LatticeBase¶

class sknano.core.crystallography.LatticeBase(nd=None, cell_matrix=None, orientation_matrix=None, offset=None)[source] [edit on github][source]¶

Bases: sknano.core.strings.TabulateMixin, sknano.core.meta.BaseClass

Base class for crystallographic lattice objects.

Parameters:	nd (int) – cell_matrix (array_like) – orientation_matrix (array_like, optional) – offset (array_like, optional) –

Attributes

`bounding_box`	`region` `bounding_box`.
`cell`	Alias for `cell_matrix`.
`cell_matrix`	Matrix of lattice row vectors.
`centroid`	Region centroid.
`fmtstr`	Format string.
`fractional_matrix`	Transformation matrix to convert from cartesian coordinates to fractional coordinates.
`matrix`	Alias for `cell_matrix`.
`metric_tensor`	Metric tensor.
`offset`	Lattice offset.
`ortho_matrix`	Transformation matrix to convert from fractional coordinates to cartesian coordinates.
`region`	`Parallelepiped` defined by lattice vectors.

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.
`rotate`(**kwargs)	Rotate unit cell.
`todict`()	Return `dict` of constructor 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

`bounding_box`	`region` `bounding_box`.
`cell`	Alias for `cell_matrix`.
`cell_matrix`	Matrix of lattice row vectors.
`centroid`	Region centroid.
`fractional_matrix`	Transformation matrix to convert from cartesian coordinates to fractional coordinates.
`matrix`	Alias for `cell_matrix`.
`metric_tensor`	Metric tensor.
`offset`	Lattice offset.
`ortho_matrix`	Transformation matrix to convert from fractional coordinates to cartesian coordinates.
`region`	`Parallelepiped` defined by lattice vectors.

Methods Summary

`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.
`rotate`(**kwargs)	Rotate unit cell.
`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 Documentation

bounding_box¶: region bounding_box.

cell¶: Alias for cell_matrix.

cell_matrix¶

Matrix of lattice row vectors.

Same as the matrix transpose of the matrix product LatticeBase.orientation_matrix \(\times\) LatticeBase.ortho_matrix:

\[\begin{split}[A] = ([R][M])^T \begin{pmatrix} \mathbf{a}\\ \mathbf{b}\\ \mathbf{c} \end{pmatrix} =([R][\mathbf{a}\,\mathbf{b}\,\mathbf{c}])^T\end{split}\]

centroid¶: Region centroid.

fractional_matrix¶

Transformation matrix to convert from cartesian coordinates to fractional coordinates.

The fractional matrix \([Q]\) is given by the inverse of the orthogonal matrix \([M]\) (see: ortho_matrix), i.e. \([Q]=[M]^{-1}\)

\[\begin{split}[Q] = [M]^{-1} =\begin{pmatrix} 1/a & -1/a\tan\gamma & (\cos\alpha\cos\gamma - \cos\beta)/ a\phi\sin\gamma\\ 0 & 1/b\sin\gamma & (\cos\beta\cos\gamma - \cos\alpha)/ b\phi\sin\gamma\\ 0 & 0 & \sin\gamma/c\phi \end{pmatrix}\end{split}\]

where:

\[\begin{split}\begin{align*} \phi &= \frac{V}{abc}\\ &=\sqrt{1 - \cos^2\alpha - \cos^2\beta - \cos^2\gamma + 2\cos\alpha\cos\beta\cos\gamma}\\ &=\sin\alpha\sin\beta\sin\gamma^* \end{align*}\end{split}\]

where \(V\) is the volume of the unit cell.

matrix¶: Alias for cell_matrix.

metric_tensor¶: Metric tensor.

offset¶: Lattice offset.

ortho_matrix¶: Transformation matrix to convert from fractional coordinates to cartesian coordinates.

\[\begin{split}[M] = \begin{pmatrix} \mathbf{a} & \mathbf{b} & \mathbf{c} \end{pmatrix} = \begin{pmatrix} a & b\cos\gamma & c\cos\beta\\ 0 & b\sin\gamma & c(\cos\alpha - \cos\beta\cos\gamma)/\sin\gamma\\ 0 & 0 & c\sin\alpha\sin\beta\sin\gamma^*/\sin\gamma \end{pmatrix}\end{split}\]

region¶: Parallelepiped defined by lattice vectors.

Methods Documentation

cartesian_to_fractional(ccoords)[source] [edit on github][source]¶

Convert cartesian coordinate to fractional coordinate.

Parameters:	ccoords (array_like) –
Returns:
Return type:	`ndarray`

fractional_diff(fcoords1, fcoords2)[source] [edit on github][source]¶: Compute difference between fractional coordinates.

See also

core.crystallography.pbc_diff

fractional_to_cartesian(fcoords)[source] [edit on github][source]¶

Convert fractional coordinate to cartesian coordinate.

Parameters:	fcoords (array_like) –
Returns:
Return type:	`ndarray`

rotate(**kwargs)[source] [edit on github][source]¶

Rotate unit cell.

Parameters:	angle (float) – axis (`Vector`, optional) – anchor_point (`Point`, optional) – rot_point (`Point`, optional) – to_vector (from_vector,) – degrees (bool, optional) – transform_matrix (`ndarray`) –

Parameters:	p (array_like) –
Returns:
Return type:	`ndarray`

Navigation

LatticeBase¶