ISOSPACEGROUP

Version 1.2.1, Oct 2022
Harold T. Stokes and Branton J. Campbell, Department of Physics and Astronomy, Brigham Young University, Provo, Utah, 84602, USA, branton_campbell@byu.edu

Description: Display information about crystallographic space groups.
Help, Version History

How to cite ISOSPACEGROUP:
H. T. Stokes and B. J. Campbell, ISOSPACEGROUP, ISOTROPY Software Suite, iso.byu.edu.

3-Dimensional Nonmagnetic Space Groups

3-Dimensional Magnetic Space Groups

If you want the OG setting, be sure to select OG for the magnetic space group preference below.

(3+d)-Dimensional Nonmagnetic Superspace Groups, d=1,2,3

Note that the drop-down list contains only the (3+1)-dimensional superspace groups.

(3+d)-Dimensional Magnetic Superspace Groups, d=1,2,3

Display options:
Use ITA (x,y,z,...) and/or Seitz notation for generators and operators
For ITA notation, use x,y,z,t,... x1,x2,x3,x4,... xs1,xs2,xs3,xs4,... for superspace-group generators and operators
Show Wyckoff positions
Show Fourier coefficients for displacive and/or magnetic and/or occupational modulations for superspace groups
Show supercentered setting for superspace groups

Space group preferences (Settings in ITA)
Monoclinic axes: a(b)c c(-b)a ab(c) ba(-c) (a)bc (-a)cb
Monoclinic cell choices: 1 2 3
Orthorhombic axes: abc ba-c cab -cba bca a-cb
Trigonal axes: hexagonal rhombohedral
Origin choice: 1 2
Note that these settings apply to both the nonmagnetic and magnetic space groups, as well as the nonmagnetic and magnetic superspace groups when the basic setting is selected below.

Magnetic space group preference
BNS setting (Belov-Neronova-Smirnova)
OG setting (Opechowski-Guccione)

Superspace group preference
standard setting (given in ITC for (3+1)-dimensional superspace groups)
basic setting (ITA settings as selected above)
Note that if the standard setting is selected, none of the ITA settings selected above will apply.

Use alternate (possibly nonstandard) setting entered below

3-dimensional space group setting (matrix S^-1t)
Basis vectors of alternate lattice in standard coordinates (rational numbers):

a' =	a +	b +	c
b' =	a +	b +	c
c' =	a +	b +	c
Alternate origin in standard coordinates (rational numbers):
τ' =	a +	b +	c

(3+d)-dimensional superspace group setting (matrix S^-1t)
Basis vectors of alternate lattice in standard coordinates (rational numbers):

a'_s1 =	a_s1 +	a_s2 +	a_s3 +	a_s4 +	a_s5 +	a_s6
a'_s2 =	a_s1 +	a_s2 +	a_s3 +	a_s4 +	a_s5 +	a_s6
a'_s3 =	a_s1 +	a_s2 +	a_s3 +	a_s4 +	a_s5 +	a_s6
a'_s4 =				a_s4 +	a_s5 +	a_s6
a'_s5 =				a_s4 +	a_s5 +	a_s6
a'_s6 =				a_s4 +	a_s5 +	a_s6
Alternate origin in standard coordinates (rational numbers):
τ' =	a_s1 +	a_s2 +	a_s3 +	a_s4 +	a_s5 +	a_s6