hR1

Reference

POSCAR files with the crystal structure for these examples are taken from the seekpath repository with the permission of its authors. We refer you to seekpath for the original copies of the files and the license for those. To read more about the extended Bravais lattice symbols, chosen high-symmetry points and k-paths we refer you to the HPKOT paper.

Getting an example

To get an example crystal use wulfric.crystal.hpkot_get_example().

import wulfric

# For every extended bravais lattice symbol two examples are defined:
# with and without inversion symmetry.
cell, atoms = wulfric.crystal.hpkot_get_example(
    extended_bl_symbol="hR1", with_inversion=False
)

# 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="HPKOT", with_time_reversal=True
)

kp_no_tr = wulfric.Kpoints.from_crystal(
    cell=cell, atoms=atoms, convention="HPKOT", with_time_reversal=False
)

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

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

K-path

print(kp.path_string)

GAMMA-T-H2|H0-L-GAMMA-S0|S2-F-GAMMA

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
T      -0.0000  0.0000  1.0000  -0.0000  0.0000  0.6131
L       0.3333  0.0000  0.3333   0.4861  0.2806  0.2044
L2      0.3333 -0.3333 -0.3333   0.4861 -0.2806 -0.2044
L4      0.0000  0.3333 -0.3333   0.0000  0.5612 -0.2044
F       0.3333 -0.3333  0.6667   0.4861 -0.2806  0.4087
F2      0.0000  0.3333  0.6667   0.0000  0.5612  0.4087
S0      0.5034 -0.2517 -0.0000   0.7340  0.0000 -0.0000
S2      0.4150 -0.2517  0.6667   0.6051 -0.0744  0.4087
S4      0.2517  0.2517 -0.0000   0.3670  0.6357 -0.0000
S6      0.1633  0.2517  0.6667   0.2381  0.5612  0.4087
H0      0.5034 -0.3401  0.3333   0.7340 -0.1488  0.2044
H2      0.3266 -0.1633  1.0000   0.4762  0.0000  0.6131
H4      0.1633  0.1633  1.0000   0.2381  0.4124  0.6131
H6      0.1633  0.3401  0.3333   0.2381  0.7101  0.2044
M0      0.4217 -0.4217  0.3333   0.6149 -0.3550  0.2044
M2      0.2449 -0.2449  1.0000   0.3572 -0.2062  0.6131
M4      0.2449  0.0000  1.0000   0.3572  0.2062  0.6131
M6      0.0000  0.2449  1.0000   0.0000  0.4124  0.6131
M8      0.0000  0.4217  0.3333   0.0000  0.7101  0.2044

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, legend_group="with TR", legend_label="With time-reversal")
pe.plot_kpoints(kp=kp, only_from_kpath=True, legend_group="with TR")

pe.plot_kpath(
    kp=kp_no_tr,
    color="#7D7D7D",
    legend_group="without TR",
    legend_label="Without time-reversal",
)
pe.plot_kpoints(
    kp=kp_no_tr, only_from_kpath=True, color="#7D7D7D", legend_group="without TR"
)

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)