Hexagonal (HEX)#

Pearson symbol: hP

Hexagonal lattice is described by the class HEX.

It is defined by two parameter: \(a\) and \(c\) with primitive and conventional lattice:

\[ \begin{align}\begin{aligned}\boldsymbol{a}_1 = (a/2, -a\sqrt{3}, 0)\\\boldsymbol{a}_2 = (a/2, a\sqrt{3}, 0)\\\boldsymbol{a}_3 = (0, 0, c)\end{aligned}\end{align} \]

Variations#

There are no variations for hexagonal lattice. One example is predefined: hex with \(a = \pi\) and \(c = 2\pi\).

Example structure#

Default kpath: \(\Gamma-M-K-\Gamma-A-L-H-A\vert L-M\vert K-H\).

Brillouin zone and default kpath#

Picture

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

l = rad.lattice_example(f"HEX")
l.plot("brillouin-kpath")
# Save an image:
l.savefig(
    "hex_brillouin.png",
    elev=19,
    azim=20,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=19, azim=20)
Primitive and conventional cell#

Picture

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

l = rad.lattice_example(f"HEX")
l.plot("primitive")
# Save an image:
l.savefig(
    "hex_real.png",
    elev=35,
    azim=23,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=35, azim=23)
Wigner-Seitz cell#

Picture

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

l = rad.lattice_example(f"HEX")
l.plot("wigner-seitz")
# Save an image:
l.savefig(
    "hex_wigner-seitz.png",
    elev=32,
    azim=10,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=32, azim=10)