sisl.Lattice

class sisl.Lattice(cell: sisl.typing.CellLike, nsc: numpy.typing.ArrayLike = None, origin=None, boundary_condition: BoundaryCondition | int | str | bool | Sequence[BoundaryCondition | int | str | bool] = BoundaryCondition.PERIODIC)

Bases: _Dispatchs

A cell class to retain lattice vectors and a supercell structure

The supercell structure is comprising the primary unit-cell and neighboring unit-cells. The number of supercells is given by the attribute nsc which is a vector with 3 elements, one per lattice vector. It describes how many times the primary unit-cell is extended along the i’th lattice vector. For nsc[i] == 3 the supercell is made up of 3 unit-cells. One behind, the primary unit-cell and one after.

Parameters:

cell – the lattice parameters of the unit cell (the actual cell is returned from tocell.
nsc – number of supercells along each lattice vector
origin ((3,) of float, optional) – the origin of the supercell.
boundary_condition – the boundary conditions for each of the cell’s planes. Defaults to periodic boundary condition. See BoundaryCondition for valid enumerations.

Conversion

`new`
`new.Sile`
`new.ase`
`new.ndarray`
`to`	A dispatcher for classes, using __get__ it converts into ObjectDispatcher upon invocation from an object, or a TypeDispatcher when invoked from a class
`to.Cuboid`([center, origin, orthogonal])	Convert lattice parameters to a `Cuboid`
`to.Path`(args, *kwargs)	`Lattice` writing to a sile.
`to.Sile`(args, *kwargs)	`Lattice` writing to a sile.
`to.ase`(**kwargs)	`Lattice` conversion to an ase.Cell object.
`to.str`(args, *kwargs)	`Lattice` writing to a sile.

Methods

`add`(other)	Add two supercell lattice vectors to each other
`add_vacuum`(vacuum, axis[, orthogonal_to_plane])	Returns a new object with vacuum along the axis lattice vector
`angle`(axis1, axis2[, rad])	The angle between two of the cell vectors
`append`(other, axis)	Appends other `Lattice` to this grid along axis
`area`(axis1, axis2)	Calculate the area spanned by the two axis ax0 and ax1
`cell2length`(length[, axes])	Calculate cell vectors such that they each have length `length`
`center`([axes])	Returns center of the `Lattice`, possibly with respect to axes
`copy`([cell])	A deepcopy of the object
`equal`(other[, atol])	Check whether two lattices are equivalent
`fit`(xyz[, axes, atol])	Fit the supercell to xyz such that the unit-cell becomes periodic in the specified directions
`is_cartesian`([atol])	Checks if cell vectors a,b,c are multiples of the cartesian axis vectors (x, y, z)
`is_orthogonal`([rtol])	Returns true if the cell vectors are orthogonal.
`lengthf`([axes])	Length of specific lattice vectors (as a function) :Parameters: axes -- only calculate the volume based on a subset of axes
`offset`([isc])	Returns the supercell offset of the supercell index
`parallel`(other[, axes])	Returns true if the cell vectors are parallel to other
`parameters`([rad])	Cell parameters of this cell in 3 lengths and 3 angles
`plane`(axis1, axis2[, origin])	Query point and plane-normal for the plane spanning ax1 and ax2
`prepend`(other, axis)	Prepends other `Lattice` to this grid along axis
`read`(sile, args, *kwargs)	Reads the supercell from the `Sile` using `Sile.read_lattice`
`repeat`(reps, axis)	Extend the unit-cell reps times along the axis lattice vector
`rotate`(angle, v[, rad, what])	Rotates the supercell, in-place by the angle around the vector
`sc_index`(sc_off)	Returns the integer index in the sc_off list that corresponds to `sc_off`
`scale`(scale[, what])	Scale lattice vectors
`set_boundary_condition`([boundary, a, b, c])	Set the boundary conditions on the grid
`set_nsc`([nsc, a, b, c])	Sets the number of supercells in the 3 different cell directions
`swapaxes`(axes1, axes2[, what])	Swaps axes axes1 and axes2
`tile`(reps, axis)	Extend the unit-cell reps times along the axis lattice vector
`toCuboid`(args, *kwargs)	A cuboid with vectors as this unit-cell and center with respect to its origin
`tocell`(*args)	Returns a 3x3 unit-cell dependent on the input
`unrepeat`(reps, axis)	Reverses a `Lattice.tile` and returns the segmented version
`untile`(reps, axis)	Reverses a `Lattice.tile` and returns the segmented version
`vertices`()	Vertices of the cell
`volumef`([axes])	Volume of cell (as a function)
`write`(sile, args, *kwargs)	Writes latticey to the sile using sile.write_lattice

