def test_multiplicity(self, nickel_phase, silicon_carbide_phase):
assert np.allclose(
ReciprocalLatticePoint.from_min_dspacing(
phase=nickel_phase, min_dspacing=1
).multiplicity,
# fmt: off
np.array([
8, 24, 24, 24, 12, 24, 48, 48, 24, 24, 48, 24, 24, 24, 6, 8, 24,
24, 12, 24, 48, 24, 24, 24, 6, 8, 24, 12, 24, 24, 6, 8, 12, 6
])
# fmt: on
)
assert np.allclose(
ReciprocalLatticePoint.from_min_dspacing(
phase=silicon_carbide_phase, min_dspacing=1
).multiplicity,
# fmt: off
np.array([
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6,
6, 6, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 12,
12, 12, 12, 12, 12, 12, 12, 12, 12, 6, 6, 6, 6, 6, 6, 6, 6, 6, 1, 1,
1, 1, 1, 1, 1, 1
])
# fmt: on
)
def test_init_from_min_dspacing(self, ferrite_phase, min_dspacing, desired_size):
assert (
ReciprocalLatticePoint.from_min_dspacing(
phase=ferrite_phase, min_dspacing=min_dspacing
).size
== desired_size
)
def test_gspacing_dspacing_scattering_parameter(self, ferrite_phase):
rlp = ReciprocalLatticePoint.from_min_dspacing(
phase=ferrite_phase, min_dspacing=2
)
# fmt: off
assert np.allclose(
rlp.gspacing,
np.array([
1.2084778, 1.04657248, 0.98671799, 0.85452285, 0.78006907, 0.69771498,
0.604238, 0.493359, 0.34885749
])
)
assert np.allclose(
rlp.dspacing,
np.array([
0.82748727, 0.9555, 1.01346079, 1.17024372, 1.28193777, 1.43325,
1.65497455, 2.02692159, 2.8665
])
)
assert np.allclose(
rlp.scattering_parameter,
np.array([
0.6042389, 0.52328624, 0.493359, 0.42726142, 0.39003453, 0.34885749,
0.30211945, 0.2466795, 0.17442875
])
)
def test_get_hkl(self, silicon_carbide_phase):
rlp = ReciprocalLatticePoint.from_min_dspacing(
silicon_carbide_phase, min_dspacing=3
)
assert np.allclose(rlp.h, [1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 0, 0])
assert np.allclose(rlp.k, [1, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0])
assert np.allclose(rlp.l, [4, 3, 2, 1, 0, 4, 3, 2, 0, 4, 3, 2])
def test_repr(self, ferrite_phase):
rlp = ReciprocalLatticePoint.from_min_dspacing(ferrite_phase, min_dspacing=2)
assert repr(rlp) == (
f"ReciprocalLatticePoint (9,)\n"
f"Phase: ferrite (m-3m)\n"
"[[2 2 2]\n [2 2 1]\n [2 2 0]\n [2 1 1]\n [2 1 0]\n [2 0 0]\n [1 1 1]\n"
" [1 1 0]\n [1 0 0]]"
)
def test_get_item(self, ferrite_phase):
rlp = ReciprocalLatticePoint.from_min_dspacing(
phase=ferrite_phase, min_dspacing=1.5
)
rlp.calculate_structure_factor()
rlp.calculate_theta(voltage=20e3)
assert rlp[0].size == 1
assert rlp[:2].size == 2
assert np.allclose(rlp[5:7].hkl.data, rlp.hkl[5:7].data)
assert np.allclose(rlp[10:13].structure_factor, rlp.structure_factor[10:13])
assert np.allclose(rlp[20:23].theta, rlp.theta[20:23])
assert rlp.phase.space_group.number == rlp[0].phase.space_group.number
assert rlp.phase.point_group.name == rlp[10:15].phase.point_group.name
assert np.allclose(
rlp.phase.structure.lattice.abcABG(),
rlp[20:23].phase.structure.lattice.abcABG(),
)
def test_allowed_raises(self, silicon_carbide_phase):
with pytest.raises(NotImplementedError):
_ = ReciprocalLatticePoint.from_min_dspacing(
phase=silicon_carbide_phase, min_dspacing=1
).allowed
def geometrical_simulation(
self,
reciprocal_lattice_point: Optional[ReciprocalLatticePoint] = None
) -> GeometricalEBSDSimulation:
"""Project a set of Kikuchi bands and zone axes onto the
detector, one set for each rotation of the unit cell.
