def periodicVoronoiCell(a=1.3968418,
L=numpy.array([10, 10]),
N=10,
cType='tr',
**kwargs):
"""
Returns a cell of size L with N grains made according to the voronoi constructions.
The positions and orientations of the grains are random.
"""
# Get origins
if 'x0' not in kwargs:
x0, y0 = ptsInBox(N, L)
else:
x0 = kwargs['x0']
y0 = kwargs['y0']
N = len(x0)
# Get a list of axes
ax = kwargs.get('axes', randomAxes(N))
z0 = numpy.zeros(N)
# Repeat for double periodic geometry
ax = ax * 9 # Repeat 9 times
x, y, z = [], [], []
for i in [0, -1, 1]:
for j in [0, -1, 1]:
x.extend(x0 + L[0] * i)
y.extend(y0 + L[1] * j)
z.extend(z0)
x, y, z = numpy.array(x), numpy.array(y), numpy.array(z)
orgs = numpy.concatenate(
(x.reshape(N * 9, 1), y.reshape(N * 9, 1), z.reshape(N * 9, 1)),
axis=1)
# Get the number of repeats needed for the crystals
D = numpy.linalg.norm(L) * 3 # Diagonal of the periodic box
r = (int(D / a) + 2) * 2 # repeats
rc = rotatedCrystal(numpy.eye(3), size=(r, r, 1), a=a, cType=cType)
rc.positions[:, 2] = 0
orgPos = rc.positions
# ---- Find the grain boundaries with a voronoi tesselation
# ---- we do this to mark the atoms near the grain boundary.
centers = numpy.zeros((len(x), 2))
centers[:, 0], centers[:, 1] = x, y
vor = Voronoi(centers)
edges = vorEdges(vor, D)
# positions = [] # positions of the atoms in the cell
bulkPositions = numpy.ndarray(
shape=(0, 3)) # positions of the bulk atoms in the cell
gbPositions = numpy.ndarray(
shape=(0, 3)) # positions of the grain boundary atoms in the cell
unRatPositions = numpy.ndarray(
shape=(0, 3)) # positions of the unrattlable atoms in the cell
padPositions = numpy.ndarray(
shape=(0, 3)) # positions of the pad atoms in the cell
tags = numpy.ndarray(
shape=(0, 1)
) # tags of the atoms 0 = bulk, 1 = grain boundary, 2 = pad region, 3 = unrattlable
gn = 0
overlap = kwargs.get('overlap', 0.5)
for v, x1, y1, z1 in zip(ax, x0, y0, z0):
gn += 1
p0 = numpy.array([x1, y1, z1])
p = copy.copy(orgPos)
p = numpy.dot(v, p.T).T
p += p0 # Center the crystal at the center of the grain
# Choose all in the big box
p = p[numpy.logical_and(*[
numpy.logical_and(p[:, i] > -L[i], p[:, i] <= 2 * L[i])
for i in range(2)
])]
# Find the grain number to which we are closest
# allDist = cdist(p, orgs, 'euclidean')
# gNum = numpy.argmin(allDist,axis=1)
if overlap == 0:
# Find gNum with c routine
gNum = numpy.zeros(len(p))
_cPolyUtils.closest(p[:, 0], p[:, 1], orgs[:, 0], orgs[:, 1], gNum)
gNum = gNum.astype(int)
p = p[gNum == gn - 1] # Choose all that belong to the grain
else:
# finite overlap means we need to use voronoi edges to determine which points lie within an overlap region
# voronoi region associated with the point
reg = vor.regions[vor.point_region[
gn - 1]] # region associated with the point
if -1 in reg:
raise Exception('Open region associated with generator')
nVerts = len(reg) # number of verticies in the region
p = pointsInRegion(gn - 1, vor, p, overlap=overlap)
# Correct for periodic boundaries
for i in range(2):
p[p[:, i] < 0, i] += L[i]
p[p[:, i] >= L[i], i] -= L[i]
# Find a strip close to the grain boundary
t = numpy.zeros(len(p)).reshape((len(p), 1)) # Default tag bulk
bWidth = kwargs.get('bWidth', 10.0)
pad = kwargs.get('pad', 5.0)
ratPad = kwargs.get('ratPad', 2.0)
for edge in edges:
# for edge in pt2edge[(x1,y1,z1)]:
p1, p2, slope = [numpy.ndarray((1, 3)) * 0 for i in range(3)]
p1[:, :2], p2[:, :2], slope[:, :2] = edge['p1'], edge['p2'], edge[
't']
