Reciprocal3DLattice

class sknano.core.crystallography.Reciprocal3DLattice(a_star=None, b_star=None, c_star=None, alpha_star=None, beta_star=None, gamma_star=None, b1=None, b2=None, b3=None, cell_matrix=None, orientation_matrix=None, offset=None)

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

3D reciprocal lattice class.

Parameters:

• b_star, c_star (a_star,) –
• beta_star, gamma_star (alpha_star,) –
• b2, b3 (b1,) –
• cell_matrix (array_like) –
• orientation_matrix (array_like) –

Attributes

a1	3D lattice vector $\mathbf{a}_1=\mathbf{a}$.
a2	3D lattice vector $\mathbf{a}_2=\mathbf{b}$.
a3	3D lattice vector $\mathbf{a}_3=\mathbf{c}$.
a_star	Length of lattice vector $\mathbf{a^*}$.
alpha_star	Angle between lattice vectors $\mathbf{b}^{\ast}$ and $\mathbf{c}^{\ast}$ in degrees.
angles	Tuple of lattice parameter angles $\alpha^*, \beta^*, \gamma^*$.
b1	Lattice vector $\mathbf{b}_1=\mathbf{a}^{\ast}$.
b2	Lattice vector $\mathbf{b}_2=\mathbf{b}^{\ast}$.
b3	Lattice vector $\mathbf{b}_3=\mathbf{c}^{\ast}$.
b_star	Length of lattice_vector $\mathbf{b^*}$.
beta_star	Angle between lattice vectors $\mathbf{c}^{\ast}$ and $\mathbf{a}^{\ast}$ in degrees.
bounding_box	region bounding_box.
c_star	Length of lattice vector $\mathbf{c^*}$.
cell	Alias for cell_matrix.
cell_matrix	Matrix of lattice row vectors.
centroid	Region centroid.
cos_alpha	$\cos\alpha$
cos_alpha_star	$\cos\alpha^{\ast}$
cos_beta	$\cos\beta$
cos_beta_star	$\cos\beta^{\ast}$
cos_gamma	$\cos\gamma$
cos_gamma_star	$\cos\gamma^{\ast}$
fmtstr	Format string.
fractional_matrix	Transformation matrix to convert from cartesian coordinates to fractional coordinates.
gamma_star	Angle between lattice vectors $\mathbf{a}^{\ast}$ and $\mathbf{b}^{\ast}$ in degrees.
lattice_parameters	Tuple of lattice parameters a^*, b^*, c^*, alpha^*, beta^*, gamma^*.
lattice_vectors	Tuple of lattice vectors $\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3$.
lengths	Tuple of lattice vector lengths $a^*, b^*, c^*$.
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 Reciprocal3DLattice.
region	Parallelepiped defined by lattice vectors.
sin_alpha	$\sin\alpha$
sin_alpha_star	$\sin\alpha^{\ast}$
sin_beta	$\sin\beta$
sin_beta_star	$\sin\beta^{\ast}$
sin_gamma	$\sin\gamma$
sin_gamma_star	$\sin\gamma^{\ast}$

Methods

cartesian_to_fractional(ccoords)	Convert cartesian coordinate to fractional coordinate.
cubic(a_star)	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_star, c_star)	Generate a hexagonal 3D lattice with lattice parameters $a^*, c^*$.
monoclinic(a_star, b_star, c_star, beta_star)	Generate a monoclinic 3D lattice with lattice parameters $a^*, b^*, c^*, \beta^*$.
orthorhombic(a_star, b_star, c_star)	Generate an orthorhombic 3D lattice with lattice parameters $a^*, b^*, c^*$.
rotate(**kwargs)	Rotate unit cell.
tetragonal(a_star, c_star)	Generate a tetragonal 3D lattice with lattice parameters $a^*, c^*$.
todict()	Return dict of Reciprocal3DLattice parameters.
translate(t)	Translate lattice.
triclinic(a_star, b_star, c_star, ...)	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_star	Length of lattice vector $\mathbf{a^*}$.
alpha_star	Angle between lattice vectors $\mathbf{b}^{\ast}$ and $\mathbf{c}^{\ast}$ in degrees.
angles	Tuple of lattice parameter angles $\alpha^*, \beta^*, \gamma^*$.
b1	Lattice vector $\mathbf{b}_1=\mathbf{a}^{\ast}$.
b2	Lattice vector $\mathbf{b}_2=\mathbf{b}^{\ast}$.
b3	Lattice vector $\mathbf{b}_3=\mathbf{c}^{\ast}$.
b_star	Length of lattice_vector $\mathbf{b^*}$.
beta_star	Angle between lattice vectors $\mathbf{c}^{\ast}$ and $\mathbf{a}^{\ast}$ in degrees.
c_star	Length of lattice vector $\mathbf{c^*}$.
cos_alpha_star	$\cos\alpha^{\ast}$
cos_beta_star	$\cos\beta^{\ast}$
cos_gamma_star	$\cos\gamma^{\ast}$
gamma_star	Angle between lattice vectors $\mathbf{a}^{\ast}$ and $\mathbf{b}^{\ast}$ in degrees.
lattice_parameters	Tuple of lattice parameters a^*, b^*, c^*, alpha^*, beta^*, gamma^*.
lattice_vectors	Tuple of lattice vectors $\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3$.
lengths	Tuple of lattice vector lengths $a^*, b^*, c^*$.
reciprocal_lattice	Reciprocal lattice of this Reciprocal3DLattice.
sin_alpha_star	$\sin\alpha^{\ast}$
sin_beta_star	$\sin\beta^{\ast}$
sin_gamma_star	$\sin\gamma^{\ast}$

