sisl.Lattice

class sisl.Lattice

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 deep copy 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) :param 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)

Add two supercell lattice vectors to each other

Parameters:

• other (LatticeLike) – the lattice vectors of the other supercell to add

• lattice (Lattice)

Return type:

Lattice

add_vacuum(vacuum, axis, orthogonal_to_plane=False)

Returns a new object with vacuum along the axis lattice vector

Parameters:

• vacuum (float) – amount of vacuum added, in Ang

• axis (Literal[0, 1, 2, 'a', 'b', 'c']) – 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.

Return type:

Lattice

angle(axis1, axis2, rad=False)

The angle between two of the cell vectors

Parameters:

• axis1 (Literal[0, 1, 2, 'a', 'b', 'c']) – the first cell vector

• axis2 (Literal[0, 1, 2, 'a', 'b', 'c']) – the second cell vector

• rad (bool, optional) – whether the returned value is in radians

Return type:

float

append(other, axis)

Appends other Lattice to this grid along axis

Parameters:

• lattice (Lattice)

• axis (Literal[0, 1, 2, 'a', 'b', 'c'])

Return type:

Lattice

area(axis1, axis2)

Calculate the area spanned by the two axis ax0 and ax1

Parameters:

• axis1 (Literal[0, 1, 2, 'a', 'b', 'c'])

• axis2 (Literal[0, 1, 2, 'a', 'b', 'c'])

Return type:

float

cell2length(length, axes=(0, 1, 2))

Calculate cell vectors such that they each have length length

Parameters:

• length (float or ndarray) – length for cell vectors, if an array it corresponds to the individual vectors and it must have length equal to axes

• axes (Literal[0, 1, 2] | ~typing.Literal['a', 'b', 'c'] | ~collections.abc.Sequence[~typing.Literal[0, 1, 2, 'a', 'b', 'c']]) – which axes the length variable refers too.

Returns:

cell-vectors with prescribed length, same order as axes

Return type:

numpy.ndarray

center(axes=(0, 1, 2))

Returns center of the Lattice, possibly with respect to axes

Parameters:

• lattice (Lattice)

• axes (Literal[0, 1, 2] | ~typing.Literal['a', 'b', 'c'] | ~collections.abc.Sequence[~typing.Literal[0, 1, 2, 'a', 'b', 'c']])

Return type:

ndarray

copy(cell=None, **kwargs)

A deep copy of the object

Parameters:

• cell (ndarray | None) – the new cell parameters

• lattice (Lattice)

Return type:

Lattice

equal(other, atol=1e-4)

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

Return type:

bool

fit(xyz, axes=(0, 1, 2), atol=0.05)

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 (Literal[0, 1, 2] | ~typing.Literal['a', 'b', 'c'] | ~collections.abc.Sequence[~typing.Literal[0, 1, 2, 'a', 'b', 'c']]) – only the cell-vectors along the provided axes will be used

• atol (float) – 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).

Return type:

Lattice

is_cartesian(atol=0.001)

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.

Return type:

bool

is_orthogonal(rtol=0.001)

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.

Return type:

bool

lengthf(axes=(0, 1, 2))

Length of specific lattice vectors (as a function) :param 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])

Parameters:

axes (Literal[0, 1, 2] | ~typing.Literal['a', 'b', 'c'] | ~collections.abc.Sequence[~typing.Literal[0, 1, 2, 'a', 'b', 'c']])

Return type:

ndarray

new.Sile(**kwargs)

new.ase(**kwargs)

new.ndarray(**kwargs)

offset(isc=None)

Returns the supercell offset of the supercell index

Return type:

tuple[float, float, float]

parallel(other, axes=(0, 1, 2))

Returns true if the cell vectors are parallel to other

Parameters:

• other (Lattice) – the other object to check whether the axis are parallel

• axes (Literal[0, 1, 2] | ~typing.Literal['a', 'b', 'c'] | ~collections.abc.Sequence[~typing.Literal[0, 1, 2, 'a', 'b', 'c']]) – only check the specified axes (default to all)

Return type:

bool

parameters(rad=False)

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.

Return type:

tuple[float, float, float, float, float, float]

plane(axis1, axis2, origin=True)

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

Parameters:

• axis1 (Literal[0, 1, 2, 'a', 'b', 'c']) – the first axis vector

• axis2 (Literal[0, 1, 2, 'a', 'b', 'c']) – 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

Return type:

tuple[ndarray, ndarray]

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)

Prepends other Lattice to this grid along axis

For a Lattice object this is equivalent to append.

Parameters:

• lattice (Lattice)

• axis (Literal[0, 1, 2, 'a', 'b', 'c'])

Return type:

Lattice

static read(sile, *args, **kwargs)

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.

Return type:

Lattice

repeat(reps, axis)

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

Notes

This is exactly equivalent to the tile routine.

Parameters:

• reps (int) – number of times the unit-cell is repeated along the specified lattice vector

• axis (Literal[0, 1, 2, 'a', 'b', 'c']) – the lattice vector along which the repetition is performed

• lattice (Lattice)

Return type:

Lattice

rotate(angle, v, rad=False, what='abc')

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 (float) – the angle of which the geometry should be rotated

• v (Union[str, int, Coord]) – the vector around the rotation is going to happen [1, 0, 0] will rotate in the yz plane

• rad (bool) – Whether the angle is in radians (True) or in degrees (False)

• what (Literal['abc', 'a', ...]) – only rotate the designated cell vectors.

• lattice (Lattice)

Return type:

Lattice

sc_index(sc_off)

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.

Return type:

int | Sequence[int]

scale(scale, what='abc')

Scale lattice vectors

Does not scale origin.

