June 20, 2013

Symmetry Search

The Symmetry Search (Fig. 1) enables the user to look up the following information:

  • Space Group
  • Wyckoff Sequence 
  • Centering 
  • Crystal Class 
  • Pearson Symbol
  • Crystal System
  • Laue Class

 

Figure 1: Symmetry Search
Figure 1: Symmetry Search

 

Space Group

Space groups can be entered as numbers or symbols in Hermann–Mauguin (H–M) notation. The symbol for inversion (“bar”) is entered as a minus sign (“-“) in front of the according axis. It is possible to enter H–M symbols in two ways:

  1. Without blanks between symmetry directions, e.g. P-1, F-43m, Pmmm
  2. With blanks between symmetry directions; in that case the space group symbol has to be enclosed in quotation marks, e.g. “P 21/c”, “P 21 21 21”

Multiple entries are separated by a blank. They are combined by logical OR.

Clicking the button “Display corresponding HM symbols” will show a list with equivalent space group notations for the space group given in the corresponding field.

Examples:

Space Group

Result

P-1

P-1 and corresponding, e.g. A-1, B-1 etc.

F-43m

F-43m

“F -4 3 m”

3-15

all monoclinic space groups in all allowed settings

2 4 6 12

P-1 OR P21 OR Pm OR C2/m and corresponding

 

Wyckoff Sequence

The Wyckoff Sequence is a descending ordered sequence of Wyckoff symbols. Wyckoff sequences have to be entered without blanks. A blank between entries will be interpreted as a separator between two sequences and cause them to be combined by logical OR. Wildcards ("*") are allowed at the beginning, in the middle and at the end of the input string. Apart from Pmmm all space groups need less than 26 Wyckoff letters, so the International Tables use for the 27th Wyckoff position an "α", which can not be used due to technical reasons. Thus, the ICSD uses an "A" instead.

Examples:

Wyckoff Sequence

Result

a

entries with Wyckoff symbol a, e.g. 4a, 8a etc.

cb2a3

entries with Wyckoff symbols e.g. (8c, 4b, 4b, 2a, 2a, 2a)

A4a

entries with Wyckoff symbols e.g. (8A, 8A, 8A, 8A, 1a)

 

Centering

Possible centerings may be entered according to the usual notation.

Examples:

Centering

Result

A

entries that are A-centered

R

Rhombohedral centering

A B C

entries in space groups e.g. Bbcm, Cmca, Ammm

 

Crystal Class

Valid entries can be either made in Hermann–Mauguin or Schönflies notation.

Examples:

Crystal Class

Result

4/mmm

entries in spacegroups e.g. C4/mcc

S4

entries in spacegroups e.g. I-4, P-4

-1

entries in spacegroups e.g. P-1, A-1, B-1

 

Pearson Symbol

The Pearson Symbol consists of a single letter for the crystal class (Tab. 1), followed by the Bravais lattice type symbol (Tab. 2), followed by the number of atoms in the unit cell.

 

Table 1: Crystal Class letters

Crystal Class

Abbreviation

triclinic (anorthic)

a

monoclinic

m

orthorhombic

o

tetragonal

t

cubic

c

hexagonal

h

 

Table 2: Bravais lattice types

Bravais lattice

Abbreviation

primitive

P

side-centered (A, B, or C)

S

face-centered

F

body-centered

I

rhombohedral

R

 

Examples:

Pearson symbol

Result

oF100

all orthorhombic, face-centered structures with 100 atoms in the unit cell

mS20

all monoclinic, side-centered structures with 20 atoms in the unit cell, e.g. structures in spacegroups Bb, C2/m etc.

 

Crystal System

The following entries are allowed:

  • triclinic,
  • monoclinic,
  • orthorhombic,
  • tetragonal,
  • cubic,
  • trigonal, 
  • hexagonal.

 

Laue Class

The following entries are allowed: 

  • -1
  • 2/m 
  • -3
  • -3m 
  • 4/m 
  • 4/mmm 
  • 6/m 
  • 6/mmm
  • m-3
  • m-3m
  • mmm
© FIZ Karlsruhe 2013