def test_parameters(self):
folder = os.path.abspath(os.path.join(directory, '..', 'data'))
constants = crystal.parameters(folder=folder, filename='CaTiOSiO4.cif')
a, b, c, alpha, beta, gamma = constants
self.assertAlmostEqual(a, 7.069)
self.assertAlmostEqual(b, 8.722)
self.assertAlmostEqual(c, 6.566)
self.assertAlmostEqual(alpha, np.deg2rad(90))
self.assertAlmostEqual(beta, np.deg2rad(113.86))
self.assertAlmostEqual(gamma, np.deg2rad(90))
def test_pairs(self):
folder = os.path.abspath(os.path.join(directory, '..', 'data'))
uc_dict = crystal.unitcell(folder=folder, filename='CaTiOSiO4.cif')
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
atms = uc_dict['atom']
constants = crystal.parameters(folder=folder, filename='CaTiOSiO4.cif')
A = crystal.cartesian(*constants)
pair_dict = crystal.pairs(u, v, w, atms, A)
pairs = []
coordination = []
for i in pair_dict.keys():
atm = atms[i]
if (atm != 'O'):
pair_num, pair_atm = list(pair_dict[i])[0]
coord_num = len(pair_dict[i][(pair_num, pair_atm)][0])
pairs.append('_'.join((atm, pair_atm)))
coordination.append(coord_num)
pairs = np.array(pairs)
coordination = np.array(coordination)
mask = pairs == 'Ca_O'
np.testing.assert_array_equal(coordination[mask], 7)
mask = pairs == 'Ti_O'
np.testing.assert_array_equal(coordination[mask], 6)
mask = pairs == 'Si_O'
np.testing.assert_array_equal(coordination[mask], 4)
uc_dict = crystal.unitcell(folder=folder, filename='Tb2Ir3Ga9.cif')
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
atms = uc_dict['atom']
constants = crystal.parameters(folder=folder, filename='Tb2Ir3Ga9.cif')
A = crystal.cartesian(*constants)
pair_dict = crystal.pairs(u, v, w, atms, A)
pairs = []
for i in pair_dict.keys():
atm = atms[i]
if (atm == 'Tb'):
for pair in pair_dict[i].keys():
if pair[1] == 'Tb':
for ind in pair_dict[i][pair][0]:
pairs.append([i, ind])
pairs = np.unique(pairs)
self.assertEqual(pairs.size, (atms == 'Tb').sum())
pair_dict = crystal.pairs(u, v, w, atms, A, extend=True)
for i in pair_dict.keys():
d_ref = 0
for pair in pair_dict[i].keys():
j, atm_j = pair
for j, img in zip(*pair_dict[i][pair]):
du = u[j] - u[i] + img[0]
dv = v[j] - v[i] + img[1]
dw = w[j] - w[i] + img[2]
dx, dy, dz = crystal.transform(du, dv, dw, A)
d = np.sqrt(dx**2 + dy**2 + dz**2)
self.assertGreaterEqual(np.round(d, 6), np.round(d_ref, 6))
self.assertEqual(atms[j], atm_j)
d_ref = d
def test_disordered(self):
folder = os.path.abspath(os.path.join(directory, '..', 'data'))
uc_dict = crystal.unitcell(folder=folder,
filename='CaTiOSiO4.cif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
mom = uc_dict['moment']
atm = uc_dict['atom']
n_atm = uc_dict['n_atom']
nu, nv, nw = 2, 3, 4
constants = crystal.parameters(folder=folder, filename='CaTiOSiO4.cif')
A = crystal.cartesian(*constants)
C = crystal.cartesian_moment(*constants)
D = crystal.cartesian_displacement(*constants)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
U11, U22, U33, U23, U13, U12 = disp.T
U = np.row_stack(displacive.cartesian(U11, U22, U33, U23, U13, U12, D))
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, U)
A_r = occupational.composition(nu, nv, nw, n_atm, occ)
delta = (occ * (1 + A_r.reshape(nu, nv, nw, n_atm))).flatten()
mu1, mu2, mu3 = mom.T
mu = np.row_stack(magnetic.cartesian(mu1, mu2, mu3, C))
Sx, Sy, Sz = magnetic.spin(nu, nv, nw, n_atm, mu)
crystal.disordered(delta,
Ux,
Uy,
Uz,
Sx,
Sy,
Sz,
rx,
ry,
rz,
nu,
nv,
nw,
atm,
A,
folder + '/disordered_CaTiOSiO4.cif',
folder=folder,