# The library sometimes returns nan due to the 2d nature of the problem. Reset it.
slope[:, 2] = 0
p1[:, 2] = 0
p2[:, 2] = 0
proj1, proj2 = numpy.dot(p - p1,
slope.T), numpy.dot(p - p2, slope.T)
distToEdge = (numpy.sum(((p1 - p) + proj1 * slope)**2.0,
axis=1)**0.5).reshape((len(p), 1))
# tag pad region
t[numpy.logical_and(
numpy.logical_and(t != 1, t != 3),
numpy.logical_and(
numpy.logical_and(distToEdge < bWidth + pad,
distToEdge >= bWidth),
proj1 * proj2 < 0))] = 2
# tag unrattlable
t[numpy.logical_and(
t != 1,
numpy.logical_and(
numpy.logical_and(distToEdge < bWidth,
distToEdge > bWidth - ratPad),
proj1 * proj2 < 0))] = 3
# tag grain boundary
t[numpy.logical_and(distToEdge <= bWidth - ratPad,
proj1 * proj2 < 0)] = 1
bulkPositions = numpy.concatenate((bulkPositions, p[(t == 0)[:,
0], :]))
padPositions = numpy.concatenate((padPositions, p[(t == 2)[:, 0], :]))
unRatPositions = numpy.concatenate((unRatPositions, p[(t == 3)[:,
0], :]))
# Filter out 'close' atoms in grain boundary
cutoff = kwargs.get('cutoff', 0.2)
thisGB = p[(t == 1)[:, 0], :]
if len(gbPositions) > 0:
# gbDist = cdist(thisGB,gbPositions)
# minDist = numpy.min(gbDist,axis=1)
# Find minDist with c routine
minInd = numpy.zeros(len(thisGB)).astype('int')
_cPolyUtils.closest(thisGB[:, 0], thisGB[:, 1], gbPositions[:, 0],
gbPositions[:, 1], minInd)
minDist = numpy.sum((thisGB - gbPositions[minInd])**2.0,
axis=1)**0.5
thisGB = numpy.delete(thisGB,
numpy.where(minDist < a * cutoff),
axis=0)
gbPositions = numpy.concatenate((gbPositions, thisGB))
# Filter out close atoms in the gb again; possible to have anamolies due to multiple grain overlap
cutoff = kwargs.get('cutoff', 0.2)
if len(gbPositions) > 0:
closeAtoms = True
while closeAtoms:
# Find minDist with c routine
minInd = numpy.zeros(len(gbPositions) - 1)
minDist = numpy.zeros(len(gbPositions) - 1)
_cPolyUtils.selfClosest(L[0], L[1], gbPositions[:, 0],
gbPositions[:, 1], minInd, minDist)
gbPositions = numpy.delete(gbPositions,
numpy.where(minDist < cutoff * a),
axis=0)
minInd = numpy.zeros(len(gbPositions) - 1)
minDist = numpy.zeros(len(gbPositions) - 1)
_cPolyUtils.selfClosest(L[0], L[1], gbPositions[:, 0],
gbPositions[:, 1], minInd, minDist)
if minDist.min() >= cutoff * a:
closeAtoms = False
# collect all positions
positions = numpy.concatenate((bulkPositions, unRatPositions))
positions = numpy.concatenate((positions, gbPositions))
positions = numpy.concatenate((positions, padPositions))
tags = numpy.zeros(len(positions))
tags[-len(unRatPositions) - len(gbPositions) - len(padPositions):] = 3
tags[-len(gbPositions) - len(padPositions):] = 1
tags[-len(padPositions):] = 2
# Set the gbPositions as rattlable, and then merge the unRat and gb
rattlable = numpy.zeros(len(tags))
rattlable[tags == 1] = 1
tags[tags == 3] = 1
cell = numpy.diag([L[0], L[1], 10])
# cr = Atoms(symbols=symbols, positions=positions, cell = cell, pbc=[True,True,True])
numbers = numpy.ones(len(positions)) * 6
symbols = ['C'] * len(positions)
cr = Atoms(numbers=numbers,
positions=positions,
cell=cell,
tags=tags,
pbc=[True, True, True])
cr.ax = ax
cr.centers = centers
cr.orgs = orgs
cr.rattlable = rattlable
if sum(tags == 0) == 0 or sum(tags == 1) == 0 or sum(tags == 2) == 0:
print "It seems that either the cell is too small or there are too many grains. You might want to fix this"
return cr
def periodicVoronoiCell(a=1.3968418, L=numpy.array([10, 10]), N=10, cType='tr', **kwargs):
"""
Returns a cell of size L with N grains made according to the voronoi constructions.
