SeqQuest input: Symmetry examples

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Overview

The following are a sequence of examples of symmetry input to the code for a variety of different crystal structures. Note that the specification of symmetry depends on the location of the high-symmetry point and the cell shape. For example, note the different representations of the HCP symmetry below depending on whether the symmetry is defined about an atom coordinate or around an interstitial site (or around a bond midpoint). The specification of the symmetry is not unique, and the "best" symmetry input is ofter a matter of convenience (i.e. using the coordinate origin of the atomic input as the high-symmetry point to define a symmetry. Note the presence of several non-symmorphic space groups in the following. The symmetry input scheme is general enough to allow for any space group.

Example input symmetry definitions

Cubic (fcc,bcc,sc)

symops - cubic
  4
definitions
  4   0.0  0.0  1.0    0.0  0.0  0.0
  3   1.0  1.0  1.0    0.0  0.0  0.0
  2   1.0  1.0  0.0    0.0  0.0  0.0
 -1   0.0  0.0  0.0    0.0  0.0  0.0

Td (zinc-blende), atom-centered

symops - tetrahedral
  3
definitions
 -4   0.0  0.0  1.0    0.0  0.0  0.0
  3   1.0  1.0  1.0    0.0  0.0  0.0
 -2   1.0  1.0  0.0    0.0  0.0  0.0

Wurtzite, 4-atom hexagonal cell, interstitial-centered

symops - wurtzite
  2
definitions
  6   0.0  0.0  1.0    0.0  0.0  0.5
 -2   1.0  0.0  0.0    0.0  0.0  0.0

HCP (atom-centered)

symops - hcp/atom
  3
definitions
 -6   0.0  0.0  1.0    0.3333333333  0.3333333333  0.5
  2   0.0  1.0  0.0    0.0  0.0  0.0
 -2   1.0  0.0  0.0    0.0  0.0  0.0

HCP (interstitial-centered)

symops - hcp/interstitial
  3
definitions
  6   0.0  0.0  1.0    0.0  0.0  0.5
  2   1.0  0.0  0.0    0.0  0.0  0.0
 -1   0.0  0.0  0.0    0.0  0.0  0.0

BC8 structure, 8-atom cubic cell

symops - BC8
  5
definitions of symmetry operations
  2   1.0  0.0  0.0    0.0  0.5  0.0
  2   0.0  1.0  0.0    0.5  0.5  0.0
  2   0.0  0.0  1.0    0.5  0.0  0.0
  3   1.0  1.0  1.0    0.0  0.5  0.0
 -1   0.0  0.0  0.0    0.0  0.0  0.0

Sapphire (Al2O3), two-layer/10-atom rhombohedral cell

symops - sapphire
  2
definitions
  3   0.0  0.0  1.0    0.0  0.0  0.0
 -1   0.0  0.0  1.0    0.0  0.0  0.0

K-Al2O3 kappa phase alumina, 40-atom orthorhombic

symops - K-Al2O3
 3
definition of symmetry operations
  2   0.0  0.0  1.0    0.0  0.0  0.5
 -2   1.0  0.0  0.0    0.5  0.5  0.5
 -2   0.0  1.0  0.0    0.5  0.5  0.0

Quartz Alpha-SiO2, 9-atom hexagonal cell, interstitial-centered

symops - alpha-Quartz
  2
definitions of 3d symmetry operations
  3   0.0  0.0  1.0    0.0  0.0 -0.333333333333
  2   1.0  0.0  0.0    0.0  0.0  0.0

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Send questions and comments to: Peter Schultz at paschul@sandia.gov
Last updated: December 16, 2004