Bravais lattices

For the full technical reference see wulfric.cell

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

For each Bravais lattice type wulfric can compute the standard form of the primitive: \(\boldsymbol{A}^s\) and the conventional \(\boldsymbol{A}^{cs}\) cells as defined in the reference paper [1].

The cell can be given to wulfric in any orientation. Standardization procedure does not change the orientation of the lattice/crystal, but redefine the lattice vectors. For instance, the cell and relative positions of atoms might change, but the underlying lattice and positions of atoms in the real space are not modified. The K-points are computed for the original (given) unit cell, using the transformation matrix \(\boldsymbol{S}\) from given to standardized cell.

In each individual page, relative positions of the high symmetry k-points are written for the standardized primitive cell in the default orientation. The actual relative coordinates of the k-points that wulfric computes are specific to the cell that user provides (original cell) and may differ from the ones written in those pages.

There is no need for the user to standardize the cell to have access to the k-points. However, it is the user's responsibility to track whether the given cell is primitive. The k-points will be computed even if the cell is not primitive and the Bravais lattice type will be defined by interpreting the given cell as primitive.

Note

The images are interactive.

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()

References

[1] (1,2)

Setyawan, W. and Curtarolo, S., 2010. High-throughput electronic band structure calculations: Challenges and tools. Computational materials science, 49(2), pp. 299-312.