Open this Brillouin zone full-screen
``` `-c`/`--cell` selects the structure file (default: `POSCAR`); the former `--poscar` spelling is kept as an alias. The space group of the structure is detected, and the corresponding high-symmetry k-path (e.g. GM-X-M-GM-R-X, M-R for Pm-3m) is generated automatically with [seekpath](https://github.com/giovannipizzi/seekpath). Disconnected path segments are drawn separately so that every plotted line is a continuous band path. The detected space group, the high-symmetry k points with their fractional coordinates, and the k-path are also printed to the terminal. If `--output` is omitted, the plot is saved in the current directory as `BZ_{structure name}.html` (e.g. `BZ_221_PPOSCAR_ScF3.html`). A custom path can be supplied instead of the automatic one with `--band` / `--band-labels`; coordinates may be given as decimals or fractions, comma-separated into continuous segments: ```bash crystod-bz -c 221_PPOSCAR_ScF3 \ --band "0 0 0 0 1/2 0 1/2 1/2 0 0 0 0 1/2 1/2 1/2 0 1/2 0, 1/2 1/2 0 1/2 1/2 1/2" \ --band-labels "GM X M GM R X M R" ``` Note: if the input cell differs from the seekpath standardized primitive cell, the Brillouin zone and k-path are drawn for the standardized primitive cell (a NOTE is printed in that case). Manual `--band` coordinates always refer to the reciprocal basis of the input structure. ### Special k points of a space group (`--show-kpoint`) With `--show-kpoint`, no plot is produced; instead the special (high-symmetry) k points of the space group given by `--space-group` are printed: ```bash crystod-bz --show-kpoint --space-group Pnma ``` ``` * Space group * Pnma (No. 62) * K points (primitive) * GM: (0, 0, 0) X: (1/2, 0, 0) Y: (0, 1/2, 0) Z: (0, 0, 1/2) S: (1/2, 1/2, 0) T: (0, 1/2, 1/2) U: (1/2, 0, 1/2) R: (1/2, 1/2, 1/2) ``` The k points and their ISO-IR (ISOTROPY, Miller-Love) labels are taken from the bundled ISO-IR tables — the same definition used by the SALC/irrep analyses (`crystod`, `crystod-mag`, `crystod-group`, `crystod-phonon --irreps`) — and are given in the primitive reciprocal basis. For centred lattices (F, I, C, A, B, R), whose conventional and primitive cells differ, the coordinates in the conventional reciprocal basis are printed as well: ```bash crystod-bz --show-kpoint --space-group Fm-3m ``` ``` * Space group * Fm-3m (No. 225) * K points (primitive) * GM: (0, 0, 0) X: (1/2, 0, 1/2) L: (1/2, 1/2, 1/2) W: (1/2, 1/4, 3/4) * K points (conventional) * GM: (0, 0, 0) X: (0, 1, 0) L: (1/2, 1/2, 1/2) W: (1/2, 1, 0) ``` ## 19. Supercell Brillouin zone (`--trans-mat`) *Example directory: `example/19_bz_supercell` (testsuite section 19)* Plot the first Brillouin zone of a unit cell (black, dotted) together with the Brillouin zone of a transformed (super)lattice (red) as an interactive 3D HTML file: ```bash crystod-bz -c example/test_POSCARs/221_PPOSCAR_ScF3 \ --trans-mat "0 1 2 -1 0 2 1 -1 2" --output BZ_supercell.html ``` ``` Transformation matrix (unit cell -> supercell): [ 0.0000 1.0000 2.0000] [ -1.0000 0.0000 2.0000] [ 1.0000 -1.0000 2.0000] Volume ratio |det T| = 6 Unit-cell q-points folding onto the supercell Gamma point (6): (0, 0, 0) (1/3, -1/3, 1/6) (-1/3, 1/3, 1/3) (0, 0, 1/2) (1/3, -1/3, -1/3) (-1/3, 1/3, -1/6) Wrote supercell Brillouin-zone visualization: BZ_supercell_221_PPOSCAR_ScF3.html ``` ```{raw} htmlOpen the folded-BZ plot full-screen — the small red polyhedra are the supercell BZ tiled at the six folded q points; the black dotted cell is the unit-cell BZ.
``` `--trans-mat` is the row-wise unit-cell-to-supercell transformation matrix (`L_super = T L_unit`; fractions such as `1/2` are allowed). It defaults to the identity matrix, which plots the unit-cell BZ only (section 18); any non-identity matrix switches to this combined unit-cell + supercell plot. The supercell BZ is automatically tiled at every supercell reciprocal-lattice point folded into the unit-cell BZ — exactly the `|det T|` unit-cell q points that fold onto the Gamma point of the supercell, which are also printed to the terminal and shown on hover in the plot. This visualizes Brillouin-zone folding when lowering the symmetry from a supergroup to a subgroup cell (e.g. a Pm-3m perovskite into a 6x larger cell). Both reciprocal bases are drawn (unit cell: black dotted, supercell: red/green/blue). If `--output` is omitted, the plot is saved as `BZ_supercell_{POSCAR name}.html`. Based on `script/supercell_BZ.py` by Hiroki Koiso.