radtools.BCC

class radtools.BCC(a: float = None, cell=None, eps_rel=1e-05)

Body-centered cubic (BCC, cI)

Conventional lattice:

\[ \begin{align}\begin{aligned}\boldsymbol{a}_1 = (a, 0, 0)\\\boldsymbol{a}_2 = (0, a, 0)\\\boldsymbol{a}_3 = (0, 0, a)\end{aligned}\end{align} \]

Primitive lattice:

\[ \begin{align}\begin{aligned}\boldsymbol{a}_1 = (-a/2, a/2, a/2)\\\boldsymbol{a}_2 = (a/2, -a/2, a/2)\\\boldsymbol{a}_3 = (a/2, a/2, -a/2)\end{aligned}\end{align} \]

See also

Body-centered cubic (BCC) for more information.

Parameters:

afloat, optional

Length of the lattice vector of the conventional lattice.

cell(3,3) array-like, optional

Primitive cell matrix, rows are interpreted as vectors.

cell = [[a1_x, a1_y, a1_z],
        [a2_x, a2_y, a2_z],
        [a3_x, a3_y, a3_z]]

eps_relfloat, default 1e-5

Relative epsilon as defined in [1].

Attributes:

conv_afloat

Length of the lattice vector of the conventional lattice.

conv_cell(3,3) numpy.ndarray

Conventional unit cell.

conv_cell = [[a_x, a_y, a_z],
             [b_x, b_y, b_z],
             [c_x, c_y, c_z]]

References

[1]

Grosse-Kunstleve, R.W., Sauter, N.K. and Adams, P.D., 2004. Numerically stable algorithms for the computation of reduced unit cells. Acta Crystallographica Section A: Foundations of Crystallography, 60(1), pp.1-6.

Methods:

add_kpoint(name, coordinates[, plot_name])	Add named kpoint to the lattice.
clear()	Clear the axis.
get_kpoints([n])	Getter for the instance of Kpoints.
identify()	Identify the Bravais lattice type.
lattice_points([relative, reciprocal, normalize])	Compute lattice points
legend(**kwargs)	Add legend to the figure.
plot([kind, ax])	Main plotting function of the Lattice.
plot_brillouin([ax, vectors, colour, label, ...])	Plot brillouin zone.
plot_brillouin_kpath([zone_colour, path_colour])	Plot brillouin zone and kpath.
plot_conventional(**kwargs)	Plot conventional unit cell.
plot_kpath([ax, colour, label, normalize])	Plot k path in the reciprocal space.
plot_primitive(**kwargs)	Plot primitive unit cell.
plot_real_space([ax, vectors, colour, ...])	Plot real space unit cell.
plot_wigner_seitz([ax, vectors, colour, ...])	Plot Wigner-Seitz unit cell.
prepare_figure([background, focal_length])	Prepare style of the figure for the plot.
remove([kind, ax])	Remove a set of artists from the plot.
savefig([output_name, elev, azim])	Save the figure in the file
show([elev, azim])	Show the figure in the interactive matplotlib window.
voronoi_cell([reciprocal, normalize])	Computes Voronoy edges around (0,0,0) point.

Properties:

a	Length of the first lattice vector \(\vert\vec{a}_1\vert\).
a1	First lattice vector \(\vec{a}_1\).
a2	Second lattice vector \(\vec{a}_2\).
a3	Third lattice vector \(\vec{a}_3\).
alpha	Angle between second and third lattice vector.
b	Length of the second lattice vector \(\vert\vec{a}_2\vert\).
b1	First reciprocal lattice vector.
b2	Second reciprocal lattice vector.
b3	Third reciprocal lattice vector.
beta	Angle between first and third lattice vector.
c	Length of the third lattice vector \(\vert\vec{a}_3\vert\).
cell	Unit cell of the lattice.
centring_type	Centring type.
crystal_family	Crystal family.
gamma	Angle between first and second lattice vector.
k_a	Length of the first reciprocal lattice vector \(\vert\vec{b}_1\vert\).
k_alpha	Angle between second and third reciprocal lattice vector.
k_b	Length of the second reciprocal lattice vector \(\vert\vec{b}_2\vert\).
k_beta	Angle between first and third reciprocal lattice vector.
k_c	Length of the third reciprocal lattice vector \(\vert\vec{b}_3\vert\).
k_gamma	Angle between first and second reciprocal lattice vector.
parameters	Return cell parameters.
path	K-point path.
pearson_symbol	Pearson symbol.
reciprocal_cell	Reciprocal cell.
reciprocal_cell_volume	Volume of the reciprocal cell.
unit_cell_volume	Volume of the unit cell.
variation	Variation of the lattice, if any.