The positions and orientations of the grains are random.
"""
# Get origins
if 'x0' not in kwargs:
x0, y0 = ptsInBox(N, L)
else:
x0 = kwargs['x0']
y0 = kwargs['y0']
N = len(x0)
# Get a list of axes
ax = kwargs.get('axes', randomAxes(N))
z0 = numpy.zeros(N)
# Repeat for double periodic geometry
ax = ax * 9 # Repeat 9 times
x, y, z = [], [], []
for i in [0, -1, 1]:
for j in [0, -1, 1]:
x.extend(x0 + L[0] * i)
y.extend(y0 + L[1] * j)
z.extend(z0)
x, y, z = numpy.array(x), numpy.array(y), numpy.array(z)
orgs = numpy.concatenate((x.reshape(N * 9, 1), y.reshape(N * 9, 1), z.reshape(N * 9, 1)), axis=1)
# Get the number of repeats needed for the crystals
D = numpy.linalg.norm(L) * 3 # Diagonal of the periodic box
r = (int(D / a) + 2) * 2 # repeats
rc = rotatedCrystal(numpy.eye(3), size=(r, r, 1), a=a, cType=cType)
rc.positions[:, 2] = 0
orgPos = rc.positions
# ---- Find the grain boundaries with a voronoi tesselation
# ---- we do this to mark the atoms near the grain boundary.
centers = numpy.zeros((len(x), 2))
centers[:, 0], centers[:, 1] = x, y
vor = Voronoi(centers)
edges = vorEdges(vor, D)
# positions = [] # positions of the atoms in the cell
bulkPositions = numpy.ndarray(shape=(0, 3)) # positions of the bulk atoms in the cell
gbPositions = numpy.ndarray(shape=(0, 3)) # positions of the grain boundary atoms in the cell
unRatPositions = numpy.ndarray(shape=(0, 3)) # positions of the unrattlable atoms in the cell
padPositions = numpy.ndarray(shape=(0, 3)) # positions of the pad atoms in the cell
tags = numpy.ndarray(
shape=(0, 1)) # tags of the atoms 0 = bulk, 1 = grain boundary, 2 = pad region, 3 = unrattlable
gn = 0
overlap = kwargs.get('overlap', 0.5)
for v, x1, y1, z1 in zip(ax, x0, y0, z0):
gn += 1
p0 = numpy.array([x1, y1, z1])
p = copy.copy(orgPos)
p = numpy.dot(v, p.T).T
p += p0 # Center the crystal at the center of the grain
# Choose all in the big box
p = p[numpy.logical_and(*[numpy.logical_and(p[:, i] > -L[i], p[:, i] <= 2 * L[i]) for i in range(2)])]
# Find the grain number to which we are closest
# allDist = cdist(p, orgs, 'euclidean')
# gNum = numpy.argmin(allDist,axis=1)
if overlap == 0:
# Find gNum with c routine
gNum = numpy.zeros(len(p))
_cPolyUtils.closest(p[:, 0], p[:, 1], orgs[:, 0], orgs[:, 1], gNum)
gNum = gNum.astype(int)
p = p[gNum == gn - 1] # Choose all that belong to the grain
else:
# finite overlap means we need to use voronoi edges to determine which points lie within an overlap region
# voronoi region associated with the point
reg = vor.regions[vor.point_region[gn - 1]] # region associated with the point
if -1 in reg:
raise Exception('Open region associated with generator')
nVerts = len(reg) # number of verticies in the region
p = pointsInRegion(gn - 1, vor, p, overlap=overlap)
# Correct for periodic boundaries
for i in range(2):
p[p[:, i] < 0, i] += L[i]
p[p[:, i] >= L[i], i] -= L[i]
# Find a strip close to the grain boundary
t = numpy.zeros(len(p)).reshape((len(p), 1)) # Default tag bulk
bWidth = kwargs.get('bWidth', 10.0)
pad = kwargs.get('pad', 5.0)
ratPad = kwargs.get('ratPad', 2.0)
for edge in edges:
# for edge in pt2edge[(x1,y1,z1)]:
p1, p2, slope = [numpy.ndarray((1, 3)) * 0 for i in range(3)]
p1[:, :2], p2[:, :2], slope[:, :2] = edge['p1'], edge['p2'], edge['t']
