartesian axes.
If given, only used for transforming the
burgers_vector.
plot_scale -- scalar for multiplying the magnitude of the differential
displacement arrows.
save_file -- if given then the plot will be saved to a file with this name.
show -- Boolean flag for showing the figure. Default is True.
"""
#Burgers vector setup
if axes is not None:
T = am.tools.axes_check(axes)
burgers_vector = T.dot(burgers_vector)
burgers_vector_magnitude = np.linalg.norm(burgers_vector)
burgers_vector_uvect = burgers_vector / burgers_vector_magnitude
#neighbor list setup
if neighbor_list is not None:
assert neighbor_list_cutoff is None, 'neighbor_list and neighbor_list_cutoff cannot both be given'
elif neighbor_list_cutoff is not None:
neighbor_list = am.nlist(base_system, neighbor_list_cutoff)
elif 'nlist' in base_system.prop:
neighbor_list = base_system.prop['nlist']
#Identify atoms in plot range
base_pos = base_system.atoms_prop(key='pos')
plot_range_indices = np.where((base_pos[:, 0] > plot_range[0,0]) & (base_pos[:, 0] < plot_range[0,1]) &
(base_pos[:, 1] > plot_range[1,0]) & (base_pos[:, 1] < plot_range[1,1]) &
(base_pos[:, 2] > plot_range[2,0]) & (base_pos[:, 2] < plot_range[2,1]))[0]
#initial plot setup and parameters
fig, ax1, = plt.subplots(1, 1, squeeze=True, figsize=(7,7), dpi=72)
ax1.axis([plot_range[0,0], plot_range[0,1], plot_range[1,0], plot_range[1,1]])
atom_circle_radius = burgers_vector_magnitude / 10
arrow_width_scale = 1. / 200.
#Loop over all atoms i in plot range
for i in plot_range_indices:
#Plot a circle for atom i
color = cm.hsv((base_pos[i, 2] - plot_range[2,0]) / (plot_range[2,1] - plot_range[2,0]))
ax1.add_patch(mpatches.Circle(base_pos[i, :2], atom_circle_radius, fc=color))
#make list of all neighbors for atom i
neighbor_indices = neighbor_list[i, 1 : neighbor_list[i, 0] + 1]
#Compute distance vectors between atom i and its neighbors for both systems
base_dvectors = base_system.dvect(int(i), neighbor_indices)
disl_dvectors = disl_system.dvect(int(i), neighbor_indices)
#Compute differential displacement vectors
dd_vectors = disl_dvectors - base_dvectors
#Compute centerpoint positions for the vectors
arrow_centers = base_pos[i] + base_dvectors / 2
if component == 'standard':
#compute unit distance vectors
base_uvectors = base_dvectors / np.linalg.norm(base_dvectors, axis=1)[:,np.newaxis]
#compute component of the dd_vector parallel to the burgers vector
dd_components = dd_vectors.dot(burgers_vector_uvect)
dd_components[dd_components > burgers_vector_magnitude / 2] -= burgers_vector_magnitude
dd_components[dd_components < -burgers_vector_magnitude / 2] += burgers_vector_magnitude
#scale arrow lengths and vectors
arrow_lengths = base_uvectors * dd_components[:,np.newaxis] * plot_scale
arrow_widths = arrow_width_scale * dd_components * plot_scale
#plot the arrows
for center, length, width in zip(arrow_centers, arrow_lengths, arrow_widths):
if width > 1e-7:
ax1.quiver(center[0], center[1], length[0], length[1], pivot='middle',
angles='xy', scale_units='xy', scale=1, width=width)
elif component == 'xy':
#scale arrow lengths and vectors
arrow_lengths = dd_vectors[:, :2] * plot_scale
arrow_lengths[dd_vectors[:, 2] > 0] *= -1
arrow_widths = arrow_width_scale * (arrow_lengths[:,0]**2+arrow_lengths[:,1]**2)**0.5
#plot the arrows
for center, length, width in zip(arrow_centers, arrow_lengths, arrow_widths):
if width > 1e-7:
ax1.quiver(center[0], center[1], length[0], length[1], width=width,
pivot='middle', angles='xy', scale_units='xy', scale=1)
if save_file is not None:
plt.savefig(save_file, dpi=800)
if show == False:
plt.close(fig)
plt.show()
def nye_tensor(system, p_vectors, theta_max = 27, axes=None, neighbor_list=None, neighbor_list_cutoff=None):
"""Computes strain properties and Nye tensor for a defect containing system."""
