sisl.SuperCell

class sisl.SuperCell(cell, nsc=None, origin=None)

Bases: object

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 latticevector
origin ((3,) of float, optional) – the origin of the supercell.

Methods

`add`(other)	Add two supercell lattice vectors to each other
`add_vacuum`(vacuum, axis)	Add vacuum along the axis lattice vector
`angle`(i, j[, rad])	The angle between two of the cell vectors
`append`(other, axis)	Appends other `SuperCell` to this grid along axis
`area`(ax0, ax1)	Calculate the area spanned by the two axis ax0 and ax1
`cell_length`(length)	Calculate cell vectors such that they each have length `length`
`center`([axis])	Returns center of the `SuperCell`, possibly with respect to an axis
`copy`([cell, origin])	A deepcopy of the object
`cut`(reps, axis)	Reverses a `SuperCell.tile` and returns the segmented version
`equal`(other[, tol])	Check whether two supercell 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 `SuperCell` to this grid along axis
`read`(sile, args, *kwargs)	Reads the supercell from the `Sile` using `Sile.read_supercell`
`repeat`(reps, axis)	Extend the unit-cell reps times along the axis lattice vector
`rotate`(angle, v[, only, rad])	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_nsc`([nsc, a, b, c])	Sets the number of supercells in the 3 different cell directions
`swapaxes`(a, b)	Swap axis a and b in a new `SuperCell`
`tile`(reps, axis)	Extend the unit-cell reps times along the axis lattice vector
`toCuboid`([orthogonal])	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 `SuperCell.tile` and returns the segmented version
`untile`(reps, axis)	Reverses a `SuperCell.tile` and returns the segmented version
`vertices`()	Vertices of the cell
`cell`
`nsc`
`n_s`
`icell`	Returns the reciprocal (inverse) cell for the `SuperCell`.
`isc_off`	Internal indexed supercell `[ia, ib, ic] == i`
`length`	Length of each lattice vector
`origin`	Origin for the cell
`origo`	Origin for the cell
`rcell`	Returns the reciprocal cell for the `SuperCell` with `2*np.pi`
`sc_off`	Integer supercell offsets
`volume`	Volume of cell

__init__(cell, nsc=None, origin=None)[source]

add(other)[source]

Add two supercell lattice vectors to each other

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

add_vacuum(vacuum, axis)[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

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 SuperCell to this grid along axis

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

cell

cell_length(length)[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 3
Returns: cell-vectors with prescribed length
Return type: numpy.ndarray

center(axis=None)[source]: Returns center of the SuperCell, 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

cut(reps, axis)

Reverses a SuperCell.tile and returns the segmented version

See also

tile: opposite of this method

equal(other, tol=0.0001)[source]

Check whether two supercell 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 SuperCell.

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

property length: Length of each lattice vector

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

n_s

nsc

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

property origin: Origin for the cell

property origo: Origin for the cell

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

Returns true if the cell vectors are parallel to other

Parameters

other (SuperCell) – 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)

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

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:

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

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

>>> sc = SuperCell(4)
>>> uc = sc.cell.sum(0)
>>> n1, p1 = sc.plane(0, 1)
>>> n2 = -n1
>>> p2 = p1 + uc
>>> n3, p3 = sc.plane(0, 2)
>>> n4 = -n3
>>> p4 = p3 + uc
>>> n5, p5 = sc.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 SuperCell to this grid along axis

For a SuperCell object this is equivalent to append.

property rcell

Returns the reciprocal cell for the SuperCell 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_supercell

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

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: 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_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(a, b)[source]

Swap axis a and b in a new SuperCell

If swapaxes(0,1) it returns the 0 in the 1 values.

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

toCuboid(orthogonal=False)[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 = SuperCell.tocell(1.)
>>> cell_1_2_3 = SuperCell.tocell(1., 2., 3.)
>>> cell_1_2_3 = SuperCell.tocell([1., 2., 3.]) # same as above

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

unrepeat(reps, axis)

Reverses a SuperCell.tile and returns the segmented version