# The library sometimes returns nan due to the 2d nature of the problem. Reset it.
slope[:, 2] = 0
p1[:, 2] = 0
p2[:, 2] = 0
proj1, proj2 = numpy.dot(p - p1, slope.T), numpy.dot(p - p2, slope.T)
distToEdge = (numpy.sum(((p1 - p) + proj1 * slope) ** 2.0, axis=1) ** 0.5).reshape((len(p), 1))
# tag pad region
t[numpy.logical_and(numpy.logical_and(t != 1, t != 3),
numpy.logical_and(numpy.logical_and(distToEdge < bWidth + pad, distToEdge >= bWidth),
proj1 * proj2 < 0))] = 2
# tag unrattlable
t[numpy.logical_and(t != 1,
numpy.logical_and(numpy.logical_and(distToEdge < bWidth, distToEdge > bWidth - ratPad),
proj1 * proj2 < 0))] = 3
# tag grain boundary
t[numpy.logical_and(distToEdge <= bWidth - ratPad, proj1 * proj2 < 0)] = 1
bulkPositions = numpy.concatenate((bulkPositions, p[(t == 0)[:, 0], :]))
padPositions = numpy.concatenate((padPositions, p[(t == 2)[:, 0], :]))
unRatPositions = numpy.concatenate((unRatPositions, p[(t == 3)[:, 0], :]))
# Filter out 'close' atoms in grain boundary
cutoff = kwargs.get('cutoff', 0.2)
thisGB = p[(t == 1)[:, 0], :]
if len(gbPositions) > 0:
# gbDist = cdist(thisGB,gbPositions)
# minDist = numpy.min(gbDist,axis=1)
# Find minDist with c routine
minInd = numpy.zeros(len(thisGB)).astype('int')
_cPolyUtils.closest(thisGB[:, 0], thisGB[:, 1], gbPositions[:, 0], gbPositions[:, 1], minInd)
minDist = numpy.sum((thisGB - gbPositions[minInd]) ** 2.0, axis=1) ** 0.5
thisGB = numpy.delete(thisGB, numpy.where(minDist < a * cutoff), axis=0)
gbPositions = numpy.concatenate((gbPositions, thisGB))
# Filter out close atoms in the gb again; possible to have anamolies due to multiple grain overlap
cutoff = kwargs.get('cutoff', 0.2)
if len(gbPositions) > 0:
closeAtoms = True
while closeAtoms:
# Find minDist with c routine
minInd = numpy.zeros(len(gbPositions) - 1)
minDist = numpy.zeros(len(gbPositions) - 1)
_cPolyUtils.selfClosest(L[0], L[1], gbPositions[:, 0], gbPositions[:, 1], minInd, minDist)
gbPositions = numpy.delete(gbPositions, numpy.where(minDist < cutoff * a), axis=0)
minInd = numpy.zeros(len(gbPositions) - 1)
minDist = numpy.zeros(len(gbPositions) - 1)
_cPolyUtils.selfClosest(L[0], L[1], gbPositions[:, 0], gbPositions[:, 1], minInd, minDist)
if minDist.min() >= cutoff * a:
closeAtoms = False
# collect all positions
positions = numpy.concatenate((bulkPositions, unRatPositions))
positions = numpy.concatenate((positions, gbPositions))
positions = numpy.concatenate((positions, padPositions))
tags = numpy.zeros(len(positions))
tags[-len(unRatPositions) - len(gbPositions) - len(padPositions):] = 3
tags[-len(gbPositions) - len(padPositions):] = 1
tags[-len(padPositions):] = 2
# Set the gbPositions as rattlable, and then merge the unRat and gb
rattlable = numpy.zeros(len(tags))
rattlable[tags == 1] = 1
tags[tags == 3] = 1
cell = numpy.diag([L[0], L[1], 10])
# cr = Atoms(symbols=symbols, positions=positions, cell = cell, pbc=[True,True,True])
numbers = numpy.ones(len(positions)) * 6
symbols = ['C'] * len(positions)
cr = Atoms(numbers=numbers, positions=positions, cell=cell, tags=tags, pbc=[True, True, True])
cr.ax = ax
cr.centers = centers
cr.orgs = orgs
cr.rattlable = rattlable
if sum(tags == 0) == 0 or sum(tags == 1) == 0 or sum(tags == 2) == 0:
print "It seems that either the cell is too small or there are too many grains. You might want to fix this"
return cr
