Bravais lattices#

For the full technical reference see Crystal

For the module guide on Bravais lattices see Bravais lattices

Bravais lattice notation and standardization follows Setyawan and Curtarolo [1].

For eah Bravais lattice type we provide the standard form of the primitive: \((\boldsymbol{a}_1, \boldsymbol{a}_2, \boldsymbol{a}_3)\) and the conventional: \((\boldsymbol{a}_1^c, \boldsymbol{a}_2^c, \boldsymbol{a}_3^c)\) cell in the same Cartesian coordinate system as in the reference paper.

In practice the cell can be given to Wulfric in any Cartesian coordinate system. Standardization procedure does not change the crystal, but redefine the lattice vectors. Relative positions of the high symmetry k-points are given for the standardized primitive cell in the default orientation.

Cubic lattice system#

Name	Examples	Parameters	Constructor
Cubic (CUB)	`cub`	\(a\)	`CUB()`
Face-centred cubic (FCC)	`fcc`	\(a\)	`FCC()`
Body-centered cubic (BCC)	`bcc`	\(a\)	`BCC()`

Tetragonal lattice system#

Name	Examples	Parameters	Constructor
Tetragonal (TET)	`tet`	\(a\), \(c\)	`TET()`
Body-centred tetragonal (BCT)	`bct`, `bct1`, `bct2`	\(a\), \(c\)	`BCT()`

Orthorhombic lattice system#

Name	Examples	Parameters	Constructor
Orthorhombic (ORC)	`orc`	\(a\), \(b\), \(c\)	`ORC()`
Face-centred orthorhombic (ORCF)	`orcf`, `orcf1`, `orcf2`, `orcf3`	\(a\), \(b\), \(c\)	`ORCF()`
Body-centred orthorhombic (ORCI)	`orci`	\(a\), \(b\), \(c\)	`ORCI()`
Base-centred orthorhombic (ORCC)	`orcc`	\(a\), \(b\), \(c\)	`ORCC()`

Hexagonal lattice system#

Name	Examples	Parameters	Constructor
Hexagonal (HEX)	`hex`	\(a\), \(c\)	`HEX()`

Rhombohedral lattice system#

Name	Examples	Parameters	Constructor
Rhombohedral (RHL)	`rhl`, `rhl1`, `rhl2`	\(a\), \(c\)	`RHL()`

Monoclinic lattice system#

Name	Examples	Parameters	Constructor
Monoclinic (MCL)	`mcl`	\(a\), \(b\), \(c\), \(\alpha\)	`MCL()`
Base-centred monoclinic (MCLC)	`mclc`, `mclc1`, `mclc2`, `mclc3`, `mclc4`, `mclc5`	\(a\), \(b\), \(c\), \(\alpha\)	`MCLC()`

Triclinic lattice system#

Predefined examples: tri1a, tri1b, tri2a, tri2b.

Name	Examples	Parameters	Constructor
Triclinic (TRI)	`tri1a`, `tri1b`, `tri2a`, `tri2b`	\(a\), \(b\), \(c\), \(\alpha\), \(\beta\), \(\gamma\)	`TRI()`