Crystal3DLattice

class sknano.core.crystallography.Crystal3DLattice(a=None, b=None, c=None, alpha=None, beta=None, gamma=None, a1=None, a2=None, a3=None, cell_matrix=None, orientation_matrix=None, offset=None)

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

3D crystal lattice class.

Parameters:

• b, c (a,) –
• beta, gamma (alpha,) –
• a2, a3 (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 \(\mathbf{a}_2=\mathbf{b}\).
a3	Lattice vector \(\mathbf{a}_3=\mathbf{c}\).
alpha	Angle between lattice vectors \(\mathbf{b}\) and \(\mathbf{c}\) in degrees.
angles	Tuple of lattice parameter angles \(\alpha, \beta, \gamma\).
b	Length of lattice_vector \(\mathbf{b}\).
b1	3D reciprocal lattice vector \(\mathbf{b}_1=\mathbf{a}^{*}\).
b2	3D reciprocal lattice vector \(\mathbf{b}_2=\mathbf{b}^{*}\).
b3	3D reciprocal lattice vector \(\mathbf{b}_3=\mathbf{c}^{*}\).
beta	Angle between lattice vectors \(\mathbf{a}\) and \(\mathbf{c}\) in degrees.
bounding_box	region bounding_box.
c	Length of lattice vector \(\mathbf{c}\).
cell	Alias for cell_matrix.
cell_matrix	Matrix of lattice row vectors.
cell_volume	Alias for volume.
centroid	Region centroid.
cos_alpha	\(\cos\alpha\)
cos_alpha_star	\(\cos\alpha^*\)
cos_beta	\(\cos\beta\)
cos_beta_star	\(\cos\beta^*\)
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, c, alpha, beta, gamma.
lattice_vectors	Tuple of lattice vectors \(\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3\).
lengths	Tuple of lattice vector lengths \(a, b, c\).
lengths_and_angles	Alias for attr:Crystal3DLattice.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	Reciprocal lattice of this Crystal3DLattice.
region	Parallelepiped defined by lattice vectors.
sin_alpha	\(\sin\alpha\)
sin_alpha_star	\(\sin\alpha^*\)
sin_beta	\(\sin\beta\)
sin_beta_star	\(\sin\beta^*\)
sin_gamma	\(\sin\gamma\)
sin_gamma_star	\(\sin\gamma^*\)
volume	Crystal cell volume.

Methods

cartesian_to_fractional(ccoords)	Convert cartesian coordinate to fractional coordinate.
cubic(a)	Generate a cubic 3D lattice with lattice parameter \(a\).
fractional_diff(fcoords1, fcoords2)	Compute difference between fractional coordinates.
fractional_to_cartesian(fcoords)	Convert fractional coordinate to cartesian coordinate.
hexagonal(a, c)	Generate a hexagonal 3D lattice with lattice parameters \(a, c\).
monoclinic(a, b, c, beta)	Generate a monoclinic 3D lattice with lattice parameters \(a, b, c, \beta\).
orthorhombic(a, b, c)	Generate an orthorhombic 3D lattice with lattice parameters \(a, b, c\).
rotate(**kwargs)	Rotate unit cell.
tetragonal(a, c)	Generate a tetragonal 3D lattice with lattice parameters \(a, c\).
todict()	Return dict of Crystal3DLattice parameters.
translate(t)	Translate lattice.
triclinic(a, b, c, alpha, beta, gamma)	Generate a triclinic 3D lattice with lattice parameters \(a, b, c, \alpha, \beta, \gamma\).
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 \(\mathbf{a}_2=\mathbf{b}\).
a3	Lattice vector \(\mathbf{a}_3=\mathbf{c}\).
alpha	Angle between lattice vectors \(\mathbf{b}\) and \(\mathbf{c}\) in degrees.
angles	Tuple of lattice parameter angles \(\alpha, \beta, \gamma\).
b	Length of lattice_vector \(\mathbf{b}\).
beta	Angle between lattice vectors \(\mathbf{a}\) and \(\mathbf{c}\) in degrees.
c	Length of lattice vector \(\mathbf{c}\).
cell_volume	Alias for volume.
cos_alpha	\(\cos\alpha\)
cos_beta	\(\cos\beta\)
cos_gamma	\(\cos\gamma\)
gamma	Angle between lattice vectors \(\mathbf{a}\) and \(\mathbf{b}\) in degrees.
lattice_parameters	Tuple of lattice parameters a, b, c, alpha, beta, gamma.
lattice_vectors	Tuple of lattice vectors \(\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3\).
lengths	Tuple of lattice vector lengths \(a, b, c\).
lengths_and_angles	Alias for attr:Crystal3DLattice.lattice_parameters.
ortho_matrix	Transformation matrix to convert from fractional coordinates to cartesian coordinates.
reciprocal_lattice	Reciprocal lattice of this Crystal3DLattice.
sin_alpha	\(\sin\alpha\)
sin_beta	\(\sin\beta\)
sin_gamma	\(\sin\gamma\)
volume	Crystal cell volume.

