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.