Attributes

`cell`
`nsc`
`n_s`
`boundary_condition`	Boundary conditions for each lattice vector (lower/upper) sides `(3, 2)`
`icell`	Returns the reciprocal (inverse) cell for the `Lattice`.
`isc_off`	Internal indexed supercell `[ia, ib, ic] == i`
`length`	Length of each lattice vector
`origin`	Origin for the cell
`pbc`	Boolean array to specify whether the boundary conditions are periodic`
`rcell`	Returns the reciprocal cell for the `Lattice` with `2*np.pi`
`sc_off`	Integer supercell offsets
`volume`	Volume of cell

BC: alias of BoundaryCondition

add(other) → Lattice

Add two supercell lattice vectors to each other

Parameters:: other (Lattice, array_like) – the lattice vectors of the other supercell to add

add_vacuum(vacuum: float, axis: sisl.typing.CellAxis, orthogonal_to_plane: bool = False) → Lattice[source]

Returns a new object with vacuum along the axis lattice vector

Parameters:

vacuum (float) – amount of vacuum added, in Ang
axis – the lattice vector to add vacuum along
orthogonal_to_plane (bool, optional) – whether the lattice vector should be elongated so that it is vacuum longer when projected onto the normal vector of the other two axis.

angle(axis1: sisl.typing.CellAxis, axis2: sisl.typing.CellAxis, rad: bool = False) → float[source]

The angle between two of the cell vectors

Parameters:

axis1 – the first cell vector
axis2 – the second cell vector
rad (bool, optional) – whether the returned value is in radians

append(other, axis: sisl.typing.CellAxis) → Lattice: Appends other Lattice to this grid along axis

area(axis1: sisl.typing.CellAxis, axis2: sisl.typing.CellAxis) → float[source]: Calculate the area spanned by the two axis ax0 and ax1

cell2length(length, axes: sisl.typing.CellAxes = (0, 1, 2)) → ndarray[source]

Calculate cell vectors such that they each have length length

Parameters:

length (float or array_like) – length for cell vectors, if an array it corresponds to the individual vectors and it must have length equal to axes
axes – which axes the length variable refers too.

Returns:

numpy.ndarray – cell-vectors with prescribed length, same order as axes

center(axes: sisl.typing.CellAxes = (0, 1, 2)) → ndarray: Returns center of the Lattice, possibly with respect to axes

copy(cell=None, **kwargs) → Lattice

A deepcopy of the object

Parameters:: cell (array_like) – the new cell parameters

equal(other, atol: float = 1e-4) → bool[source]

Check whether two lattices are equivalent

Parameters:

other (Lattice) – the other object to check whether the lattice is equivalent
atol (float, optional) – tolerance value for the cell vectors and origin

fit(xyz, axes: sisl.typing.CellAxes = (0, 1, 2), atol: float = 0.05) → Lattice[source]

Fit the supercell to xyz such that the unit-cell becomes periodic in the specified directions

The fitted supercell tries to determine the unit-cell parameters by solving a set of linear equations corresponding to the current supercell vectors.

>>> numpy.linalg.solve(self.cell.T, xyz.T)

It is important to know that this routine will only work if at least some of the atoms are integer offsets of the lattice vectors. I.e. the resulting fit will depend on the translation of the coordinates.

Parameters:

xyz (array_like ``shape(*, 3)``) – the coordinates that we will wish to encompass and analyze.
axes – only the cell-vectors along the provided axes will be used
atol – tolerance (in Angstrom) of the positions. I.e. we neglect coordinates which are not within the radius of this magnitude

Raises:

RuntimeError : – when the cell-parameters does not fit within the given tolerance (atol).

is_cartesian(atol: float = 0.001) → bool[source]

Checks if cell vectors a,b,c are multiples of the cartesian axis vectors (x, y, z)

Parameters:: atol (float, optional) – the threshold above which an off diagonal term will be considered non-zero.

is_orthogonal(rtol: float = 0.001) → bool[source]

Returns true if the cell vectors are orthogonal.

Internally this will be done on the normalized lattice vectors to ensure no numerical instability.

Parameters:: rtol (float, optional) – the threshold above which the scalar product of two normalized cell vectors will be considered non-zero.

lengthf(axes: sisl.typing.CellAxes = (0, 1, 2)) → ndarray[source]

Length of specific lattice vectors (as a function) :Parameters: axes – only calculate the volume based on a subset of axes

Examples

Only get lengths of two lattice vectors:

>>> lat = Lattice(1)
>>> lat.lengthf([0, 1])

new.Sile(**kwargs)

new.ase(**kwargs)

new.ndarray(**kwargs)

offset(isc=None) → tuple[float, float, float][source]: Returns the supercell offset of the supercell index

parallel(other, axes: sisl.typing.CellAxes = (0, 1, 2)) → bool[source]

Returns true if the cell vectors are parallel to other

Parameters:

other (Lattice) – the other object to check whether the axis are parallel
axes – only check the specified axes (default to all)

parameters(rad: bool = False) → tuple[float, float, float, float, float, float][source]

Cell parameters of this cell in 3 lengths and 3 angles

Notes

Since we return the length and angles between vectors it may not be possible to recreate the same cell. Only in the case where the first lattice vector only has a Cartesian \(x\) component will this be the case.

