Bilbao Crystallographic Server CORREL Help

Correlations Between Space Group Representations


Space group representations and correlations
Space group irreps are labeled by k-vector star and corresponding little group representation number. This program calculates how does given irreducible represenation of a supergroup (which is in general reducible for the subgroups of that supergroup) splits into irreducible constituents in the subgroup.

Input data :
  1. Supergroup number as given in ITA.
  2. Subgroup number as given in ITA.
  3. Transformation that relates the conventional bases of the sub- and supergroups. The transformation, in general, consists of a linear part and an origin shift.
  4. k-vector data :
    • Reciprocal lattice basis type, which may be primitive (as in Cracknell-Davies-Miller-Love tables [1]), or dual to the conventional (ITA).
    • k-vector coordinates relative to chosen basis as any three decimal numbers or fractions.
    • Label of the k-vector (up to three letters).

  5. The program can also calculate the matrix that performs the reduction of the representation. If you wish to see it - put a mark at the corresponding field.
[1] Cracknell, A. P., Davies, B. L., Miller, S. C., and Love, W. F. (1979). Kronecker Product Tables. Vol. 1. General Introduction and Tables of Irreducible Representations of Space Groups. New York: IFI/Plenum.



If you are using this program in the preparation of a paper, please cite it in the following form:

M. I. Aroyo, A. Kirov, C. Capillas, J. M. Perez-Mato & H. Wondratschek."Bilbao Crystallographic Server II: Representations of crystallographic point groups and space groups". Acta Cryst. A62, 115-128 (2006).
Supergroup number: Please, enter the sequential number of group as given in International Tables for Crystallography, Vol. A or choose it:
Subgroup number: Please, enter the sequential number of group as given in International Tables for Crystallography, Vol. A or choose it:

  Enter the transformation matrix below:

Linear part
Origin Shift

k vector data Reciprocal basis
Coordinates
kx ky kz
Label

  Optional: If you wish to see the reduction matrix check this

  Optional: If you wish to see the full-group irreps for the generators of the supergroup check this

or


[Bilbao Crystallographic Server Main Menu]

Bilbao Crystallographic Server
http://www.cryst.ehu.es
Licencia de Creative Commons
For comments, please mail to
cryst@wm.lc.ehu.es