# lattice

Specify a set of lattice vectors according to cell parameters, cell angles and bravais lattice type. For example, the diamond crystal can be constructed:

structure(
fractional = [[C, 0.0,  0.0,  0.0 ],
[C, 0.25, 0.25, 0.25]]
lattice(a = 3.57 angstrom
bravais = fcc)
)

Lattice vectors follow the conventions defined in High-throughput electronic band structure calculations: Challenges and tools.

This command can appear in the global context.

### Options

a

Lattice parameter a

• The type is quantity
• There is no default value.
alpha

Lattice angle alpha

• The type is quantity
• There is no default value.
b

Lattice parameter b

• The type is quantity
• There is no default value.
beta

Lattice angle beta

• The type is quantity
• There is no default value.
bravais

Specifies the Bravais lattice.

The lattice parameters supplied must be exactly satisfy the bravais type. For example, when specifying a fcc cell, only the a option should be given:

structure(
fractional = [[C, 0.0,  0.0,  0.0 ],
[C, 0.25, 0.25, 0.25]]
lattice(a = 3.57 angstrom
bravais = fcc)
)


In some instances, there are multiple conventions with which one can define the bravais lattice vectors. For all lattices, we follow the conventions set out in High-throughput electronic band structure calculations: Challenges and tools. Consistent with the paper, the base-centred orthorhombic lattice is defined according to the C-convention. That is, the cell has the translation in the a-b plane (space groups beginning with C) rather than b-c plane. The base-centred monoclinic lattice is also defined according to the C-convention, and the rhombohedral lattice is defined according to the rhombohedral setting. Additional details relating to other convention choices can be found on the AFLOW database.

• The type is string
• There is no default value.
• The value must be one of:
• triclinic - The triclinic lattice is defined by the lattice parameters $$(a, b, c)$$ and angles $$(\alpha, \beta, \gamma)$$. There are no restrictions on the choice of lattice parameters and angles for the triclinic lattice. It can therefore be used to define any Bravais lattice type, however $$c^2 \leq c_x^2 + c_y^2$$, where $$c_x = c\cos(\beta)$$ and $$c_y = c (\cos(\alpha) - \cos(\beta) \cos(\gamma) / \sin(\gamma))$$.
• monoclinic - The conventional monoclinic unit cell is defined by primitive vectors, $$a$$, $$b$$ and $$c$$, and the angle $$\alpha$$. One of the lattice vectors is perpendicular to the other two. We choose the unique axis to be along vector $$\mathbf{a}$$ with length $$a$$. The ordering of the lattice follows as: $$a,b \leq c$$, $$\alpha \lt 90^\circ$$ and $$\beta = \gamma = 90^\circ$$.
• base_centred_monoclinic - The base-centred monoclinic unit cell is defined by primitive vectors, $$a$$, $$b$$ and $$c$$, and the angle $$\alpha$$.
• orthorhombic - The orthorhombic lattice is defined by the lattice parameters, $$a$$, $$b$$ and $$c$$. The ordering of the conventional lattice follows as: $$a \lt b \lt c$$.
• base_centred_orthorhombic - The base-centred orthorhombic lattice is defined by the lattice parameters, $$a$$, $$b$$ and $$c$$. The orientation of the lattice vectors is only considered for centring in the C plane.
• body_centred_orthorhombic - The body-centred orthorhombic lattice is defined by the lattice parameters, $$a$$, $$b$$ and $$c$$.
• face_centred_orthorhombic - The face-centred orthorhombic lattice is defined by the lattice parameters, $$a$$, $$b$$ and $$c$$.
• tetragonal - The tetragonal lattice is defined by the lattice parameters, $$a$$ and $$c$$.
• body_centred_tetragonal - The body-centred tetragonal lattice is defined by the lattice parameters, $$a$$ and $$c$$.
• hexagonal - The hexagonal lattice is defined by the lattice parameters, $$a$$ and $$c$$.
• rhombohedral - The rhombohedral lattice can be defined in two ways. As a trigonal lattice with additional translational vectors (hexagonal setting), or as a simple lattice with primitive vectors of equal length and equal angles (rhombohedral setting). We use the rhombohedral setting, which is defined by the lattice parameter $$a$$ (sometimes reported as $$a'$$) and angle $$\alpha$$.
• cubic - The cubic lattice is defined by the lattice parameter, $$a$$.
• fcc - The face-centred lattice is defined by the lattice parameter, $$a$$.
• bcc - The body-centred lattice is defined by the lattice parameter, $$a$$.
c

Lattice parameter c

• The type is quantity
• There is no default value.
gamma

Lattice angle gamma

• The type is quantity
• There is no default value.