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
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:
- Without blanks between symmetry directions, e.g. P-1, F-43m, Pmmm
- 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 |
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 |
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