# sknano.core.crystallography.Reciprocal2DLattice¶

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.

Parameters: a_star, b_star : float gamma_star : float b1, b2 : array_like cell_matrix : array_like orientation_matrix : array_like

Attributes

 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 $$\sin\gamma^*$$

Methods

 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.