def setup(self, omega_step, grain_ids=None):
"""Setup the forward simulation.
:param float omega_step: the angular integration step (in degrees) use to compute the diffraction comditions.
:param list grain_ids: a list of grain ids to restrict the forward simulation (use all grains by default).
"""
assert self.exp.source.min_energy == self.exp.source.max_energy # monochromatic case
lambda_keV = self.exp.source.max_energy
self.omegas = np.linspace(0.0,
360.0,
num=int(360.0 / omega_step),
endpoint=False)
self.reflections = []
for omega in self.omegas:
self.reflections.append([])
if grain_ids:
# make a list of the grains selected for the forward simulation
grains = [
self.exp.sample.microstructure.get_grain(gid)
for gid in grain_ids
]
else:
grains = self.exp.sample.microstructure.grains
for g in grains:
for plane in self.hkl_planes:
(h, k, i,
l) = HklPlane.three_to_four_indices(*plane.miller_indices())
try:
(w1, w2) = g.dct_omega_angles(plane,
lambda_keV,
verbose=False)
except ValueError:
if self.verbose:
print(
'plane {} does not fulfil the Bragg condition for grain {:d}'
.format((h, k, i, l), g.id))
continue
# add angles for Friedel pairs
w3 = (w1 + 180.) % 360
w4 = (w2 + 180.) % 360
if self.verbose and g.id == self.check:
print(
'grain %d, angles for plane %d%d%d: w1=%.3f and w2=%.3f | delta=%.1f'
% (g.id, h, k, l, w1, w2, w1 - w2))
print('(%3d, %3d, %3d, %3d) -- %6.2f & %6.2f' %
(h, k, i, l, w1, w2))
self.reflections[int(w1 / omega_step)].append(
[g.id, (h, k, l)])
self.reflections[int(w2 / omega_step)].append(
[g.id, (h, k, l)])
self.reflections[int(w3 / omega_step)].append(
[g.id, (-h, -k, -l)])
self.reflections[int(w4 / omega_step)].append(
[g.id, (-h, -k, -l)])
def setup(self, omega_step):
"""Setup the forward simulation."""
assert self.exp.source.min_energy == self.exp.source.max_energy # monochromatic case
lambda_keV = self.exp.source.max_energy
self.omegas = np.linspace(0.0,
360.0,
num=int(360.0 / omega_step),
endpoint=False)
self.reflections = []
for omega in self.omegas:
self.reflections.append([])
for g in self.exp.sample.microstructure.grains:
for plane in self.hkl_planes:
(h, k, i,
l) = HklPlane.three_to_four_indices(*plane.miller_indices())
try:
(w1, w2) = g.dct_omega_angles(plane,
lambda_keV,
verbose=False)
except ValueError:
if self.verbose:
print(
'plane {} does not fulfil the Bragg condition for grain {:d}'
.format((h, k, i, l), g.id))
continue
# add angles for Friedel pairs
w3 = (w1 + 180.) % 360
w4 = (w2 + 180.) % 360
if self.verbose and g.id == self.check:
print(
'grain %d, angles for plane %d%d%d: w1=%.3f and w2=%.3f | delta=%.1f'
% (g.id, h, k, l, w1, w2, w1 - w2))
print('(%3d, %3d, %3d, %3d) -- %6.2f & %6.2f' %
(h, k, i, l, w1, w2))
self.reflections[int(w1 / omega_step)].append(
[g.id, (h, k, l)])
self.reflections[int(w2 / omega_step)].append(
[g.id, (h, k, l)])
self.reflections[int(w3 / omega_step)].append(
[g.id, (-h, -k, -l)])
self.reflections[int(w4 / omega_step)].append(
[g.id, (-h, -k, -l)])
def plot_sst(self, ax=None, mk='s', ann=False):
""" Create the inverse pole figure in the unit standard triangle.
:param ax: a reference to a pyplot ax to draw the poles.
:param mk: marker used to plot the poles (square by default).
:param bool ann: Annotate the pole with the coordinates of the vector if True (False by default).
"""
# first draw the boundary of the symmetry domain limited by 3 hkl plane normals, called here A, B and C
symmetry = self.lattice._symmetry
if symmetry is Symmetry.cubic:
sst_poles = [(0, 0, 1), (1, 0, 1), (1, 1, 1)]
ax.axis([-0.05, 0.45, -0.05, 0.40])
elif symmetry is Symmetry.hexagonal:
sst_poles = [(0, 0, 1), (2, -1, 0), (1, 0, 0)]
ax.axis([-0.05, 1.05, -0.05, 0.6])
else:
print('unssuported symmetry: %s' % symmetry)
A = HklPlane(*sst_poles[0], lattice=self.lattice)
B = HklPlane(*sst_poles[1], lattice=self.lattice)
C = HklPlane(*sst_poles[2], lattice=self.lattice)
self.plot_line_between_crystal_dir(A.normal(),
B.normal(),
ax=ax,
col='k')
self.plot_line_between_crystal_dir(B.normal(),
C.normal(),
ax=ax,
col='k')
self.plot_line_between_crystal_dir(C.normal(),
A.normal(),
ax=ax,
col='k')
# display the 3 crystal axes
poles = [A, B, C]
v_align = ['top', 'top', 'bottom']
for i in range(3):
hkl = poles[i]
c_dir = hkl.normal()
c = c_dir + self.z
c /= c[2] # SP'/SP = r/z with r=1
pole_str = '%d%d%d' % hkl.miller_indices()
if symmetry is Symmetry.hexagonal:
pole_str = '%d%d%d%d' % HklPlane.three_to_four_indices(
*hkl.miller_indices())
ax.annotate(pole_str, (c[0], c[1] - (2 * (i < 2) - 1) * 0.01),
xycoords='data',
fontsize=12,
horizontalalignment='center',
verticalalignment=v_align[i])
# now plot the sample axis
for grain in self.microstructure.grains:
# move to the fundamental zone
g = grain.orientation_matrix()
# compute axis and apply SST symmetry
if self.axis == 'Z':
axis = self.z
elif self.axis == 'Y':
axis = self.y
else:
axis = self.x
axis_rot = self.sst_symmetry(g.dot(axis))
label = ''
if self.map_field == 'grain_id':
label = 'grain ' + str(grain.id)
self.plot_crystal_dir(axis_rot,
mk=mk,
col=self.get_color_from_field(grain),
ax=ax,
ann=ann,
lab=label)
if self.verbose:
print('plotting %s in crystal CS: %s' % (self.axis, axis_rot))
ax.axis('off')
ax.set_title('%s-axis SST inverse %s projection' %
(self.axis, self.proj))