MCLC3

Base-centered monoclinic cell is defined by four parameters \(a\), \(b\), \(c\) and \(\alpha\) with \(b \le c\), \(\alpha < 90^{\circ}\).

MCLC lattice has variation MCLC3 when \(k_{\gamma} < 90^{\circ}\) and \(\dfrac{b\cos(\alpha)}{c} + \dfrac{b^2\sin(\alpha)^2}{a^2} < 1\).

Cell constructor

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

wulfric.cell.sc_get_example() returns an example where \(a = 1.1\cdot\sin(78)\cdot\pi\), \(b = \pi\), \(c = 1.8\cdot 121\cdot\cos(65)\cdot\pi/21\) and \(\alpha = 78^{\circ}\).

import wulfric

cell = wulfric.cell.sc_get_example("MCLC3")
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 == "MCLC3"

print(variation)

MCLC3

K-path

print(kp.path_string)

GAMMA-Y-F-H-Z-I-F1|H1-Y1-X-GAMMA-N|M-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
F       0.4798  0.4798  0.4819   0.0000  1.9194  0.0490
F1      0.5202 -0.4798  0.5181   1.8588  0.0806  0.4741
F2      0.4798 -0.5202  0.4819   1.8588 -0.0806  0.4741
H       0.4520  0.4520  0.9053   0.0000  1.8082  0.4741
H1      0.5480 -0.4520  0.0947   1.8588  0.1918  0.0490
H2     -0.4520 -0.4520  0.0947  -0.0000 -1.8082  0.4741
I       0.5000 -0.5000  0.5000   1.8588  0.0000  0.4741
M       0.5000  0.0000  0.5000   0.9294  1.0000  0.2616
N       0.5000  0.0000 -0.0000   0.9294  1.0000 -0.2126
N1      0.0000 -0.5000  0.0000   0.9294 -1.0000  0.2126
X       0.5000 -0.5000  0.0000   1.8588  0.0000  0.0000
Y       0.4659  0.4659  0.1936   0.0000  1.8638 -0.2126
Y1      0.5341 -0.4659 -0.1936   1.8588  0.1362 -0.2126
Y2     -0.4659 -0.4659 -0.1936  -0.0000 -1.8638  0.2126
Y3      0.4659 -0.5341  0.1936   1.8588 -0.1362  0.2126
Z       0.0000  0.0000  0.5000   0.0000  0.0000  0.4741

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)