Using the spacegroup subpackage

The most evident usage of the spacegroup subpackage is to set up an initial unit of a bulk structure. For this you only need to supply the unique atoms and their scaled positions, space group and lattice parameters.

Examples of setting up bulk structures

We start by showing some examples of how to set up some common or interesting bulk structures using ase.spacegroup.crystal(). This function takes a lot of arguments:

ase.spacegroup.crystal(symbols=None, basis=None, occupancies=None, spacegroup=1, setting=1, cell=None, cellpar=None, ab_normal=(0, 0, 1), a_direction=None, size=(1, 1, 1), onduplicates='warn', symprec=0.001, pbc=True, primitive_cell=False, **kwargs)[source]

Create an Atoms instance for a conventional unit cell of a space group.

Parameters:

symbols : str | sequence of str | sequence of Atom | Atoms
Element symbols of the unique sites. Can either be a string formula or a sequence of element symbols. E.g. (‘Na’, ‘Cl’) and ‘NaCl’ are equivalent. Can also be given as a sequence of Atom objects or an Atoms object.
basis : list of scaled coordinates
Positions of the unique sites corresponding to symbols given either as scaled positions or through an atoms instance. Not needed if symbols is a sequence of Atom objects or an Atoms object.
occupancies : list of site occupancies
Occupancies of the unique sites. Defaults to 1.0 and thus no mixed occupancies are considered if not explicitly asked for. If occupancies are given, the most dominant species will yield the atomic number.
spacegroup : int | string | Spacegroup instance
Space group given either as its number in International Tables or as its Hermann-Mauguin symbol.
setting : 1 | 2
Space group setting.
cell : 3x3 matrix
Unit cell vectors.
cellpar : [a, b, c, alpha, beta, gamma]
Cell parameters with angles in degree. Is not used when \(cell\) is given.
ab_normal : vector
Is used to define the orientation of the unit cell relative to the Cartesian system when \(cell\) is not given. It is the normal vector of the plane spanned by a and b.
a_direction : vector
Defines the orientation of the unit cell a vector. a will be parallel to the projection of \(a_direction\) onto the a-b plane.
size : 3 positive integers
How many times the conventional unit cell should be repeated in each direction.
onduplicates : ‘keep’ | ‘replace’ | ‘warn’ | ‘error’
Action if \(basis\) contain symmetry-equivalent positions:
‘keep’ - ignore additional symmetry-equivalent positions ‘replace’ - replace ‘warn’ - like ‘keep’, but issue an UserWarning ‘error’ - raises a SpacegroupValueError
symprec : float
Minimum “distance” betweed two sites in scaled coordinates before they are counted as the same site.
pbc : one or three bools
Periodic boundary conditions flags. Examples: True, False, 0, 1, (1, 1, 0), (True, False, False). Default is True.
primitive_cell : bool
Wheter to return the primitive instead of the conventional unit cell.

Keyword arguments:

All additional keyword arguments are passed on to the Atoms constructor. Currently, probably the most useful additional keyword arguments are \(info\), \(constraint\) and \(calculator\).

Examples:

Two diamond unit cells (space group number 227)

>>> diamond = crystal('C', [(0,0,0)], spacegroup=227,
...     cellpar=[3.57, 3.57, 3.57, 90, 90, 90], size=(2,1,1))
>>> ase.view(diamond)  

A CoSb3 skutterudite unit cell containing 32 atoms

>>> skutterudite = crystal(('Co', 'Sb'),
...     basis=[(0.25,0.25,0.25), (0.0, 0.335, 0.158)],
...     spacegroup=204, cellpar=[9.04, 9.04, 9.04, 90, 90, 90])
>>> len(skutterudite)
32

There is also a get_spacegroup() function that will return a spacegroup object from an Atoms object.

Aluminium (fcc)

../../_images/spacegroup-al.png
from ase.spacegroup import crystal

a = 4.05
al = crystal('Al', [(0,0,0)], spacegroup=225, cellpar=[a, a, a, 90, 90, 90])

The spacegroup argument can also be entered with its Hermann-Mauguin symbol, e.g. spacegroup=225 is equivalent to spacegroup=’F m -3 m’.