The zone axes are calculated from the Kikuchi bands.
Parameters
----------
reciprocal_lattice_point
Crystal planes to project onto the detector. If None, and
the generator has a phase with a unit cell with a point
group, a set of planes with minimum distance of 1 Å and
their symmetrically equivalent planes are used.
Returns
-------
GeometricalEBSDSimulation
Examples
--------
>>> from diffsims.crystallography import ReciprocalLatticePoint
>>> simgen
EBSDSimulationGenerator (1,)
EBSDDetector (60, 60), px_size 1 um, binning 1, tilt 0, pc
(0.5, 0.5, 0.5)
<name: . space group: None. point group: None. proper point
group: None. color: tab:blue>
Rotation (1,)
>>> sim1 = simgen.geometrical_simulation()
>>> sim1.bands.size
94
>>> rlp = ReciprocalLatticePoint(
... phase=simgen.phase, hkl=[[1, 1, 1], [2, 0, 0]]
... )
>>> sim2 = simgen.geometrical_simulation()
>>> sim2.bands.size
13
"""
rlp = reciprocal_lattice_point
if rlp is None and (hasattr(self.phase.point_group, "name") and
hasattr(self.phase.structure.lattice, "abcABG")):
rlp = ReciprocalLatticePoint.from_min_dspacing(self.phase,
min_dspacing=1)
rlp = rlp[rlp.allowed].symmetrise()
elif rlp is None:
raise ValueError("A ReciprocalLatticePoint object must be passed")
self._rlp_phase_is_compatible(rlp)
# Unit cell parameters (called more than once)
phase = rlp.phase
hkl = rlp._hkldata
# Get number of navigation dimensions and navigation axes
# indices
n_nav_dims = self.navigation_dimension
navigation_axes = (1, 2)[:n_nav_dims]
# Get Kikuchi band coordinates for all bands in all patterns
# U_Kstar, transformation from detector frame D to reciprocal
# crystal lattice frame Kstar.
# Output shape is (3, n, 3) or (3, ny, nx, 3)
det2recip = detector2reciprocal_lattice(
sample_tilt=self.detector.sample_tilt,
detector_tilt=self.detector.tilt,
lattice=phase.structure.lattice,
rotation=self.rotations,
)
# Output shape is (nhkl, n, 3) or (nhkl, ny, nx, 3)
hkl_detector = np.tensordot(hkl, det2recip, axes=(1, 0))
if n_nav_dims == 0:
hkl_detector = hkl_detector.squeeze()
# Get bands that are in some pattern
hkl_is_upper, hkl_in_a_pattern = _get_coordinates_in_upper_hemisphere(
z_coordinates=hkl_detector[..., 2],
navigation_axes=navigation_axes)
hkl = hkl[hkl_in_a_pattern, ...]
hkl_in_pattern = hkl_is_upper[hkl_in_a_pattern, ...].T
# Get coordinates in the proper shape
hkl_detector = np.moveaxis(hkl_detector[hkl_in_a_pattern],
source=0,
destination=n_nav_dims)
# And store it all
bands = KikuchiBand(
phase=phase,
hkl=hkl,
hkl_detector=hkl_detector,
in_pattern=hkl_in_pattern,
gnomonic_radius=self.detector.r_max,
)
# Get zone axes coordinates from Kikuchi bands
uvw = _get_uvw_from_hkl(hkl=hkl)
det2direct = detector2direct_lattice(
sample_tilt=self.detector.sample_tilt,
detector_tilt=self.detector.tilt,
lattice=self.phase.structure.lattice,
rotation=self.rotations,
)
uvw_detector = np.tensordot(uvw, det2direct, axes=(1, 0))
if n_nav_dims == 0:
uvw_detector = uvw_detector.squeeze()
uvw_is_upper, uvw_in_a_pattern = _get_coordinates_in_upper_hemisphere(
z_coordinates=uvw_detector[..., 2],
navigation_axes=navigation_axes)
uvw = uvw[uvw_in_a_pattern, ...]
uvw_in_pattern = uvw_is_upper[uvw_in_a_pattern, ...].T
uvw_detector = np.moveaxis(uvw_detector[uvw_in_a_pattern],
source=0,
destination=n_nav_dims)
zone_axes = ZoneAxis(
phase=phase,
uvw=uvw,
uvw_detector=uvw_detector,
in_pattern=uvw_in_pattern,
gnomonic_radius=self.detector.r_max,
)
return GeometricalEBSDSimulation(
detector=self.detector,
rotations=self.rotations,
bands=bands,
zone_axes=zone_axes,
)
def geometrical_simulation(
self,
reciprocal_lattice_point: Optional[ReciprocalLatticePoint] = None,
) -> GeometricalEBSDSimulation:
"""Project a set of center positions of Kikuchi bands on the
detector, one set for each rotation of the unit cell.