filename='CaTiOSiO4.cif',
ulim=[0, nu],
vlim=[0, nv],
wlim=[0, nw])
UC_dict = crystal.unitcell(folder=folder,
filename='disordered_CaTiOSiO4.cif',
tol=1e-4)
Atm = UC_dict['atom']
np.testing.assert_array_equal(atms == Atm, True)
os.remove(folder + '/disordered_CaTiOSiO4.cif')
uc_dict = crystal.unitcell(folder=folder,
filename='CuMnO2.mcif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
mom = uc_dict['moment']
atm = uc_dict['atom']
n_atm = uc_dict['n_atom']
nu, nv, nw = 2, 3, 4
constants = crystal.parameters(folder=folder, filename='CuMnO2.mcif')
A = crystal.cartesian(*constants)
C = crystal.cartesian_moment(*constants)
D = crystal.cartesian_displacement(*constants)
ux, uy, uz = crystal.transform(u, v, w, A)
ix, iy, iz = space.cell(nu, nv, nw, A)
rx, ry, rz, atms = space.real(ux, uy, uz, ix, iy, iz, atm)
Uiso = disp.flatten()
Ux, Uy, Uz = displacive.expansion(nu, nv, nw, n_atm, Uiso)
A_r = occupational.composition(nu, nv, nw, n_atm, occ)
delta = (occ * (1 + A_r.reshape(nu, nv, nw, n_atm))).flatten()
mu1, mu2, mu3 = mom.T
mu = np.row_stack(magnetic.cartesian(mu1, mu2, mu3, C))
Sx, Sy, Sz = magnetic.spin(nu, nv, nw, n_atm, mu)
crystal.disordered(delta,
Ux,
Uy,
Uz,
Sx,
Sy,
Sz,
rx,
ry,
rz,
nu,
nv,
nw,
atm,
A,
folder + '/disordered_CuMnO2.mcif',
folder=folder,
filename='CuMnO2.mcif',
ulim=[0, nu],
vlim=[0, nv],
wlim=[0, nw])
UC_dict = crystal.unitcell(folder=folder,
filename='disordered_CuMnO2.mcif',
tol=1e-4)
Atm = UC_dict['atom']
np.testing.assert_array_equal(atms == Atm, True)
os.remove(folder + '/disordered_CuMnO2.mcif')
def test_supercell(self):
folder = os.path.abspath(os.path.join(directory, '..', 'data'))
uc_dict = crystal.unitcell(folder=folder,
filename='CaTiOSiO4.cif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
mom = uc_dict['moment']
atm = uc_dict['atom']
n_atm = uc_dict['n_atom']
constants = crystal.parameters(folder=folder, filename='CaTiOSiO4.cif')
a, b, c, alpha, beta, gamma = constants
nu, nv, nw = 2, 3, 1
crystal.supercell(atm,
occ,
disp,
mom,
u,
v,
w,
nu,
nv,
nw,
folder + '/supercell_CaTiOSiO4.cif',
folder=folder,
filename='CaTiOSiO4.cif')
UC_dict = crystal.unitcell(folder=folder,
filename='supercell_CaTiOSiO4.cif',
tol=1e-4)
U = UC_dict['u']
V = UC_dict['v']
W = UC_dict['w']
Occ = UC_dict['occupancy']
Disp = UC_dict['displacement']
Mom = UC_dict['moment']
Atm = UC_dict['atom']
N_atm = UC_dict['n_atom']
Constants = crystal.parameters(folder=folder,
filename='supercell_CaTiOSiO4.cif')
A, B, C, Alpha, Beta, Gamma = Constants
n_uvw = nu * nv * nw
i, j, k = np.meshgrid(np.arange(nu),
np.arange(nv),
np.arange(nw),
indexing='ij')
i = i.flatten()[:, np.newaxis]
j = j.flatten()[:, np.newaxis]
k = k.flatten()[:, np.newaxis]
np.testing.assert_array_almost_equal((i + u).flatten(), nu * U, 4)
np.testing.assert_array_almost_equal((j + v).flatten(), nv * V, 4)
np.testing.assert_array_almost_equal((k + w).flatten(), nw * W, 4)
np.testing.assert_array_equal(np.tile(atm, n_uvw), Atm)
np.testing.assert_array_almost_equal(np.tile(occ, n_uvw), Occ)
np.testing.assert_array_almost_equal(np.tile(disp.T, n_uvw).T, Disp)
self.assertEqual(n_atm * n_uvw, N_atm)
self.assertAlmostEqual(a * nu, A)
self.assertAlmostEqual(b * nv, B)
self.assertAlmostEqual(c * nw, C)
self.assertAlmostEqual(alpha, Alpha)
self.assertAlmostEqual(beta, Beta)
self.assertAlmostEqual(gamma, Gamma)
os.remove(folder + '/supercell_CaTiOSiO4.cif')
# ---
uc_dict = crystal.unitcell(folder=folder,
filename='CuMnO2.mcif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
