Tetragonal (TET)#

Pearson symbol: tP

Tetragonal lattice is described by the class TET.

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

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

Variations#

There are no variations for tetragonal lattice. One example is predefined: tet with \(a = \pi\) and \(c = 1.5\pi\)

Example structure#

Default kpath: \(\Gamma-X-M-\Gamma-Z-R-A-Z\vert X-R\vert M-A\).

Brillouin zone and default kpath#

Picture

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

l = rad.lattice_example(f"TET")
l.plot("brillouin-kpath")
# Save an image:
l.savefig(
    "tet_brillouin.png",
    elev=30,
    azim=23,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=30, azim=23)
Primitive and conventional cell#

Picture

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

l = rad.lattice_example(f"TET")
l.plot("primitive")
# Save an image:
l.savefig(
    "tet_real.png",
    elev=30,
    azim=30,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=30, azim=30)
Wigner-Seitz cell#

Picture

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

l = rad.lattice_example(f"TET")
l.plot("wigner-seitz")
# Save an image:
l.savefig(
    "tet_wigner-seitz.png",
    elev=30,
    azim=30,
    dpi=300,
   bbox_inches="tight",
)
# Interactive plot:
l.show(elev=30, azim=30)

Edge cases#

If \(a = c\), then the lattice is Cubic (CUB).