Module: xrd.spacegroup

Interface with sglite for hkl generation and Laue group determination

This module contains mappings from space group number to either Hall or Hermann-Mauguin notation, as well as the inverse notations.

Space groups can be mapped to crystal class (one of 32 point groups) and then to crystal system .

NOTES:

  • Laue group is the cyrstal class if you add a center of symmetry. There are 11 Laue groups, determined directly from the point group.
  • This module avoids the use of numpy and uses math module instead. That means the hkl lists are not numpy arrays, but simple lists of tuples.
  • Rhombohedral lattices:

REFERENCES

1. Mappings among space group number, Hall symbols and Hermann-Mauguin symbols. http://cci.lbl.gov/sginfo/hall_symbols.html

  1. For mapping space group number to point group (crystal class in Schonflies notation)

http://en.wikipedia.org/wiki/Space_group

  1. Crystallography and crystal defects By Anthony Kelly, G. W. Groves, P. Kidd

4. Contains point group from sgnum. http://en.wikipedia.org/wiki/Space_group#Classification_systems_for_space_groups

5. Point group to laue group http://www.ruppweb.org/Xray/tutorial/32point.htm

6. For discussion of rhombohedral lattice and “obverse” and “reverse” settings for lattice parameters. Crystal structure determination (book) By Werner Massa

TESTING

Run this module as main to generate all space groups and test the HKL evaluation.

1 Class

class hexrd.xrd.spacegroup.SpaceGroup(sgnum)[source]

Bases: object

Wrapper on sglite

__init__(sgnum)[source]

Constructor for SpaceGroup

INPUTS sgnum – (int) space group number (between 1 and 230)

HallSymbol[source]

(read only) Hall symbol

SgOps[source]

(read only) An sglite.SgOps instance

getHKLs(ssmax)[source]

Return a list of HKLs with a cutoff sum of square

INPUTS ssmax – cutoff sum of squares

OUTPUTS hkls – a list of all HKLs with sum of squares less than

or equal to the cutoff, excluding systematic absences and symmetrically equivalent hkls

DESCRIPTION

hermannMauguin[source]

(read only) Hermann-Mauguin symbol

latticeType[source]

Lattice type

Possible values are ‘cubic’, ‘hexagonal’, ‘trigonal’, ‘tetragonal’, ‘orthorhombic’, ‘monoclinic’ and ‘triclinic’

Rhombohedral lattices are treated as trigonal using the “obverse” setting.

laueGroup[source]

Schonflies symbol for Laue group (read only)

pointGroup[source]

Schonflies symbol for point group (read only)

reqParams[source]

(read only) Zero-based indices of required lattice parameters

sgnum

Space group number

sixLatticeParams(lparams)[source]

Return the complete set of six lattice parameters from the abbreviated set

INPUTS lparams – (tuple) the abbreviated set of lattice parameters

OUTPUTS sparams – (tuple) the complete set of lattice parameters;

(a, b, c, alpha, beta, gamma)

DESCRIPTION * Output angles are in degrees

1 Function

hexrd.xrd.spacegroup.testHKLs()[source]