ipymd.data_input.spacegroup package

Submodules

ipymd.data_input.spacegroup.cell module

ipymd.data_input.spacegroup.cell.cell_to_cellpar(cell)

Returns the cell parameters [a, b, c, alpha, beta, gamma] as a numpy array.

ipymd.data_input.spacegroup.cell.cellpar_to_cell(cellpar, ab_normal=(0, 0, 1), a_direction=None)

Return a 3x3 cell matrix from cellpar = [a, b, c, alpha, beta, gamma]. The returned cell is orientated such that a and b are normal to ab_normal and a is parallel to the projection of a_direction in the a-b plane.

Default a_direction is (1,0,0), unless this is parallel to ab_normal, in which case default a_direction is (0,0,1).

The returned cell has the vectors va, vb and vc along the rows. The cell will be oriented such that va and vb are normal to ab_normal and va will be along the projection of a_direction onto the a-b plane.

Example:

>>> cell = cellpar_to_cell([1, 2, 4,  10,  20, 30], (0,1,1), (1,2,3))
>>> np.round(cell, 3)
array([[ 0.816, -0.408,  0.408],
       [ 1.992, -0.13 ,  0.13 ],
       [ 3.859, -0.745,  0.745]])

ipymd.data_input.spacegroup.cell.metric_from_cell(cell)

Calculates the metric matrix from cell, which is given in the Cartesian system.

ipymd.data_input.spacegroup.spacegroup module

Definition of the Spacegroup class.

This module only depends on NumPy and the space group database.

class ipymd.data_input.spacegroup.spacegroup.Spacegroup(spacegroup, setting=1, datafile=None)

Bases: object

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.

__eq__(other)

Chech whether self and other refer to the same spacegroup number and setting.

__str__()

Return a string representation of the space group data in the same format as found the database.

centrosymmetric

Whether a center of symmetry exists.

equivalent_reflections(hkl)

Return all equivalent reflections to the list of Miller indices in hkl.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sg.equivalent_reflections([[0, 0, 2]])
array([[ 0,  0, -2],
       [ 0, -2,  0],
       [-2,  0,  0],
       [ 2,  0,  0],
       [ 0,  2,  0],
       [ 0,  0,  2]])

equivalent_sites(scaled_positions, ondublicates='error', symprec=0.001)

Returns the scaled positions and all their equivalent sites.

Parameters:

scaled_positions: list | array

List of non-equivalent sites given in unit cell coordinates.

ondublicates : ‘keep’ | ‘replace’ | ‘warn’ | ‘error’

Action if scaled_positions 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.

Returns:

sites: array

A NumPy array of equivalent sites.

kinds: list

A list of integer indices specifying which input site is equivalent to the corresponding returned site.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sites, kinds = sg.equivalent_sites([[0, 0, 0], [0.5, 0.0, 0.0]])
>>> sites
array([[ 0. ,  0. ,  0. ],
       [ 0. ,  0.5,  0.5],
       [ 0.5,  0. ,  0.5],
       [ 0.5,  0.5,  0. ],
       [ 0.5,  0. ,  0. ],
       [ 0. ,  0.5,  0. ],
       [ 0. ,  0. ,  0.5],
       [ 0.5,  0.5,  0.5]])
>>> kinds
[0, 0, 0, 0, 1, 1, 1, 1]

get_op()

Returns all symmetry operations (including inversions and subtranslations), but unlike get_symop(), they are returned as two ndarrays.

get_rotations()

Return all rotations, including inversions for centrosymmetric crystals.

get_symop()

Returns all symmetry operations (including inversions and subtranslations) as a sequence of (rotation, translation) tuples.

lattice

Lattice type: P primitive I body centering, h+k+l=2n F face centering, h,k,l all odd or even A,B,C single face centering, k+l=2n, h+l=2n, h+k=2n R rhombohedral centering, -h+k+l=3n (obverse); h-k+l=3n (reverse)

no

Space group number in International Tables of Crystallography.

nsubtrans

Number of cell-subtranslation vectors.

nsymop

Total number of symmetry operations.

reciprocal_cell

Tree Miller indices that span all kinematically non-forbidden reflections as a matrix with the Miller indices along the rows.

rotations

Symmetry rotation matrices. The invertions are not included for centrosymmetrical crystals.

scaled_primitive_cell

Primitive cell in scaled coordinates as a matrix with the primitive vectors along the rows.

setting

Space group setting. Either one or two.

subtrans

Translations vectors belonging to cell-sub-translations.

symbol

Hermann-Mauguin (or international) symbol for the space group.

symmetry_normalised_reflections(hkl)

Returns an array of same size as hkl, containing the corresponding symmetry-equivalent reflections of lowest indices.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sg.symmetry_normalised_reflections([[2, 0, 0], [0, 2, 0]])
array([[ 0,  0, -2],
       [ 0,  0, -2]])

symmetry_normalised_sites(scaled_positions)

Returns an array of same size as scaled_positions, containing the corresponding symmetry-equivalent sites within the unit cell of lowest indices.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sg.symmetry_normalised_sites([[0.0, 0.5, 0.5], [1.0, 1.0, 0.0]])
array([[ 0.,  0.,  0.],
       [ 0.,  0.,  0.]])

tag_sites(scaled_positions, symprec=0.001)

Returns an integer array of the same length as scaled_positions, tagging all equivalent atoms with the same index.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sg.tag_sites([[0.0, 0.0, 0.0],
...               [0.5, 0.5, 0.0],
...               [1.0, 0.0, 0.0],
...               [0.5, 0.0, 0.0]])
array([0, 0, 0, 1])

translations

Symmetry translations. The invertions are not included for centrosymmetrical crystals.

unique_reflections(hkl)

Returns a subset hkl containing only the symmetry-unique reflections.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sg.unique_reflections([[ 2,  0,  0],
...                        [ 0, -2,  0],
...                        [ 2,  2,  0],
...                        [ 0, -2, -2]])
array([[2, 0, 0],
       [2, 2, 0]])

unique_sites(scaled_positions, symprec=0.001, output_mask=False)

Returns a subset of scaled_positions containing only the symmetry-unique positions. If output_mask is True, a boolean array masking the subset is also returned.

Example:

>>> from ase.lattice.spacegroup import Spacegroup
>>> sg = Spacegroup(225)  # fcc
>>> sg.unique_sites([[0.0, 0.0, 0.0],
...                  [0.5, 0.5, 0.0],
...                  [1.0, 0.0, 0.0],
...                  [0.5, 0.0, 0.0]])
array([[ 0. ,  0. ,  0. ],
       [ 0.5,  0. ,  0. ]])

Module contents

Created on Sat Jul 16 05:26:00 2016

@author: cjs14