Parameters:

rad (bool, optional) – whether the angles are returned in radians (otherwise in degree)

Returns:

length (numpy.ndarray) – length of each lattice vector
angles (numpy.ndarray) – angles between the lattice vectors (in Voigt notation) [0] is between 2nd and 3rd lattice vector, etc.

plane(axis1: sisl.typing.CellAxis, axis2: sisl.typing.CellAxis, origin: bool = True) → tuple[ndarray, ndarray][source]

Query point and plane-normal for the plane spanning ax1 and ax2

Parameters:

axis1 – the first axis vector
axis2 – the second axis vector
origin (bool, optional) – whether the plane intersects the origin or the opposite corner of the unit-cell.

Returns:

normal_V (numpy.ndarray) – planes normal vector (pointing outwards with regards to the cell)
p (numpy.ndarray) – a point on the plane

Examples

All 6 faces of the supercell can be retrieved like this:

>>> lattice = Lattice(4)
>>> n1, p1 = lattice.plane(0, 1, True)
>>> n2, p2 = lattice.plane(0, 1, False)
>>> n3, p3 = lattice.plane(0, 2, True)
>>> n4, p4 = lattice.plane(0, 2, False)
>>> n5, p5 = lattice.plane(1, 2, True)
>>> n6, p6 = lattice.plane(1, 2, False)

However, for performance critical calculations it may be advantageous to do this:

>>> lattice = Lattice(4)
>>> uc = lattice.cell.sum(0)
>>> n1, p1 = lattice.plane(0, 1)
>>> n2 = -n1
>>> p2 = p1 + uc
>>> n3, p3 = lattice.plane(0, 2)
>>> n4 = -n3
>>> p4 = p3 + uc
>>> n5, p5 = lattice.plane(1, 2)
>>> n6 = -n5
>>> p6 = p5 + uc

Secondly, the variables p1, p3 and p5 are always [0, 0, 0] and p2, p4 and p6 are always uc. Hence this may be used to further reduce certain computations.

prepend(other, axis: sisl.typing.CellAxis) → Lattice

Prepends other Lattice to this grid along axis

For a Lattice object this is equivalent to append.

static read(sile, *args, **kwargs) → Lattice[source]

Reads the supercell from the Sile using Sile.read_lattice

Parameters:: sile (Sile, str or pathlib.Path) – a Sile object which will be used to read the supercell if it is a string it will create a new sile using sisl.io.get_sile.

repeat(reps: int, axis: sisl.typing.CellAxis) → Lattice

Extend the unit-cell reps times along the axis lattice vector

Notes

This is exactly equivalent to the tile routine.

Parameters:

reps – number of times the unit-cell is repeated along the specified lattice vector
axis – the lattice vector along which the repetition is performed

rotate(angle: float, v: str | int | Coord, rad: bool = False, what: Literal['abc', 'a', ...] = 'abc') → Lattice

Rotates the supercell, in-place by the angle around the vector

One can control which cell vectors are rotated by designating them individually with only='[abc]'.

Parameters:

angle – the angle of which the geometry should be rotated
v – the vector around the rotation is going to happen [1, 0, 0] will rotate in the yz plane
rad – Whether the angle is in radians (True) or in degrees (False)
what – only rotate the designated cell vectors.

sc_index(sc_off) → int | Sequence[int][source]

Returns the integer index in the sc_off list that corresponds to sc_off

Returns the index for the supercell in the global offset.

Parameters:: sc_off ((3,) or list of (3,)) – super cell specification. For each axis having value None all supercells along that axis is returned.

scale(scale: CoordOrScalar, what: Literal['abc', 'xyz'] = 'abc') → Lattice

Scale lattice vectors

Does not scale origin.

Parameters:

scale – the scale factor for the new lattice vectors.
what – If three different scale factors are provided, whether each scaling factor is to be applied on the corresponding lattice vector (“abc”) or on the corresponding cartesian coordinate (“xyz”).

set_boundary_condition(boundary: BoundaryCondition | int | str | bool | Sequence[BoundaryCondition | int | str | bool] | None = None, a: BoundaryCondition | int | str | bool | Sequence[BoundaryCondition | int | str | bool] | None = None, b: BoundaryCondition | int | str | bool | Sequence[BoundaryCondition | int | str | bool] | None = None, c: BoundaryCondition | int | str | bool | Sequence[BoundaryCondition | int | str | bool] | None = None)[source]

