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.. module:: ase.spacegroup
===============================
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
:func:`ase.spacegroup.crystal`. This function takes a lot of
arguments:
.. autofunction:: crystal
There is also a :func:`get_spacegroup` function that will return a spacegroup object from an
Atoms object.
Aluminium (fcc)
---------------
.. image:: spacegroup-al.png
.. literalinclude:: spacegroup-al.py
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)
----------
.. image:: spacegroup-fe.png
.. literalinclude:: spacegroup-fe.py
Magnesium (hcp)
---------------
.. image:: spacegroup-mg.png
.. literalinclude:: spacegroup-mg.py
Diamond
-------
.. image:: spacegroup-diamond.png
.. literalinclude:: spacegroup-diamond.py
.. _nacl:
Sodium chloride
---------------
.. image:: spacegroup-nacl.png
.. literalinclude:: spacegroup-nacl.py
Rutile
------
.. image:: spacegroup-rutile.png
.. literalinclude:: spacegroup-rutile.py
CoSb3 skutterudite
------------------
.. image:: spacegroup-skutterudite.png
Skutterudites_ are quite interesting structures with 32 atoms
in the unit cell.
.. _Skutterudites: https://en.wikipedia.org/wiki/Skutterudite
.. literalinclude:: spacegroup-skutterudite.py
Often this structure is visualised with the Cobalt atoms on the
corners. This can easily be accomplished with ASE using
:func:`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.
.. image:: spacegroup-cosb3.png
.. literalinclude:: spacegroup-cosb3.py
The Spacegroup class
====================
The :class:`ase.spacegroup.Spacegroup` class is used
internally by the :func:`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
:class:`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
<BLANKLINE>
<BLANKLINE>
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.
.. autoclass:: Spacegroup
.. autofunction:: get_spacegroup
Getting a reduced atomic basis
===============================
You can also get a basis representation of a given crystal within a particular spagegroup,
using the :func:`ase.spacegroup.get_basis` function.
As an example, let's look at rocksalt NaCl, and see how we can reproduce the basis from an :class:`ase.Atoms` object:
>>> from ase.build import bulk
>>> from ase.spacegroup import get_basis
>>> atoms = bulk('NaCl', crystalstructure='rocksalt', a=5.64)
>>> spacegroup = 225 # Rocksalt
>>> basis = get_basis(atoms, spacegroup=spacegroup)
>>> basis
[[0. 0. 0. ]
[0.5 0.5 0.5]]
which gives us our expected 2 basis vectors for rocksalt, from the :ref:`previous example<nacl>`.
.. _spglib: https://spglib.github.io/spglib/
.. note::
Inferring the spacegroup requires the installation of `spglib`_, otherwise the space group must be passed explicitly.
.. autofunction:: get_basis
|
