Body-centered cubic (BCC)#

Pearson symbol: cI

Body-centered cubic lattice is described by the class BCC.

It is defined by one parameter: \(a\) with conventional lattice:

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

And primitive lattice:

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

Variations#

There are no variations for body-centered cubic lattice. One example is predefined: bcc with \(a = \pi\).

Example structure#

Default kpath: \(\Gamma-H-N-\Gamma-P-H\vert P-N\).

Brillouin zone and default kpath#

Picture

Code
../../../../../_images/bcc_brillouin.png 
import radtools as rad

l = rad.lattice_example(f"BCC")
l.plot("brillouin-kpath")
# Save an image:
l.savefig(
    "bcc_brillouin.png",
    elev=11,
    azim=25,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=11, azim=25)
Primitive and conventional cell#

Picture

Code
../../../../../_images/bcc_real.png 
import radtools as rad

l = rad.lattice_example(f"BCC")
l.plot(
    "primitive",
    label="primitive",
)
l.legend()
l.plot(
    "conventional",
    label="conventional",
    colour="black"
)
l.legend()
# Save an image:
l.savefig(
    "bcc_real.png",
    elev=30,
    azim=-180,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=30, azim=-180)
Wigner-Seitz cell#

Picture

Code
../../../../../_images/bcc_wigner-seitz.png 
import radtools as rad

l = rad.lattice_example(f"BCC")
l.plot("wigner-seitz")
# Save an image:
l.savefig(
    "bcc_wigner-seitz.png",
    elev=46,
    azim=19,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=46, azim=19)