Cubic (CUB)

Pearson symbol: cP

Constructor: CUB()

It is defined by one parameter \(a\). Standardized primitive and conventional cells in the default orientation are

\[\begin{split}\begin{matrix} \boldsymbol{a}_1^s &=& \boldsymbol{a}_1^{cs} &=& (a, &0, &0)\\ \boldsymbol{a}_2^s &=& \boldsymbol{a}_2^{cs} &=& (0, &a, &0)\\ \boldsymbol{a}_3^s &=& \boldsymbol{a}_3^{cs} &=& (0, &0, &a) \end{matrix}\end{split}\]

Transformation matrix from standardized primitive cell to standardized conventional cell is

\[\begin{split}\boldsymbol{C} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix} \qquad \boldsymbol{C}^{-1} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{pmatrix}\end{split}\]

K-path

\(\mathrm{\Gamma-X-M-\Gamma-R-X\vert M-R}\).

Point	\(\times\boldsymbol{b}_1^s\)	\(\times\boldsymbol{b}_2^s\)	\(\times\boldsymbol{b}_3^s\)
\(\mathrm{\Gamma}\)	\(0\)	\(0\)	\(0\)
\(\mathrm{M}\)	\(1/2\)	\(1/2\)	\(0\)
\(\mathrm{R}\)	\(1/2\)	\(1/2\)	\(1/2\)
\(\mathrm{X}\)	\(0\)	\(1/2\)	\(0\)

Variations

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

Examples

Brillouin zone and default kpath

import wulfric as wulf

cell = wulf.cell.get_cell_example("CUB")
backend = wulf.visualization.PlotlyBackend()
backend.plot(cell, kind="brillouin-kpath")
# Save an image:
backend.save("cub_reciprocal.png")
# Interactive plot:
backend.show()

Primitive and Wigner-Seitz cells

Click on the legend to hide a cell.

import wulfric as wulf

cell = wulf.cell.get_cell_example("CUB")
backend = wulf.visualization.PlotlyBackend()
backend.plot(cell, kind="primitive", label="primitive", color="black")
backend.plot(cell, kind="wigner-seitz", label="wigner-seitz", color="green")
# Save an image:
backend.save("cub_real.png")
# Interactive plot:
backend.show()

Cell standardization

No standardization required.

\[\begin{split}\boldsymbol{S} = \boldsymbol{S}^{-1} = \begin{pmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix}\end{split}\]