TRI1b

Triclinic cell is defined by six parameters \(a\), \(b\), \(c\) and \(\alpha\), \(\beta\), \(\gamma\).

TRI lattice has variation TRI1b when \(k_{\alpha} < 90^{\circ}, k_{\beta} < 90^{\circ}, k_{\gamma} < 90^{\circ}\) and \(k_{\gamma} = \max(k_{\alpha}, k_{\beta}, k_{\gamma})\).

Cell constructor

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

import wulfric

cell = wulfric.cell.sc_get_example("TRI1b")
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
)

variation = wulfric.crystal.sc_get_variation(
    cell=cell, atoms=atoms, spglib_data=spglib_data
)

assert variation == "TRI1b"

print(variation)

TRI1b

K-path

print(kp.path_string)

X-GAMMA-Y|L-GAMMA-Z|N-GAMMA-M|R-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
L       0.5000  1.0000 -0.5000   6.2832  3.6276 -1.0446
M       0.0000  0.0000 -0.5000   0.0000  0.0000 -3.3432
N      -0.5000  0.0000  0.0000  -6.2832  3.6276 -2.2751
R       0.0000  0.5000 -0.5000   0.0000  3.6276 -3.3315
X       0.0000  0.5000 -0.0000   0.0000  3.6276  0.0118
Y       0.5000  0.5000 -0.5000   6.2832 -0.0000 -1.0563
Z      -0.5000 -0.5000  0.0000  -6.2832  0.0000 -2.2869

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)