def test_cell_intensity(self):
# Test that bcc structure gives lower intensity for h + k + l != even.
c = TEMCalculator()
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(2, 1, 0)]
point2 = [(2, 2, 0)]
spacings = c.get_interplanar_spacings(cubic, point)
spacings2 = c.get_interplanar_spacings(cubic, point2)
angles = c.bragg_angles(spacings)
angles2 = c.bragg_angles(spacings2)
cellint = c.cell_intensity(cubic, angles)
cellint2 = c.cell_intensity(cubic, angles2)
self.assertGreater(cellint2[(2, 2, 0)], cellint[(2, 1, 0)])
def test_bragg_angles(self):
# Tests that the appropriate bragg angle is returned. Testing formula with values of x-ray diffraction in
# materials project.
c = TEMCalculator()
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(1, 1, 0)]
spacings = c.get_interplanar_spacings(cubic, point)
bragg_angles_val = np.arcsin(1.5406 / (2 * spacings[point[0]]))
self.assertAlmostEqual(bragg_angles_val, 0.262, places=3)
def test_normalized_cell_intensity(self):
# Test that the method correctly normalizes a value.
c = TEMCalculator()
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(2, 0, 0)]
spacings = c.get_interplanar_spacings(cubic, point)
angles = c.bragg_angles(spacings)
cellint = c.normalized_cell_intensity(cubic, angles)
self.assertAlmostEqual(cellint[(2, 0, 0)], 1)
def test_x_ray_factors(self):
c = TEMCalculator()
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(-10, 3, 0)]
spacings = c.get_interplanar_spacings(cubic, point)
angles = c.bragg_angles(spacings)
x_ray = c.x_ray_factors(cubic, angles)
self.assertAlmostEqual(x_ray["Cs"][(-10, 3, 0)], 14.42250869579648)
self.assertAlmostEqual(x_ray["Cl"][(-10, 3, 0)], 2.7804915737999103)
def test_cell_scattering_factors(self):
# Test that fcc structure gives 0 intensity for mixed even, odd hkl.
c = TEMCalculator()
nacl = Structure.from_spacegroup("Fm-3m", Lattice.cubic(5.692),
["Na", "Cl"],
[[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(2, 1, 0)]
spacings = c.get_interplanar_spacings(nacl, point)
angles = c.bragg_angles(spacings)
cellscatt = c.cell_scattering_factors(nacl, angles)
self.assertAlmostEqual(cellscatt[(2, 1, 0)], 0)
def test_get_s2(self):
# Tests that the appropriate s2 factor is returned.
c = TEMCalculator()
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(-10, 3, 0)]
spacings = c.get_interplanar_spacings(cubic, point)
angles = c.bragg_angles(spacings)
s2 = c.get_s2(angles)
for p in s2:
self.assertAlmostEqual(s2[p], 1.5381852947115047)
def test_get_interplanar_spacings(self):
# Tests that the appropriate interplacing spacing is returned
c = TEMCalculator()
point = [(3, 9, 0)]
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
tet = self.get_structure("Li10GeP2S12")
hexa = self.get_structure("Graphite")
ortho = self.get_structure("K2O2")
mono = self.get_structure("Li3V2(PO4)3")
spacings_cubic = c.get_interplanar_spacings(cubic, point)
spacings_tet = c.get_interplanar_spacings(tet, point)
spacings_hexa = c.get_interplanar_spacings(hexa, point)
spacings_ortho = c.get_interplanar_spacings(ortho, point)
spacings_mono = c.get_interplanar_spacings(mono, point)
for p in point:
self.assertAlmostEqual(spacings_cubic[p], 0.4436675557216236)
self.assertAlmostEqual(spacings_tet[p], 0.9164354445646701)
self.assertAlmostEqual(spacings_hexa[p], 0.19775826179547752)
self.assertAlmostEqual(spacings_ortho[p], 0.5072617738916)
self.assertAlmostEqual(spacings_mono[p], 0.84450786041677972)
def test_electron_scattering_factors(self):
# Test the electron atomic scattering factor, values approximate with
# international table of crystallography volume C. Rounding error when converting hkl to sin(theta)/lambda.
# Error increases as sin(theta)/lambda is smaller.
c = TEMCalculator()
latt = Lattice.cubic(4.209)
cubic = Structure(latt, ["Cs", "Cl"], [[0, 0, 0], [0.5, 0.5, 0.5]])
nacl = Structure.from_spacegroup("Fm-3m", Lattice.cubic(5.692),
["Na", "Cl"],
[[0, 0, 0], [0.5, 0.5, 0.5]])
point = [(2, 1, 3)]
point_nacl = [(4, 2, 0)]
spacings = c.get_interplanar_spacings(cubic, point)
spacings_nacl = c.get_interplanar_spacings(nacl, point_nacl)
angles = c.bragg_angles(spacings)
angles_nacl = c.bragg_angles(spacings_nacl)
elscatt = c.electron_scattering_factors(cubic, angles)
elscatt_nacl = c.electron_scattering_factors(nacl, angles_nacl)
self.assertAlmostEqual(elscatt["Cs"][(2, 1, 3)], 2.890, places=1)
self.assertAlmostEqual(elscatt["Cl"][(2, 1, 3)], 1.138, places=1)
self.assertAlmostEqual(elscatt_nacl["Na"][(4, 2, 0)], 0.852, places=1)
self.assertAlmostEqual(elscatt_nacl["Cl"][(4, 2, 0)], 1.372, places=1)