#neighbor list setup
if neighbor_list is not None:
assert neighbor_list_cutoff is None, 'neighbor_list and neighbor_list_cutoff cannot both be given'
elif neighbor_list_cutoff is not None:
neighbor_list = am.nlist(system, neighbor_list_cutoff)
elif 'nlist' in system.prop:
neighbor_list = system.prop['nlist']
#If p_vectors is only given for one atom, apply to all atoms
if len(p_vectors) == 1:
p_vectors = np.broadcast_to(p_vectors, (system.natoms, len(p_vectors[0]), 3))
elif len(p_vectors) != system.natoms:
p_vectors = np.broadcast_to(p_vectors, (system.natoms, len(p_vectors), 3))
#If axes are given, transform p accordingly
if axes is not None:
p_vectors = np.inner(p_vectors, am.tools.axes_check(axes))
#get cos of theta_max
cos_theta_max = np.cos(theta_max * np.pi / 180)
#Define identity and epsilon arrays
#iden =
eps = np.array([[[ 0, 0, 0],[ 0, 0, 1],[ 0,-1, 0]],
[[ 0, 0,-1],[ 0, 0, 0],[ 1, 0, 0]],
[[ 0, 1, 0],[-1, 0, 0],[ 0, 0, 0]]])
#Identify largest number of nearest neighbors
nmax = 0
for ns in neighbor_list:
if ns[0] > nmax: nmax=ns[0]
#Initialize variables (done here to reduce memory allocations making it slightly faster)
strain = np.empty((system.natoms, 3, 3))
inv1 = np.empty(system.natoms)
inv2 = np.empty(system.natoms)
ang_vel = np.empty(system.natoms)
nye = np.empty((system.natoms, 3, 3))
P = np.zeros((nmax, 3))
Q = np.zeros((nmax, 3))
G = np.empty((system.natoms, 3, 3))
gradG = np.empty((3, 3, 3))
#Loop to calculate correspondence tensor, G, and strain data
for i in xrange(system.natoms):
p = np.asarray(p_vectors[i])
if p.ndim == 1:
p = np.array([p])
p_mags = np.linalg.norm(p, axis=1)
r1 = p_mags.min()
#Calculate radial neighbor vectors, q
q = system.dvect(i, neighbor_list[i][1:neighbor_list[i][0]+1])
if q.ndim == 1:
q = np.array([q])
q_mags = np.linalg.norm(q, axis=1)
#Calculate cos_thetas between all p's and q's.
cos_thetas = (np.dot(p, q.T) /q_mags ).T / p_mags
#Identify best index matches
index_pairing = cos_thetas.argmax(1)
#Exclude values where theta is greater than theta_max
index_pairing[cos_thetas.max(1) < cos_theta_max] = -1
#Search for duplicate index_pairings
u, u_count = np.unique(index_pairing, return_counts=True)
for match in u[(u!=-1) & (u_count > 1)]:
print index_pairing==match
for n in xrange(neighbor_list[i][0]):
#Check if the particular p has already been assigned to another q
#Remove the p-q pair that is farther from r1
if index_pairing[n] >=0:
for k in xrange(n):
if index_pairing[n] == index_pairing[k]:
nrad = abs(r1 - q_mags[n])
krad = abs(r1 - q_mags[k])
if nrad < krad:
index_pairing[k]=-1
else:
index_pairing[n]=-1
#Construct reduced P, Q matrices from p-q pairs
c = 0
for n in xrange(neighbor_list[i][0]):
if index_pairing[n] >= 0:
Q[c] = q[n]
P[c] = p[index_pairing[n]]
c+=1
#Compute lattice correspondence tensor, G, from P and Q
if c == 0:
G[i] = np.identity(3)
warnings.warn('An atom lacks pair sets. Check neighbor list')
else:
G[i], resid, rank, s = np.linalg.lstsq(Q[:c], P[:c])
#Compute strain properties
strain[i] = ((np.identity(3) - G[i]) + (np.identity(3) - G[i]).T) / 2.
inv1[i] = strain[i,0,0] + strain[i,1,1] + strain[i,2,2]
inv2[i] = (strain[i,0,0] * strain[i,1,1] + strain[i,0,0] * strain[i,2,2] + strain[i,1,1] * strain[i,2,2]
- strain[i,0,1]**2 - strain[i,0,2]**2 - strain[i,1,2]**2)
rot = ((np.identity(3) - G[i]) - (np.identity(3) - G[i]).T) / 2.
ang_vel[i] = (rot[0,1]**2 + rot[0,2]**2 + rot[1,2]**2)**0.5
#Construct the gradient tensor of G, gradG
for i in xrange(system.natoms):
neighbors = neighbor_list[i][1:neighbor_list[i][0]+1]
Q = system.dvect(i, neighbors)
if Q.ndim == 1:
Q = np.array([Q])
dG = G[neighbors] - G[i]
for x in xrange(3):
gradG[x,:] = np.linalg.lstsq(Q, dG[:,x,:])[0].T
#Use gradG to build the nye tensor, nye
nye[i] = -np.einsum('ijm,ikm->jk', eps, gradG)
return {'strain':strain, 'strain_invariant_1':inv1, 'strain_invariant_2':inv2, 'angular_velocity':ang_vel, 'Nye_tensor':nye}
