Previous The symmetry file pcwspgr.dat Next

The symmetry file pcwspgr.dat contains all information about the space-group types and different settings used in PowderCell. It is possible to edit this ASCII file but mostly the data are encoded (in a simple manner). The structur of the space-group records is based on IZUMI. He developed this for the use in his Rietveld program RIETAN. In the last years a set of additional information have been inserted and some bugs could be eliminated.

The individual record for an arbitrary space-group type contains:

the number of space-group type used in IT generally
the number of setting,
the corresponding Laue group,
the existence of a inversion centre in origin (0...no, 1...yes),
the number of general positions (without consideration of an inversion centre located in origin and lattice centering vectors producing additional general positions too),
the number of special positions describing the existing local symmetries,
the number of generators selected,
the full Hermann-Mauguin symbol,
the reflection conditions,
the Wyckoff-position types and the corresponding local symmetry (described by the generator sequence) and
the generators itself, defined by the generator type an an additional translation part.

All date have been written in free format except the reflection conditions. The line containing the reflection conditions is probably based on former FORTRAN programs used by IZUMI. Respectively two characters define the reflection condition of a reflection type connected with this position in the line.

example:

spgr 227  1 15  0 48  8  5   F 4_1/d -3 2/m1917 816 931 7 0 0 5 0 6 6 0
 1 16  51 16  18 6  54 6  138 22  111 26  166 30  93 46
4   0 0.5 0.5
3   0.5 0.5 0
13  0 0 0
5   0.75 0.25 0.75
1   0.25 0.25 0.25

PowderCell uses the key-word spgr as code for the beginning of a space-group record . It follows the number of space-group type (227) and the setting (1.) The third number (15) represents the Laue group, which is important if the anomaleous dispersion is deactivated. The 0 represents a flag symbolizing the absence of an inversion centre in the origin (but there exists an inversion centre, as you can see from the last generator described by type1). Using the listed generators 48 general positions will be created. Besides the position of general symmetry 8 special positions exist. To generate all 48 different symmetry elements 5 generators are given and must be feeded into the program. At the end of the first line of the record the full Hermann-Mauguin symbol (F 4_1/d -3 2/m) will be presented.

In the second line the reflection conditions will be given in dependence on the defined reflection type. So e.g. the intensity of 00L will be calculated only than, if the condition 19 (i.e. L=4n) will be meeted. For the reflection type 0K0 the condition 17 is determined. This corresponds to the condition K=4n.

The condition of reflection type 7 has a high importance for PowderCell. It will be used to extract the lattice type. In our example the condition No 7 defines an all-face centered lattice (F).

The third line contains all information about the existing Wyckoff positions: the type and the generator sequence. The types don't shall be described here in detail. However, the encoding of the generator sequences shall be represented in a short manner.

For each Wyckoff position two values will be presented in the record. The second of this describes the generator sequence. In the line you will find the same order of special positions as listed in IT. The order starts with that position describing by the Wyckoff letter a but doesn't consider the general position, i.e. if no special position exists no value is given in this line of the record. In our example some of the 8 Wyckoff-position types will be described by the same generator sequence, e.g. for a and b will be used code 16 or c and d are described by code 6. That means that both positions will be characterized by the identical local symmetry. However, the Wyckoff positions e, f, g, h will be generated by a different generator sequence — 22, 26, 30, 46. The encoding is very simple using a bit structure. In our example the generator type 1 will be presented by bit 0, type 5 by bit 1, type 13 by bit 2, type 3 by bit 3 and type 4 by bit 4. In dependence of the generator sequence the bits are activated or not. If within the unit cell only one symmetry-equivalent position exits, no generator must be used and therefore no bit is activated. The result is code 1.


© Dr. Gert Nolze & Werner Kraus (1998)

Federal Institute for Materials Research and Testing
Unter den Eichen 87, D-12205 Berlin,
Germany