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Identification of Layer Symmetry of Periodic Sections


Identify layer group symmetry
The program SECTIONS aims to scan space groups along any scanning direction alongside with the appropriate transformations to the standard setting of the involved sectional layer groups. The program detects the relevant sections, determines their layer groups, and chooses suitable standard bases from the one provided by the user, following the established conventions as closely as possible.

When comparing the result with the current scanning tables of the International Tables for Crystallography Vol. E, note that the approach followed there is to use a unique basis for each scanning direction, the one of the so-called conventional basis of the scanning group (see the Help for details).

As input the program only requires as parameters:
  1. The space group, specified either by:

    2. OPTION A: Its number as given in the International Tables for Crystallography Vol. A (ITA) and optionally a transformation matrix and/or an origin shift, from the standard ITA setting. Only the default choice for the conventional setting of the space groups is used.

    OPTION B: A set of generators given as (x,y,z) triplets. If necessary a suitable transformation to the standard setting is calculated by the program.

  2. The reciprocal vector normal to the plane sections as a triplet of Miller indices (hkl), in the reciprocal basis corresponding to the setting chosen by the user. If the space group is input by number, the most common reciprocal vectors for each Laue class appear in a drop-down menu.
As output the program returns the whole scan of the input space groups by planes perpendicular to the given reciprocal vector (hkl).

  • OPTION A: Space group number
    Please, enter the sequential number of group as given in the International Tables for Crystallography, Vol. A or

  • OPTION B: Symmetry operations
    Enter the generators of the Space Group in the box below, given in any basis of the lattice, as in the example:

    x+1/2,y+1/2,z
    -y+1/3,x+1/4,z+1/4


    Assumed lattice translations:
    x + 1 , y , z
    x , y + 1 , z
    x , y , z + 1





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