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 $c^2\le c_x^2+c_y^2$, 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: $a,b\le c$, $\alpha <{90}^{\circ }$ 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: $a<b<c$.
  • 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 $a^{\prime }$) 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.