mom = uc_dict['moment']
atm = uc_dict['atom']
n_atm = uc_dict['n_atom']
nu, nv, nw = 1, 2, 3
crystal.supercell(atm,
occ,
disp,
mom,
u,
v,
w,
nu,
nv,
nw,
folder + '/supercell_CuMnO2.mcif',
folder=folder,
filename='CuMnO2.mcif')
UC_dict = crystal.unitcell(folder=folder,
filename='supercell_CuMnO2.mcif',
tol=1e-4)
U = UC_dict['u']
V = UC_dict['v']
W = UC_dict['w']
Occ = UC_dict['occupancy']
Disp = UC_dict['displacement']
Mom = UC_dict['moment']
Atm = UC_dict['atom']
N_atm = UC_dict['n_atom']
n_uvw = nu * nv * nw
np.testing.assert_array_almost_equal(np.tile(mom.T, n_uvw).T, Mom)
self.assertEqual((atm == 'Cu').sum() * n_uvw, (Atm == 'Cu').sum())
self.assertEqual((atm == 'Mn').sum() * n_uvw, (Atm == 'Mn').sum())
self.assertEqual((atm == 'O').sum() * n_uvw, (Atm == 'O').sum())
os.remove(folder + '/supercell_CuMnO2.mcif')
def test_factor(self):
folder = os.path.abspath(os.path.join(directory, '..', 'data'))
names = ('h', 'k', 'l', 'd(angstrom)', 'F(real)', 'F(imag)', 'mult')
formats = (int, int, int, float, float, float, int)
uc_dict = crystal.unitcell(folder=folder,
filename='Cu3Au.cif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
atm = uc_dict['atom']
constants = crystal.parameters(folder=folder, filename='Cu3Au.cif')
symops = crystal.operators(folder=folder, filename='Cu3Au.cif')
a, b, c, alpha, beta, gamma = constants
D = crystal.cartesian_displacement(a, b, c, alpha, beta, gamma)
Uiso = 1 / (8 * np.pi**2)
uiso = np.dot(np.linalg.inv(D), np.linalg.inv(D.T))
U11, U22, U33 = Uiso * uiso[0, 0], Uiso * uiso[1, 1], Uiso * uiso[2, 2]
U23, U13, U12 = Uiso * uiso[1, 2], Uiso * uiso[0, 2], Uiso * uiso[0, 1]
h, k, l, d, F, mult = structure.factor(u,
v,
w,
atm,
occ,
U11,
U22,
U33,
U23,
U13,
U12,
a,
b,
c,
alpha,
beta,
gamma,
symops,
dmin=0.7,
source='neutron')
data = np.loadtxt(os.path.join(folder, 'Cu3Au.csv'),
dtype={
'names': names,
'formats': formats
},
delimiter=',',
skiprows=1,
unpack=True)
np.testing.assert_array_equal(h, data[0])
np.testing.assert_array_equal(k, data[1])
np.testing.assert_array_equal(l, data[2])
np.testing.assert_array_equal(mult, data[6])
np.testing.assert_array_almost_equal(d, data[3])
np.testing.assert_array_almost_equal(F.real, data[4], decimal=4)
np.testing.assert_array_almost_equal(F.imag, data[5], decimal=4)
uc_dict = crystal.unitcell(folder=folder,
filename='CaTiOSiO4.cif',
tol=1e-4)
u = uc_dict['u']
v = uc_dict['v']
w = uc_dict['w']
occ = uc_dict['occupancy']
disp = uc_dict['displacement']
atm = uc_dict['atom']
constants = crystal.parameters(folder=folder, filename='CaTiOSiO4.cif')
symops = crystal.operators(folder=folder, filename='CaTiOSiO4.cif')
a, b, c, alpha, beta, gamma = constants
U11, U22, U33, U23, U13, U12 = disp.T
h, k, l, d, F, mult = structure.factor(u,
v,
w,
atm,
occ,
U11,
U22,
U33,
U23,
U13,
U12,
a,
b,
c,
alpha,
beta,
gamma,
symops,
dmin=0.7,
source='neutron')
data = np.loadtxt(os.path.join(folder, 'CaTiOSiO4.csv'),
dtype={
'names': names,
'formats': formats
},
delimiter=',',
skiprows=1,
unpack=True)
np.testing.assert_array_equal(h, data[0])
np.testing.assert_array_equal(k, data[1])
np.testing.assert_array_equal(l, data[2])
np.testing.assert_array_equal(mult, data[6])
np.testing.assert_array_almost_equal(d, data[3])
np.testing.assert_array_almost_equal(F.real, data[4], decimal=4)
np.testing.assert_array_almost_equal(F.imag, data[5], decimal=4)
def load_lattice_parameters(self, folder, filename):
return crystal.parameters(folder=folder, filename=filename)