SuperCell

class sisl.SuperCell(cell, nsc=None, origo=None)

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

origo : (3,) of float

the origo of the supercell.

Attributes:

cell : (3, 3) of float

the lattice vectors (cell[i, :] is the i’th vector)

icell : (3, 3) of float

Returns the reciprocal (inverse) cell for the SuperCell.

rcell : (3, 3) of float

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

Attributes

cell
icell	Returns the reciprocal (inverse) cell for the SuperCell.
isc_off	Internal indexed supercell [ia, ib, ic] == i
n_s
nsc
origo	Origo for the cell
rcell	Returns the reciprocal cell for the SuperCell with 2*np.pi
sc_off	Integer supercell offsets
volume

Methods

__init__(cell[, nsc, origo])	Initialize self.
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
center([axis])	Returns center of the SuperCell, possibly with respect to an axis
copy([cell, origo])	Returns a copy of the object with possibly some quantities overwritten
cut(seps, axis)	Cuts the cell into several different sections.
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_orthogonal()	Returns true if the cell vectors are orthogonal
move(v)	Appends additional space in the SuperCell 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])	Return the cell-parameters of this cell
plane(ax1, ax2[, origo])	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 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
rotatea(angle[, only, rad])
rotateb(angle[, only, rad])
rotatec(angle[, only, rad])
sc_index(sc_off)	Returns the integer index in the sc_off list that corresponds to sc_off
scale(scale)	Scale lattice vectors
set_nsc([nsc, a, b, c])	Sets the number of supercells in the 3 different cell directions
swapaxes(a, b)	Returns SuperCell with swapped axis
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 origo
tocell(*args)	Returns a 3x3 unit-cell dependent on the input
translate(v)	Appends additional space in the SuperCell object

add(other)

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)

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)

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)

Appends other SuperCell to this grid along axis

cell

center(axis=None)

Returns center of the SuperCell, possibly with respect to an axis

copy(cell=None, origo=None)

Returns a copy of the object with possibly some quantities overwritten

Parameters:

cell : array_like

the new cell parameters

origo : array_like

the new origo

cut(seps, axis)

Cuts the cell into several different sections.

equal(other, tol=0.0001)

Check whether two supercell are equivalent

Parameters:

tol : float, optional

tolerance value for the cell vectors and origo

fit(xyz, axis=None, tol=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.

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

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_orthogonal()

Returns true if the cell vectors are orthogonal

isc_off

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

move(v)

Appends additional space in the SuperCell object

n_s

nsc

offset(isc=None)

Returns the supercell offset of the supercell index

origo

Origo for the cell

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

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)

Return the cell-parameters of this cell

Parameters:

rad : bool, optional

whether the angles are returned in radians (otherwise in degree)

Returns:

a : length of first lattice vector

b : length of second lattice vector

c : length of third lattice vector

alpha : angle between b and c vectors

beta : angle between a and c vectors

gamma : angle between a and b vectors

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

plane(ax1, ax2, origo=True)

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

origo : bool, optional

whether the plane intersects the origo or the opposite corner of the unit-cell.

Returns:

n : array_like

planes normal vector (pointing outwards with regards to the cell)

p : array_like

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)

Prepends other SuperCell to this grid along axis

For a SuperCell object this is equivalent to append.

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)

Reads SuperCell from the Sile using Sile.read_supercell

Parameters:

sile : Sile or str

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)

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

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

Notes

This is exactly equivalent to the tile routine.

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

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 [3]

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.

rotatea(angle, only='abc', rad=False)

rotateb(angle, only='abc', rad=False)

rotatec(angle, only='abc', rad=False)

sc_index(sc_off)

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

Returns the integer for the supercell

sc_off

Integer supercell offsets

scale(scale)

Scale lattice vectors

Does not scale origo.

Parameters:

scale : float

the scale factor for the new lattice vectors

set_nsc(nsc=None, a=None, b=None, c=None)

Sets the number of supercells in the 3 different cell directions

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)

Returns SuperCell with swapped axis

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

tile(reps, axis)

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

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

Notes

This is exactly equivalent to the repeat routine.

toCuboid(orthogonal=False)

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

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 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 in the SuperCell object

volume