Iron (bcc)

../../_images/spacegroup-fe.png
from ase.spacegroup import crystal

a = 2.87
fe = crystal('Fe', [(0,0,0)], spacegroup=229, cellpar=[a, a, a, 90, 90, 90])

Magnesium (hcp)

../../_images/spacegroup-mg.png
from ase.spacegroup import crystal

a = 3.21
c = 5.21
mg = crystal('Mg', [(1./3., 2./3., 3./4.)], spacegroup=194,
             cellpar=[a, a, c, 90, 90, 120])

Diamond

../../_images/spacegroup-diamond.png
from ase.spacegroup import crystal

a = 3.57
diamond = crystal('C', [(0,0,0)], spacegroup=227, cellpar=[a, a, a, 90, 90, 90])

Sodium chloride

../../_images/spacegroup-nacl.png
from ase.spacegroup import crystal

a = 5.64
nacl = crystal(['Na', 'Cl'], [(0, 0, 0), (0.5, 0.5, 0.5)], spacegroup=225,
               cellpar=[a, a, a, 90, 90, 90])

Rutile

../../_images/spacegroup-rutile.png
from ase.spacegroup import crystal

a = 4.6
c = 2.95
rutile =crystal(['Ti', 'O'], basis=[(0, 0, 0), (0.3, 0.3, 0.0)],
                spacegroup=136, cellpar=[a, a, c, 90, 90, 90])

CoSb3 skutterudite

../../_images/spacegroup-skutterudite.png

Skutterudites are quite interesting structures with 32 atoms in the unit cell.

from ase.spacegroup import crystal

a = 9.04
skutterudite = crystal(('Co', 'Sb'),
                       basis=[(0.25, 0.25, 0.25), (0.0, 0.335, 0.158)],
                       spacegroup=204,
                       cellpar=[a, a, a, 90, 90, 90])

Often this structure is visualised with the Cobalt atoms on the corners. This can easily be accomplished with ASE using ase.build.cut(). Below is the origo argument used to put the Cobalt atom on the corners and extend to include all corner and edge atoms, even those belonging to neighbouring unit cells.

../../_images/spacegroup-cosb3.png
import ase.io as io
from ase.build import cut
from ase.spacegroup import crystal

a = 9.04
skutterudite = crystal(('Co', 'Sb'),
                       basis=[(0.25, 0.25, 0.25), (0.0, 0.335, 0.158)],
                       spacegroup=204,
                       cellpar=[a, a, a, 90, 90, 90])

# Create a new atoms instance with Co at origo including all atoms on the
# surface of the unit cell
cosb3 = cut(skutterudite, origo=(0.25, 0.25, 0.25), extend=1.01)

# Define the atomic bonds to show
bondatoms = []
symbols = cosb3.get_chemical_symbols()
for i in range(len(cosb3)):
    for j in range(i):
        if (symbols[i] == symbols[j] == 'Co' and
            cosb3.get_distance(i, j) < 4.53):
            bondatoms.append((i, j))
        elif (symbols[i] == symbols[j] == 'Sb' and
              cosb3.get_distance(i, j) < 2.99):
            bondatoms.append((i, j))

# Create nice-looking image using povray
io.write('spacegroup-cosb3.pov', cosb3,
         transparent=False,
         display=False,
         run_povray=True,
         camera_type='perspective',
         canvas_width=320,
         radii=0.4,
         rotation='90y',
         bondlinewidth=0.07,
         bondatoms=bondatoms)

The Spacegroup class

The ase.spacegroup.Spacegroup class is used internally by the ase.spacegroup.crystal() function, but might sometimes also be useful if you want to know e.g. the symmetry operations of a given space group. Instances of the ase.spacegroup.Spacegroup class are immutable objects holding space group information, such as symmetry operations.

Let us e.g. consider the fcc structure. To print information about the space group, do

