sisl.Lattice

class sisl.Lattice(cell, nsc=None, origin=None, boundary_condition=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 neighbouring 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 (array_like) – the lattice parameters of the unit cell (the actual cell is returned from tocell.
nsc (array_like of int) – number of supercells along each lattice vector
origin ((3,) of float, optional) – the origin of the supercell.
boundary_condition (int/str or list of int/str (3, 2) or (3, ), optional) – the boundary conditions for each of the cell’s planes. Defaults to periodic boundary condition. See BoundaryCondition for valid enumerations.

Methods

`add`(other)	Add two supercell lattice vectors to each other
`add_vacuum`(vacuum, axis[, orthogonal_to_plane])	Add vacuum along the axis lattice vector
`angle`(i, j[, rad])	The angle between two of the cell vectors
`append`(other, axis)	Appends other Lattice to this grid along axis
`area`(ax0, ax1)	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`([axis])	Returns center of the Lattice, possibly with respect to an axis
`copy`([cell, origin])	A deepcopy of the object
`equal`(other[, tol])	Check whether two lattices are equivalent
`fit`(xyz[, axis, tol])	Fit the supercell to xyz such that the unit-cell becomes periodic in the specified directions
`is_cartesian`([tol])	Checks if cell vectors a,b,c are multiples of the cartesian axis vectors (x, y, z)
`is_orthogonal`([tol])	Returns true if the cell vectors are orthogonal.
`move`(v)	Appends additional space to the object
`offset`([isc])	Returns the supercell offset of the supercell index
`parallel`(other[, axis])	Returns true if the cell vectors are parallel to other
`parameters`([rad])	Cell parameters of this cell in 3 lengths and 3 angles
`plane`(ax1, ax2[, 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`(axes_a, axes_b[, what])	Swaps axes axes_a and axes_b
`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
`translate`(v)	Appends additional space to the object
`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
`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
`new`
`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
`to`	A dispatcher for classes, using __get__ it converts into ObjectDispatcher upon invocation from an object, or a TypeDispatcher when invoked from a class
`volume`	Volume of cell

BC: alias of BoundaryCondition

__init__(cell, nsc=None, origin=None, boundary_condition=BoundaryCondition.PERIODIC)[source]

add(other)[source]

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, axis, orthogonal_to_plane=False)[source]

Add vacuum along the axis lattice vector

Parameters

vacuum (float) – amount of vacuum added, in Ang
axis (int) – 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(i, j, rad=False)[source]

The angle between two of the cell vectors

Parameters

i (int) – the first cell vector
j (int) – the second cell vector
rad (bool, optional) – whether the returned value is in radians

append(other, axis)[source]: Appends other Lattice to this grid along axis

area(ax0, ax1)[source]: Calculate the area spanned by the two axis ax0 and ax1

property boundary_condition: ndarray: Boundary conditions for each lattice vector (lower/upper) sides (3, 2)

cell

cell2length(length, axes=(0, 1, 2))[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 (int or array_like, optional) – which axes the length variable refers too.

Returns

cell-vectors with prescribed length, same order as axes

Return type

numpy.ndarray

center(axis=None)[source]: Returns center of the Lattice, possibly with respect to an axis

copy(cell=None, origin=None)[source]

A deepcopy of the object

Parameters

cell (array_like) – the new cell parameters
origin (array_like) – the new origin

equal(other, tol=0.0001)[source]

Check whether two lattices are equivalent

Parameters: tol (float, optional) – tolerance value for the cell vectors and origin

fit(xyz, axis=None, tol=0.05)[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.
axis (None or array_like) – if None equivalent to [0, 1, 2], else only the cell-vectors along the provided axis will be used
tol (float) – tolerance (in Angstrom) of the positions. I.e. we neglect coordinates which are not within the radius of this magnitude

property icell

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.

is_cartesian(tol=0.001)[source]

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

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

is_orthogonal(tol=0.001)[source]

Returns true if the cell vectors are orthogonal.

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

property isc_off: ndarray: Internal indexed supercell [ia, ib, ic] == i

property length: ndarray: Length of each lattice vector

move(v): Appends additional space to the object

n_s

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

nsc

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

property origin: ndarray: Origin for the cell

parallel(other, axis=(0, 1, 2))[source]

Returns true if the cell vectors are parallel to other

Parameters

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

parameters(rad=False)[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)

Return type

Tuple[float, float, float, float, float, float]

Returns

float – length of first lattice vector
float – length of second lattice vector
float – length of third lattice vector
float – angle between b and c vectors
float – angle between a and c vectors
float – angle between a and b vectors

property pbc: ndarray: Boolean array to specify whether the boundary conditions are periodic`

plane(ax1, ax2, origin=True)[source]

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

Parameters

ax1 (int) – the first axis vector
ax2 (int) – 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)[source]

Prepends other Lattice to this grid along axis

For a Lattice object this is equivalent to append.

property rcell

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.

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

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 (int) – the lattice vector along which the repetition is performed

rotate(angle, v, rad=False, what='abc')[source]

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 (array_like or str or int) – the vector around the rotation is going to happen v = [1,0,0] will rotate in the yz plane
what (combination of "abc", str, optional) – only rotate the designated cell vectors.
rad (bool, optional) – Whether the angle is in radians (True) or in degrees (False)

Return type

Lattice

sc_index(sc_off)[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.

property sc_off: ndarray: Integer supercell offsets

scale(scale, what='abc')[source]

Scale lattice vectors

Does not scale origin.

Parameters

scale (float or (3,)) – the scale factor for the new lattice vectors.
what ({"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”).

set_boundary_condition(boundary=None, a=None, b=None, c=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=None, b=None, c=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 (integer, optional) – number of supercells in the first unit-cell vector direction
b (integer, optional) – number of supercells in the second unit-cell vector direction
c (integer, optional) – number of supercells in the third unit-cell vector direction

swapaxes(axes_a, axes_b, what='abc')[source]

Swaps axes axes_a and axes_b

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

Parameters

axes_a (int or str) – 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.
axes_b (int or str) – the new axis indices, same as axes_a
what ({"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.

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)[source]

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 (int) – the lattice vector along which the repetition is performed

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.

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)[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 give 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

translate(v)[source]: Appends additional space to the object

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.