Parameters
----------
reciprocal_lattice_point :
Crystal planes to project onto the detector. If None, and
the generator has a phase with a unit cell with a point
group, a set of planes with minimum distance of 1 Å and
their symmetrically equivalent planes are used.
Returns
-------
GeometricalEBSDSimulation
Examples
--------
>>> from diffsims.crystallography import ReciprocalLatticePoint
>>> simgen
EBSDSimulationGenerator (1,)
EBSDDetector (60, 60), px_size 1 um, binning 1, tilt 0, pc
(0.5, 0.5, 0.5)
<name: . space group: None. point group: None. proper point
group: None. color: tab:blue>
Rotation (1,)
>>> sim1 = simgen.geometrical_simulation()
>>> sim1.bands.size
94
>>> rlp = ReciprocalLatticePoint(
... phase=simgen.phase, hkl=[[1, 1, 1], [2, 0, 0]]
... )
>>> sim2 = simgen.geometrical_simulation()
>>> sim2.bands.size
13
"""
rlp = reciprocal_lattice_point
if rlp is None and (hasattr(self.phase.point_group, "name") and
hasattr(self.phase.structure.lattice, "abcABG")):
rlp = ReciprocalLatticePoint.from_min_dspacing(self.phase,
min_dspacing=1)
rlp = rlp[rlp.allowed].symmetrise()
elif rlp is None:
raise ValueError("A ReciprocalLatticePoint object must be passed")
self._rlp_phase_is_compatible(rlp)
# Unit cell parameters (called more than once)
phase = rlp.phase
hkl = rlp._hkldata
# Get Kikuchi band coordinates for all bands in all patterns
# U_Kstar, transformation from detector frame D to reciprocal crystal
# lattice frame Kstar
# TODO: Possible bottleneck due to large dot products! Room for
# lots of improvements with dask.
# Output shape is (3, n, 3) or (3, ny, nx, 3)
det2recip = detector2reciprocal_lattice(
sample_tilt=self.detector.sample_tilt,
detector_tilt=self.detector.tilt,
lattice=phase.structure.lattice,
rotation=self.rotations,
)
# Output shape is (nhkl, n, 3) or (nhkl, ny, nx, 3)
band_coordinates = np.tensordot(hkl, det2recip, axes=(1, 0))
# Determine whether a band is visible in a pattern
upper_hemisphere = band_coordinates[..., 2] > 0
nav_dim = self.navigation_dimension
navigation_axes = (1, 2)[:nav_dim]
is_in_some_pattern = np.sum(upper_hemisphere,
axis=navigation_axes) != 0
# Get bands that were in some pattern and their coordinates in the
# proper shape
hkl = hkl[is_in_some_pattern, ...]
hkl_in_pattern = upper_hemisphere[is_in_some_pattern, ...].T
band_coordinates = np.moveaxis(band_coordinates[is_in_some_pattern],
source=0,
destination=nav_dim)
# And store it all
bands = KikuchiBand(
phase=phase,
hkl=hkl,
hkl_detector=band_coordinates,
in_pattern=hkl_in_pattern,
gnomonic_radius=self.detector.r_max,
)
# Get zone axes coordinates
# U_K, transformation from detector frame D to direct crystal lattice
# frame K
# det2direct = detector2direct_lattice(
# sample_tilt=self.detector.sample_tilt,
# detector_tilt=self.detector.tilt,
# lattice=phase.structure.lattice,
# orientation=self.orientations,
# )
# hkl_transposed_upper = hkl_transposed[..., upper_hemisphere]
# axis_coordinates = det2direct.T.dot(hkl_transposed_upper).T
# zone_axes = ZoneAxis(
# phase=phase, hkl=upper_hkl, coordinates=axis_coordinates
# )
return GeometricalEBSDSimulation(
detector=self.detector,
rotations=self.rotations,
bands=bands,
# zone_axes=zone_axes,
)