>>> from ase.spacegroup import Spacegroup
>>> sg = Spacegroup(225)
>>> print(sg)
225   F m -3 m
  setting 1
  centrosymmetric 1
  primitive vectors
     0.0000000000  0.5000000000  0.5000000000
     0.5000000000  0.0000000000  0.5000000000
     0.5000000000  0.5000000000  0.0000000000
  reciprocal vectors
     -1   1   1
      1  -1   1
      1   1  -1
  4 subtranslations
     0.0000000000  0.0000000000  0.0000000000
     0.0000000000  0.5000000000  0.5000000000
     0.5000000000  0.0000000000  0.5000000000
     0.5000000000  0.5000000000  0.0000000000
  24 symmetry operations (rot+trans)
    1  0  0     0  1  0     0  0  1    0.0000000000  0.0000000000  0.0000000000
   -1  0  0     0 -1  0     0  0  1    0.0000000000  0.0000000000  0.0000000000
   -1  0  0     0  1  0     0  0 -1    0.0000000000  0.0000000000  0.0000000000
    1  0  0     0 -1  0     0  0 -1    0.0000000000  0.0000000000  0.0000000000
    0  0  1     1  0  0     0  1  0    0.0000000000  0.0000000000  0.0000000000
    0  0  1    -1  0  0     0 -1  0    0.0000000000  0.0000000000  0.0000000000
    0  0 -1    -1  0  0     0  1  0    0.0000000000  0.0000000000  0.0000000000
    0  0 -1     1  0  0     0 -1  0    0.0000000000  0.0000000000  0.0000000000
    0  1  0     0  0  1     1  0  0    0.0000000000  0.0000000000  0.0000000000
    0 -1  0     0  0  1    -1  0  0    0.0000000000  0.0000000000  0.0000000000
    0  1  0     0  0 -1    -1  0  0    0.0000000000  0.0000000000  0.0000000000
    0 -1  0     0  0 -1     1  0  0    0.0000000000  0.0000000000  0.0000000000
    0  1  0     1  0  0     0  0 -1    0.0000000000  0.0000000000  0.0000000000
    0 -1  0    -1  0  0     0  0 -1    0.0000000000  0.0000000000  0.0000000000
    0  1  0    -1  0  0     0  0  1    0.0000000000  0.0000000000  0.0000000000
    0 -1  0     1  0  0     0  0  1    0.0000000000  0.0000000000  0.0000000000
    1  0  0     0  0  1     0 -1  0    0.0000000000  0.0000000000  0.0000000000
   -1  0  0     0  0  1     0  1  0    0.0000000000  0.0000000000  0.0000000000
   -1  0  0     0  0 -1     0 -1  0    0.0000000000  0.0000000000  0.0000000000
    1  0  0     0  0 -1     0  1  0    0.0000000000  0.0000000000  0.0000000000
    0  0  1     0  1  0    -1  0  0    0.0000000000  0.0000000000  0.0000000000
    0  0  1     0 -1  0     1  0  0    0.0000000000  0.0000000000  0.0000000000
    0  0 -1     0  1  0     1  0  0    0.0000000000  0.0000000000  0.0000000000
    0  0 -1     0 -1  0    -1  0  0    0.0000000000  0.0000000000  0.0000000000

Or, if you want to figure out what sites in the unit cell are equivalent to (0, 0, 0.5), simply do

>>> sites,kinds = sg.equivalent_sites([(0, 0, 0.5)])
>>> sites
array([[ 0. ,  0. ,  0.5],
       [ 0.5,  0. ,  0. ],
       [ 0. ,  0.5,  0. ],
       [ 0.5,  0.5,  0.5]])
>>> kinds
[0, 0, 0, 0]

where sites will be an array containing the scaled positions of the four symmetry-equivalent sites.

class ase.spacegroup.Spacegroup(spacegroup, setting=1, datafile=None)[source]

A space group class.

The instances of Spacegroup describes the symmetry operations for the given space group.

Example:

>>> from ase.spacegroup import Spacegroup
>>>
>>> sg = Spacegroup(225)
>>> print('Space group', sg.no, sg.symbol)
Space group 225 F m -3 m
>>> sg.scaled_primitive_cell
array([[ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ]])
>>> sites, kinds = sg.equivalent_sites([[0,0,0]])
>>> sites
array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ]])

Returns a new Spacegroup instance.

Parameters:

spacegroup : int | string | Spacegroup instance
The space group number in International Tables of Crystallography or its Hermann-Mauguin symbol. E.g. spacegroup=225 and spacegroup=’F m -3 m’ are equivalent.
setting : 1 | 2
Some space groups have more than one setting. \(setting\) determines Which of these should be used.
datafile : None | string
Path to database file. If \(None\), the the default database will be used.
ase.spacegroup.get_spacegroup(atoms, symprec=1e-05)[source]

Determine the spacegroup to which belongs the Atoms object.

This requires spglib: https://atztogo.github.io/spglib/ .

Parameters:

atoms: Atoms object
Types, positions and unit-cell.
symprec: float
Symmetry tolerance, i.e. distance tolerance in Cartesian coordinates to find crystal symmetry.

The Spacegroup object is returned.