Crystal2DLattice

class sknano.core.crystallography.Crystal2DLattice(a=None, b=None, gamma=None, a1=None, a2=None, cell_matrix=None, orientation_matrix=None, offset=None)

Bases: sknano.core.crystallography.LatticeBase, sknano.core.crystallography.Reciprocal2DLatticeMixin

2D crystal lattice class.

Parameters:

• b (a,) –
• gamma (float) –
• a2 (a1,) –
• cell_matrix (array_like) –
• orientation_matrix (array_like, optional) –

Attributes

a	Length of lattice vector $\mathbf{a}$.
a1	Lattice vector $\mathbf{a}_1=\mathbf{a}$.
a2	Lattice vector $\mathbf{a}_2=\mathbf{b}$.
angles	Lattice parameter angle gamma`.
area	Crystal cell area.
b	Length of lattice_vector $\mathbf{b}$.
b1	2D reciprocal lattice vector $\mathbf{b}_1=\mathbf{a}^{*}$.
b2	2D reciprocal lattice vector $\mathbf{b}_2=\mathbf{b}^{*}$.
bounding_box	region bounding_box.
cell	Alias for cell_matrix.
cell_area	Alias for area.
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	Angle between lattice vectors $\mathbf{a}$ and $\mathbf{b}$ in degrees.
lattice_parameters	Tuple of lattice parameters a, b, gamma.
lattice_vectors	Tuple of lattice vectors $\mathbf{a}_1, \mathbf{a}_2$.
lengths	Tuple of lattice parameter lengths $a, b$.
lengths_and_angles	Alias for attr:Crystal2DLattice.lattice_parameters.
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	Return Crystal2DLattice reciprocal lattice.
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)	Generate a hexagonal 2D lattice with lattice parameter $a$.
oblique(a, b, gamma)	Generate an oblique 2D lattice with lattice parameters $a, b, \gamma$.
rectangular(a, b)	Generate a rectangular 2D lattice with lattice parameters $a, b$.
rotate(**kwargs)	Rotate unit cell.
square(a)	Generate a square 2D lattice with lattice parameter $a$.
todict()	Return dict of Crystal2DLattice 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	Length of lattice vector $\mathbf{a}$.
a1	Lattice vector $\mathbf{a}_1=\mathbf{a}$.
a2	Lattice vector $\mathbf{a}_2=\mathbf{b}$.
angles	Lattice parameter angle gamma`.
area	Crystal cell area.
b	Length of lattice_vector $\mathbf{b}$.
cell_area	Alias for area.
cos_gamma	$\cos\gamma$
gamma	Angle between lattice vectors $\mathbf{a}$ and $\mathbf{b}$ in degrees.
lattice_parameters	Tuple of lattice parameters a, b, gamma.
lattice_vectors	Tuple of lattice vectors $\mathbf{a}_1, \mathbf{a}_2$.
lengths	Tuple of lattice parameter lengths $a, b$.
lengths_and_angles	Alias for attr:Crystal2DLattice.lattice_parameters.
reciprocal_lattice	Return Crystal2DLattice reciprocal lattice.
sin_gamma	$\sin\gamma$

Methods Summary

hexagonal(a)	Generate a hexagonal 2D lattice with lattice parameter $a$.
oblique(a, b, gamma)	Generate an oblique 2D lattice with lattice parameters $a, b, \gamma$.
rectangular(a, b)	Generate a rectangular 2D lattice with lattice parameters $a, b$.
square(a)	Generate a square 2D lattice with lattice parameter $a$.
todict()	Return dict of Crystal2DLattice parameters.

Attributes Documentation

a

Length of lattice vector $\mathbf{a}$.

a1

Lattice vector $\mathbf{a}_1=\mathbf{a}$.

a2

Lattice vector $\mathbf{a}_2=\mathbf{b}$.

angles

Lattice parameter angle gamma`.

area

Crystal cell area.

b

Length of lattice_vector $\mathbf{b}$.

cell_area

Alias for area.

cos_gamma

$\cos\gamma$

gamma

Angle between lattice vectors $\mathbf{a}$ and $\mathbf{b}$ in degrees.

lattice_parameters

Tuple of lattice parameters a, b, gamma.

lattice_vectors

Tuple of lattice vectors $\mathbf{a}_1, \mathbf{a}_2$.

lengths

Tuple of lattice parameter lengths $a, b$.

lengths_and_angles

Alias for attr:Crystal2DLattice.lattice_parameters.

reciprocal_lattice

Return Crystal2DLattice reciprocal lattice.

sin_gamma

$\sin\gamma$

Methods Documentation

classmethod hexagonal(a)

Generate a hexagonal 2D lattice with lattice parameter $a$.

classmethod oblique(a, b, gamma)

Generate an oblique 2D lattice with lattice parameters $a, b, \gamma$.

classmethod rectangular(a, b)

Generate a rectangular 2D lattice with lattice parameters $a, b$.

classmethod square(a)

Generate a square 2D lattice with lattice parameter $a$.

todict()

Return dict of Crystal2DLattice parameters.