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.