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sknano.core.crystallography.Reciprocal3DLattice

class sknano.core.crystallography.Reciprocal3DLattice(a_star=None, b_star=None, c_star=None, alpha_star=None, beta_star=None, gamma_star=None, b1=None, b2=None, b3=None, cell_matrix=None, orientation_matrix=None, offset=None)[source][source]

3D reciprocal lattice class.

Parameters:

a_star, b_star, c_star : float

alpha_star, beta_star, gamma_star : float

b1, b2, b3 : array_like

cell_matrix : array_like

orientation_matrix : array_like

Attributes

a1 3D lattice vector a1=a.
a2 3D lattice vector a2=b.
a3 3D lattice vector a3=c.
a_star Length of lattice vector a.
alpha_star Angle between lattice vectors b and c in degrees.
angles Tuple of lattice parameter angles α,β,γ.
b1 Lattice vector b1=a.
b2 Lattice vector b2=b.
b3 Lattice vector b3=c.
b_star Length of lattice_vector b.
beta_star Angle between lattice vectors c and a in degrees.
c_star Length of lattice vector c.
cell_matrix Matrix of lattice row vectors.
cos_alpha cosα
cos_alpha_star cosα
cos_beta cosβ
cos_beta_star cosβ
cos_gamma cosγ
cos_gamma_star cosγ
fmtstr Format string.
fractional_matrix Transformation matrix to convert from cartesian coordinates to fractional coordinates.
gamma_star Angle between lattice vectors a and b in degrees.
lattice_parameters Tuple of lattice parameters a^*, b^*, c^*, alpha^*, beta^*, gamma^*.
lattice_vectors Tuple of lattice vectors b1,b2,b3.
lengths Tuple of lattice vector lengths a,b,c.
matrix Alias for cell_matrix.
metric_tensor Metric tensor.
reciprocal_lattice Reciprocal lattice of this Reciprocal3DLattice.
sin_alpha sinα
sin_alpha_star sinα
sin_beta sinβ
sin_beta_star sinβ
sin_gamma sinγ
sin_gamma_star sinγ

Methods

cartesian_to_fractional(ccoords) Convert cartesian coordinate to fractional coordinate.
cubic(a_star) Generate a cubic 3D lattice with lattice parameter a.
fractional_to_cartesian(fcoords) Convert fractional coordinate to cartesian coordinate.
hexagonal(a_star, c_star) Generate a hexagonal 3D lattice with lattice parameters a,c.
monoclinic(a_star, b_star, c_star, beta_star) Generate a monoclinic 3D lattice with lattice parameters a,b,c,β.
orthorhombic(a_star, b_star, c_star) Generate an orthorhombic 3D lattice with lattice parameters a,b,c.
rotate([angle, axis, anchor_point, ...]) Rotate unit cell.
tetragonal(a_star, c_star) Generate a tetragonal 3D lattice with lattice parameters a,c.
todict() Return dict of Reciprocal3DLattice parameters.
translate(t) Translate lattice.
triclinic(a_star, b_star, c_star, ...) Generate a triclinic 3D lattice with lattice parameters a,b,c,α,β,γ.
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.