K-path and k-points

This page explains how to plot a set of atoms.

import wulfric
import numpy as np

cell = np.array(
    [
        [5.64, 0.00, 0.00],
        [0.00, 5.64, 0.00],
        [0.00, 0.00, 5.64],
    ]
)
atoms = {
    "names": ["Cl1", "Cl2", "Cl3", "Cl4", "Na1", "Na2", "Na3", "Na4"],
    "positions": np.array(
        [
            (0, 0, 0),
            (1 / 2, 1 / 2, 0),
            (1 / 2, 0, 1 / 2),
            (0, 1 / 2, 1 / 2),
            (1 / 2, 1 / 2, 1 / 2),
            (1 / 2, 0, 0),
            (0, 1 / 2, 0),
            (0, 0, 1 / 2),
        ]
    ),
}

spglib_data = wulfric.get_spglib_data(cell, atoms)

Best way to interact with high-symmetry points and k-path is trough the wulfric.Kpoints. First, we create one

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

Now one can check the recommended k-path and pre-defined high-symmetry points

print(kp.path_string)

print(kp.hs_table())

GAMMA-X-U|K-GAMMA-L-W-X
Name        rel_b1      rel_b2      rel_b3          k_x         k_y         k_z
GAMMA   0.00000000  0.00000000  0.00000000   0.00000000  0.00000000  0.00000000
X       0.00000000  1.00000000  0.00000000   0.00000000  1.11403995  0.00000000
L       0.50000000  0.50000000  0.50000000   0.55701997  0.55701997  0.55701997
W       0.50000000  1.00000000 -0.00000000   0.55701997  1.11403995 -0.00000000
W2      0.00000000  1.00000000  0.50000000   0.00000000  1.11403995  0.55701997
K       0.75000000  0.75000000 -0.00000000   0.83552996  0.83552996 -0.00000000
U       0.25000000  1.00000000  0.25000000   0.27850999  1.11403995  0.27850999

High-symmetry points are given by relative coordinates with respect to the reciprocal cell of the original cell. However, the points correspond to the Brillouin zone of the primitive cell, which may or may not be the one that have k-path and high symmetry points lying on its edges

prim_cell, _ = wulfric.crystal.get_primitive(cell, atoms, spglib_data=spglib_data)

pe = wulfric.PlotlyEngine(_sphinx_gallery_fix=True)

pe.plot_brillouin_zone(
    cell=prim_cell, color="red", legend_label="Brillouin zone of primitive cell"
)
pe.plot_kpath(kp=kp, legend_label="K-path")
pe.plot_kpoints(kp=kp, legend_label="K-points")


pe.plot_brillouin_zone(
    cell=cell, color="chocolate", legend_label="Brillouin zone of original cell"
)

pe.show()