Methods Summary

cubic(a)	Generate a cubic 3D lattice with lattice parameter \(a\).
hexagonal(a, c)	Generate a hexagonal 3D lattice with lattice parameters \(a, c\).
monoclinic(a, b, c, beta)	Generate a monoclinic 3D lattice with lattice parameters \(a, b, c, \beta\).
orthorhombic(a, b, c)	Generate an orthorhombic 3D lattice with lattice parameters \(a, b, c\).
tetragonal(a, c)	Generate a tetragonal 3D lattice with lattice parameters \(a, c\).
todict()	Return dict of Crystal3DLattice parameters.
triclinic(a, b, c, alpha, beta, gamma)	Generate a triclinic 3D lattice with lattice parameters \(a, b, c, \alpha, \beta, \gamma\).

Attributes Documentation

a

Length of lattice vector \(\mathbf{a}\).

a1

Lattice vector \(\mathbf{a}_1=\mathbf{a}\).

a2

Lattice vector \(\mathbf{a}_2=\mathbf{b}\).

a3

Lattice vector \(\mathbf{a}_3=\mathbf{c}\).

alpha

Angle between lattice vectors \(\mathbf{b}\) and \(\mathbf{c}\) in degrees.

angles

Tuple of lattice parameter angles \(\alpha, \beta, \gamma\).

b

Length of lattice_vector \(\mathbf{b}\).

beta

Angle between lattice vectors \(\mathbf{a}\) and \(\mathbf{c}\) in degrees.

c

Length of lattice vector \(\mathbf{c}\).

cell_volume

Alias for volume.

cos_alpha

\(\cos\alpha\)

cos_beta

\(\cos\beta\)

cos_gamma

\(\cos\gamma\)

gamma

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

lattice_parameters

Tuple of lattice parameters a, b, c, alpha, beta, gamma.

lattice_vectors

Tuple of lattice vectors \(\mathbf{a}_1, \mathbf{a}_2, \mathbf{a}_3\).

lengths

Tuple of lattice vector lengths \(a, b, c\).

lengths_and_angles

Alias for attr:Crystal3DLattice.lattice_parameters.

ortho_matrix

Transformation matrix to convert from fractional coordinates to cartesian coordinates.

reciprocal_lattice

Reciprocal lattice of this Crystal3DLattice.

sin_alpha

\(\sin\alpha\)

sin_beta

\(\sin\beta\)

sin_gamma

\(\sin\gamma\)

volume

Crystal cell volume.

Methods Documentation

classmethod cubic(a)

Generate a cubic 3D lattice with lattice parameter \(a\).

classmethod hexagonal(a, c)

Generate a hexagonal 3D lattice with lattice parameters \(a, c\).

classmethod monoclinic(a, b, c, beta)

Generate a monoclinic 3D lattice with lattice parameters \(a, b, c, \beta\).

classmethod orthorhombic(a, b, c)

Generate an orthorhombic 3D lattice with lattice parameters \(a, b, c\).

classmethod tetragonal(a, c)

Generate a tetragonal 3D lattice with lattice parameters \(a, c\).

todict()

Return dict of Crystal3DLattice parameters.

classmethod triclinic(a, b, c, alpha, beta, gamma)

Generate a triclinic 3D lattice with lattice parameters \(a, b, c, \alpha, \beta, \gamma\).