Parameters:

• scale (CoordOrScalar) – the scale factor for the new lattice vectors.

• what (Literal['abc', 'xyz']) – 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”).

• lattice (Lattice)

Return type:

Lattice

set_boundary_condition(boundary=None, a=None, b=None, c=None)

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=None, b=None, c=None)

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

Return type:

None

swapaxes(axes1, axes2, what='abc')

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 (AnyAxes) – 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 (AnyAxes) – the new axis indices, same as axes1

• what (Literal['abc', 'xyz', 'abc+xyz']) – which elements to swap, lattice vectors (abc), or Cartesian coordinates (xyz), or both. This argument is only used if the axes arguments are ints.

• lattice (Lattice)

Return type:

Lattice

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, axis)

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

Notes

This is exactly equivalent to the repeat routine.

Parameters:

• reps (int) – number of times the unit-cell is repeated along the specified lattice vector

• axis (Literal[0, 1, 2, 'a', 'b', 'c']) – the lattice vector along which the repetition is performed

• lattice (Lattice)

Return type:

Lattice

to.Cuboid(center=None, origin=None, orthogonal=False)

Convert lattice parameters to a Cuboid

Return type:

Cuboid

to.Path(*args, **kwargs)

Lattice writing to a sile.

Examples

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

Return type:

Any

to.Sile(*args, **kwargs)

Lattice writing to a sile.

Examples

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

Return type:

Any

to.ase(**kwargs)

Lattice conversion to an ase.Cell object.

Return type:

ase.Cell

to.str(*args, **kwargs)

Lattice writing to a sile.

Examples

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

Return type:

Any

toCuboid(*args, **kwargs)

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)

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.

Return type:

Lattice

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, axis)

Reverses a Lattice.tile and returns the segmented version

Notes

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

See also

Lattice.tile

opposite of this method

Parameters:

• lattice (Lattice)

• reps (int)

• axis (Literal[0, 1, 2, 'a', 'b', 'c'])

Return type:

Lattice

untile(reps, axis)

Reverses a Lattice.tile and returns the segmented version

Notes

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

See also

Lattice.tile

opposite of this method

Parameters:

• lattice (Lattice)

• reps (int)

• axis (Literal[0, 1, 2, 'a', 'b', 'c'])

Return type:

Lattice

vertices()

Vertices of the cell

Returns:

The coordinates of the vertices of the cell. The first three dimensions correspond to each cell axis (off, on), and the last one contains the xyz coordinates.

Return type:

array of shape (2, 2, 2, 3)

volumef(axes=(0, 1, 2))

Volume of cell (as a function)

Default to the 3D volume. For axes with only 2 elements, it corresponds to an area. For axes with only 1 element, it corresponds to a length.

Parameters:

axes (Literal[0, 1, 2] | ~typing.Literal['a', 'b', 'c'] | ~collections.abc.Sequence[~typing.Literal[0, 1, 2, 'a', 'b', 'c']]) – only calculate the volume based on a subset of axes

Return type:

float

Examples

Only get the volume of the periodic directions:

>>> lat = Lattice(1)
>>> lat.pbc = (True, False, True)
>>> lat.volumef(lat.pbc.nonzero()[0])

write(sile, *args, **kwargs)

Writes latticey to the sile using sile.write_lattice

Parameters:

• sile (SileLike) – a Sile object which will be used to write the lattice if it is a string it will create a new sile using get_sile

• *args – Any other args will be passed directly to the underlying routine

• **kwargs – Any other args will be passed directly to the underlying routine

• lattice (Lattice)

Return type:

None

See also

Lattice.read

reads a Lattice from a given Sile/file

property boundary_condition: ndarray

Boundary conditions for each lattice vector (lower/upper) sides (3, 2)

cell

property icell: ndarray

Returns the reciprocal (inverse) cell for the Lattice.

Note: The returned vectors are still in [0, :] format and not as returned by an inverse LAPACK algorithm.

property isc_off: ndarray

Internal indexed supercell [ia, ib, ic] == i

property length: ndarray

Length of each lattice vector

n_s

new = <TypeDispatcher{obj=<class 'sisl.Lattice'>}>

Parameters:

obj (Any)

Return type:

Any

nsc

property origin: ndarray

Origin for the cell

property pbc: ndarray

Boolean array to specify whether the boundary conditions are periodic`

property rcell: ndarray

Returns the reciprocal cell for the Lattice with 2*np.pi

Note: The returned vectors are still in [0, :] format and not as returned by an inverse LAPACK algorithm.

property sc_off: ndarray

Integer supercell offsets

to

A dispatcher for classes, using __get__ it converts into ObjectDispatcher upon invocation from an object, or a TypeDispatcher when invoked from a class

This is a class-placeholder allowing a dispatcher to be a class attribute and converted into an ObjectDispatcher when invoked from an object.

If it is called on the class, it will return a TypeDispatcher.

This class should be an attribute of a class. It heavily relies on the __get__ special method.

Parameters:

• name (str) – name of the attribute in the class

• dispatchs (dict, optional) – dictionary of dispatch methods

• obj_getattr (callable, optional) – method with 2 arguments, an obj and the attr which may be used to control how the attribute is called.

• instance_dispatcher (AbstractDispatcher, optional) – control how instance dispatchers are handled through __get__ method. This controls the dispatcher used if called from an instance.

• type_dispatcher (AbstractDispatcher, optional) – control how class dispatchers are handled through __get__ method. This controls the dispatcher used if called from a class.

Examples

>>> class A:
...   new = ClassDispatcher("new", obj_getattr=lambda obj, attr: getattr(obj.sub, attr))

The above defers any attributes to the contained A.sub attribute.

property volume: float

Volume of cell