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)

Bases: sknano.core.crystallography.ReciprocalLatticeBase, sknano.core.crystallography.Direct2DLatticeMixin

2D reciprocal lattice class.

Parameters:

• b_star (a_star,) –
• gamma_star (float) –
• b2 (b1,) –
• 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 \(\mathbf{b^*}\).
bounding_box	region bounding_box.
cell	Alias for cell_matrix.
cell_matrix	Matrix of lattice row vectors.
centroid	Region centroid.
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.
offset	Lattice offset.
ortho_matrix	Transformation matrix to convert from fractional coordinates to cartesian coordinates.
reciprocal_lattice	Reciprocal lattice of this Reciprocal2DLattice.
region	Parallelepiped defined by lattice vectors.
sin_gamma	\(\sin\gamma\)
sin_gamma_star	\(\sin\gamma^*\)

Methods

cartesian_to_fractional(ccoords)	Convert cartesian coordinate to fractional coordinate.
fractional_diff(fcoords1, fcoords2)	Compute difference between fractional coordinates.
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(**kwargs)	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[, epsilon, pbc])	Wrap cartesian coordinate to lie within unit cell.
wrap_cartesian_coordinates(points[, ...])	Wrap array of cartesian coordinates to lie within unit cell.
wrap_fractional_coordinate(p[, epsilon, pbc])	Wrap fractional coordinate to lie within unit cell.
wrap_fractional_coordinates(points[, ...])	Wrap array of fractional coordinates to lie within unit cell.

Attributes Summary

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 \(\mathbf{b^*}\).
cos_gamma_star	\(\cos\gamma^*\)
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 \(a^*, b^*\).
reciprocal_lattice	Reciprocal lattice of this Reciprocal2DLattice.
sin_gamma_star	\(\sin\gamma^*\)

Methods Summary

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 \(a^*, b^*\).
square(a_star)	Generate a square 2D reciprocal lattice with lattice parameter \(a^*\).
todict()	Return dict of Reciprocal2DLattice parameters.

Attributes Documentation

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 \(\mathbf{b^*}\).

cos_gamma_star

\(\cos\gamma^*\)

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 \(a^*, b^*\).

reciprocal_lattice

Reciprocal lattice of this Reciprocal2DLattice.

sin_gamma_star

\(\sin\gamma^*\)

Methods Documentation

classmethod hexagonal(a_star)

Generate a hexagonal 2D reciprocal lattice with lattice parameter \(a^*\).

classmethod oblique(a_star, b_star, gamma_star)

Generate an oblique 2D reciprocal lattice with lattice parameters \(a^*, b^*, \gamma^*\).

classmethod rectangular(a_star, b_star)

Generate a rectangular 2D reciprocal lattice with lattice parameters \(a^*, b^*\).

classmethod square(a_star)

Generate a square 2D reciprocal lattice with lattice parameter \(a^*\).

todict()

Return dict of Reciprocal2DLattice parameters.