ORCI

Body-centered orthorhombic cell is defined by three parameters \(a\), \(b\) and \(c\) with \(a < b < c\).

Cell constructor

To get an example of the cell use wulfric.cell.SC_ORCI().

wulfric.cell.sc_get_example() returns an example where \(a = \pi\), \(b = 1.3\pi\) and \(c = 1.7\pi\).

import wulfric

cell = wulfric.cell.sc_get_example("ORCI")
atoms = dict(positions=[[0, 0, 0]], spglib_types=[1])

# To avoid multiple calls to spglib one can do it once and then pass spglib_data
# to the functions where it is needed
spglib_data = wulfric.get_spglib_data(cell=cell, atoms=atoms)

kp = wulfric.Kpoints.from_crystal(cell=cell, atoms=atoms, convention="SC")

conv_cell, conv_atoms = wulfric.crystal.get_conventional(
    cell=cell, atoms=atoms, convention="SC", spglib_data=spglib_data
)

prim_cell, prim_atoms = wulfric.crystal.get_primitive(
    cell=cell, atoms=atoms, convention="SC", spglib_data=spglib_data
)

K-path

print(kp.path_string)

GAMMA-X-L-T-W-R-X1-Z-GAMMA-Y-S-W|L1-Y|Y1-Z

High-symmetry points

print(kp.hs_table(decimals=4))

Name    rel_b1  rel_b2  rel_b3      k_x     k_y     k_z
GAMMA   0.0000  0.0000  0.0000   0.0000  0.0000  0.0000
L      -0.2327  0.2327  0.4403   1.3460  0.3194  0.0000
L1      0.2327 -0.2327  0.5597   0.6540  1.2191  0.0000
L2      0.4403  0.5597 -0.2327   0.6540  0.3194  1.1765
R      -0.0000  0.5000 -0.0000   1.0000 -0.0000  0.5882
S       0.5000  0.0000 -0.0000   0.0000  0.7692  0.5882
T       0.0000  0.0000  0.5000   1.0000  0.7692  0.0000
W       0.2500  0.2500  0.2500   1.0000  0.7692  0.5882
X      -0.3365  0.3365  0.3365   1.3460  0.0000  0.0000
X1      0.3365  0.6635 -0.3365   0.6540 -0.0000  1.1765
Y       0.3962 -0.3962  0.3962   0.0000  1.2191  0.0000
Y1      0.6038  0.3962 -0.3962   0.0000  0.3194  1.1765
Z       0.5000  0.5000 -0.5000   0.0000 -0.0000  1.1765

Brillouin zone and default k-path

pe = wulfric.PlotlyEngine(_sphinx_gallery_fix=True)

pe.plot_brillouin_zone(
    cell=prim_cell, color="red", legend_label="Brillouin zone of the primitive cell"
)
pe.plot_brillouin_zone(
    cell=cell, color="chocolate", legend_label="Brillouin zone of the original cell"
)
pe.plot_kpath(kp=kp)
pe.plot_kpoints(kp=kp, only_from_kpath=True)

pe.show(axes_visible=False)

Cells of real space

pe = wulfric.PlotlyEngine(_sphinx_gallery_fix=True)

pe.plot_cell(cell=cell, legend_label="Original cell", color="Chocolate")
pe.plot_cell(cell=prim_cell, legend_label="Primitive cell", color="Black")
pe.plot_cell(cell=conv_cell, legend_label="Conventional cell", color="Blue")
pe.plot_wigner_seitz_cell(
    cell=prim_cell, legend_label="Wigner-Seitz cell", color="green"
)

pe.show(axes_visible=False)

Edge cases

If \(a = b \ne c\) or \(a = c \ne b\) or \(b = c \ne a\), then the lattice is BCT1 or BCT2.

If \(a = b = c\), then the lattice is BCC.