class sknano.core.crystallography.Reciprocal2DLattice(a_star=None, b_star=None, gamma_star=None, b1=None, b2=None, cell_matrix=None, orientation_matrix=None, offset=None)[source][source]

2D reciprocal lattice class.


a_star, b_star : float

gamma_star : float

b1, b2 : array_like

cell_matrix : array_like

orientation_matrix : array_like


a1 2D lattice vector \(\mathbf{a}_1=\mathbf{a}\).
a2 2D lattice vector \(\mathbf{a}_2=\mathbf{b}\).
a_star Length of reciprocal lattice vector \(\mathbf{a^*}\).
angles Lattice parameter angle gamma^*`.
b1 Reciprocal lattice vector \(\mathbf{b}_1=\mathbf{a}^*\).
b2 Reciprocal lattice vector \(\mathbf{b}_2=\mathbf{b}^*\).
b_star Length of reciprocal lattice_vector \(\mathbf{b^*}\).
cell_matrix Matrix of lattice row vectors.
cos_gamma \(\cos\gamma\)
cos_gamma_star \(\cos\gamma^*\)
fmtstr Format string.
fractional_matrix Transformation matrix to convert from cartesian coordinates to fractional coordinates.
gamma_star Angle between reciprocal lattice vectors \(\mathbf{a}^{\ast}\) and \(\mathbf{b}^{\ast}\) in degrees.
lattice_parameters Tuple of lattice parameters a^*, b^*, gamma^*.
lattice_vectors Tuple of lattice vectors \(\mathbf{b}_1, \mathbf{b}_2\).
lengths Tuple of lattice parameter lengths \(a^*, b^*\).
matrix Alias for cell_matrix.
metric_tensor Metric tensor.
reciprocal_lattice Reciprocal lattice of this Reciprocal2DLattice.
sin_gamma \(\sin\gamma\)
sin_gamma_star \(\sin\gamma^*\)


cartesian_to_fractional(ccoords) Convert cartesian coordinate to fractional coordinate.
fractional_to_cartesian(fcoords) Convert fractional coordinate to cartesian coordinate.
hexagonal(a_star) Generate a hexagonal 2D reciprocal lattice with lattice parameter \(a^*\).
oblique(a_star, b_star, gamma_star) Generate an oblique 2D reciprocal lattice with lattice parameters \(a^*, b^*, \gamma^*\).
rectangular(a_star, b_star) Generate a rectangular 2D reciprocal lattice with lattice parameters \(a^*, b^*\).
rotate([angle, axis, anchor_point, ...]) Rotate unit cell.
square(a_star) Generate a square 2D reciprocal lattice with lattice parameter \(a^*\).
todict() Return dict of Reciprocal2DLattice parameters.
translate(t) Translate lattice.
wrap_cartesian_coordinate(p[, pbc]) Wrap cartesian coordinate to lie within unit cell.
wrap_fractional_coordinate(p[, epsilon, pbc]) Wrap fractional coordinate to lie within unit cell.