Methods Summary

cubic(a_star)	Generate a cubic 3D lattice with lattice parameter $a^*$.
hexagonal(a_star, c_star)	Generate a hexagonal 3D lattice with lattice parameters $a^*, c^*$.
monoclinic(a_star, b_star, c_star, beta_star)	Generate a monoclinic 3D lattice with lattice parameters $a^*, b^*, c^*, \beta^*$.
orthorhombic(a_star, b_star, c_star)	Generate an orthorhombic 3D lattice with lattice parameters $a^*, b^*, c^*$.
tetragonal(a_star, c_star)	Generate a tetragonal 3D lattice with lattice parameters $a^*, c^*$.
todict()	Return dict of Reciprocal3DLattice parameters.
triclinic(a_star, b_star, c_star, ...)	Generate a triclinic 3D lattice with lattice parameters $a^*, b^*, c^*, \alpha^*, \beta^*, \gamma^*$.

Attributes Documentation

a_star

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

alpha_star

Angle between lattice vectors $\mathbf{b}^{\ast}$ and $\mathbf{c}^{\ast}$ in degrees.

angles

Tuple of lattice parameter angles $\alpha^*, \beta^*, \gamma^*$.

b1

Lattice vector $\mathbf{b}_1=\mathbf{a}^{\ast}$.

b2

Lattice vector $\mathbf{b}_2=\mathbf{b}^{\ast}$.

b3

Lattice vector $\mathbf{b}_3=\mathbf{c}^{\ast}$.

b_star

Length of lattice_vector $\mathbf{b^*}$.

beta_star

Angle between lattice vectors $\mathbf{c}^{\ast}$ and $\mathbf{a}^{\ast}$ in degrees.

c_star

Length of lattice vector $\mathbf{c^*}$.

cos_alpha_star

$\cos\alpha^{\ast}$

cos_beta_star

$\cos\beta^{\ast}$

cos_gamma_star

$\cos\gamma^{\ast}$

gamma_star

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

lattice_parameters

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

lattice_vectors

Tuple of lattice vectors $\mathbf{b}_1, \mathbf{b}_2, \mathbf{b}_3$.

lengths

Tuple of lattice vector lengths $a^*, b^*, c^*$.

reciprocal_lattice

Reciprocal lattice of this Reciprocal3DLattice.

sin_alpha_star

$\sin\alpha^{\ast}$

sin_beta_star

$\sin\beta^{\ast}$

sin_gamma_star

$\sin\gamma^{\ast}$

Methods Documentation

classmethod cubic(a_star)

Generate a cubic 3D lattice with lattice parameter $a^*$.

classmethod hexagonal(a_star, c_star)

Generate a hexagonal 3D lattice with lattice parameters $a^*, c^*$.

classmethod monoclinic(a_star, b_star, c_star, beta_star)

Generate a monoclinic 3D lattice with lattice parameters $a^*, b^*, c^*, \beta^*$.

classmethod orthorhombic(a_star, b_star, c_star)

Generate an orthorhombic 3D lattice with lattice parameters $a^*, b^*, c^*$.

classmethod tetragonal(a_star, c_star)

Generate a tetragonal 3D lattice with lattice parameters $a^*, c^*$.

todict()

Return dict of Reciprocal3DLattice parameters.

classmethod triclinic(a_star, b_star, c_star, alpha_star, beta_star, gamma_star)

Generate a triclinic 3D lattice with lattice parameters $a^*, b^*, c^*, \alpha^*, \beta^*, \gamma^*$.