Set the boundary conditions on the grid

Parameters:

boundary ((3, 2) or (3, ) or int, optional) – boundary condition for all boundaries (or the same for all)
a (int or list of int, optional) – boundary condition for the first unit-cell vector direction
b (int or list of int, optional) – boundary condition for the second unit-cell vector direction
c (int or list of int, optional) – boundary condition for the third unit-cell vector direction

Raises:

ValueError – if specifying periodic one one boundary, so must the opposite side.

set_nsc(nsc=None, a: int | None = None, b: int | None = None, c: int | None = None) → None[source]

Sets the number of supercells in the 3 different cell directions

Parameters:

nsc (list of int, optional) – number of supercells in each direction
a (int, optional) – number of supercells in the first unit-cell vector direction
b (int, optional) – number of supercells in the second unit-cell vector direction
c (int, optional) – number of supercells in the third unit-cell vector direction

swapaxes(axes1: AnyAxes, axes2: AnyAxes, what: Literal['abc', 'xyz', 'abc+xyz'] = 'abc') → Lattice

Swaps axes axes1 and axes2

Swapaxes is a versatile method for changing the order of axes elements, either lattice vector order, or Cartesian coordinate orders.

Parameters:

axes1 – the old axis indices (or labels if str) A string will translate each character as a specific axis index. Lattice vectors are denoted by abc while the Cartesian coordinates are denote by xyz. If str, then what is not used.
axes2 – the new axis indices, same as axes1
what – which elements to swap, lattice vectors (abc), or Cartesian coordinates (xyz), or both. This argument is only used if the axes arguments are ints.

Examples

Swap the first two axes

>>> sc_ba = sc.swapaxes(0, 1)
>>> assert np.allclose(sc_ba.cell[(1, 0, 2)], sc.cell)

Swap the Cartesian coordinates of the lattice vectors

>>> sc_yx = sc.swapaxes(0, 1, what="xyz")
>>> assert np.allclose(sc_ba.cell[:, (1, 0, 2)], sc.cell)

Consecutive swapping: 1. abc -> bac 2. bac -> bca

>>> sc_bca = sc.swapaxes("ab", "bc")
>>> assert np.allclose(sc_ba.cell[:, (1, 0, 2)], sc.cell)

tile(reps: int, axis: sisl.typing.CellAxis) → Lattice

Extend the unit-cell reps times along the axis lattice vector

Notes

This is exactly equivalent to the repeat routine.

Parameters:

reps – number of times the unit-cell is repeated along the specified lattice vector
axis – the lattice vector along which the repetition is performed

to.Cuboid(center=None, origin=None, orthogonal=False) → Cuboid: Convert lattice parameters to a Cuboid

to.Path(*args, **kwargs) → Any

Lattice writing to a sile.

Examples

>>> geom = si.geom.graphene()
>>> geom.lattice.to("hello.xyz")
>>> geom.lattice.to(pathlib.Path("hello.xyz"))

to.Sile(*args, **kwargs) → Any

Lattice writing to a sile.

Examples

>>> geom = si.geom.graphene()
>>> geom.lattice.to("hello.xyz")
>>> geom.lattice.to(pathlib.Path("hello.xyz"))

to.ase(**kwargs) → ase.Cell: Lattice conversion to an ase.Cell object.

to.str(*args, **kwargs) → Any

Lattice writing to a sile.

Examples

>>> geom = si.geom.graphene()
>>> geom.lattice.to("hello.xyz")
>>> geom.lattice.to(pathlib.Path("hello.xyz"))

toCuboid(*args, **kwargs)[source]

A cuboid with vectors as this unit-cell and center with respect to its origin

Parameters:: orthogonal (bool, optional) – if true the cuboid has orthogonal sides such that the entire cell is contained

classmethod tocell(*args) → Lattice[source]

Returns a 3x3 unit-cell dependent on the input

1 argument: a unit-cell along Cartesian coordinates with side-length equal to the argument.
3 arguments: the diagonal components of a Cartesian unit-cell
6 arguments: the cell parameters given by \(a\), \(b\), \(c\), \(\alpha\), \(\beta\) and \(\gamma\) (angles in degrees).
9 arguments: a 3x3 unit-cell.

Parameters:: *args (float) – May be either, 1, 3, 6 or 9 elements. Note that the arguments will be put into an array and flattened before checking the number of arguments.

Examples

>>> cell_1_1_1 = Lattice.tocell(1.)
>>> cell_1_2_3 = Lattice.tocell(1., 2., 3.)
>>> cell_1_2_3 = Lattice.tocell([1., 2., 3.]) # same as above

unrepeat(reps: int, axis: sisl.typing.CellAxis) → Lattice

Reverses a Lattice.tile and returns the segmented version

Notes

Untiling will not correctly re-calculate nsc since it has no knowledge of connections.