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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.