<* $Id: xnd_rsym.html,v 2000/01/01 09:45:00 berar Exp $ *> XND symmetry file and formats.

Symetry data used in xnd.

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We have choosen in xnd to read the symmetry operatios rather than to generate the space group operation. This allows more flexibility in the symetry definition using by example exotic choice of the origin, introduction of non crystalline symmetry or changing the setting if the identity operation is not given.


the default file: xnd_sym.d

In order to avoid a retyping of all the symetry information in the xnd input file, some space groups have been stored in the xnd_sym.d file which is by default located in the same directory than the xnd program.

The space groups listed in this file are known by their name: an uppercase copy of the classical name. They are often followed by a comment which include their reference number in the international table and can precise the origin choice.

Sometimes there are short entries for space group of high symetry which are restricted to some of the most symetrical Wickoff position, by example FM3M_AB is a restricted entry of the group Fm3m valid for the Wickoff positions a and b only.

Please return the mistakes found in the distributed file. Entry can be added by users in the file. When a group is encountered in the input file, the program first scans its internal table read in the data file then if no match is found it scans the default up to the first name matching the definition.

description of a classical space group

All the entries in the input file or in the symetry file use the same description. Specific points are concerned by 4-D symmetry operation used in modulated structure, they are described after the classical groups.

space group header

SymName string whithout spaces The first character of the string has to be among (P, I, F, A, B, C, R) according to the kind of Bravais Lattice or to be the symbol * reserved to complement of a 3-D group in modulated structure.

After the identifier, a comment beginning with # is allowed till the end of line.

System C Cubic
QTetragonal (Quadratic)
HHexagonal (Laue classes 6/m and 6/mmm
RTrigonal (Laue classes 3 and 3m - hexagonal axis)
TTrigonal (Laue classes 3 and 3m - rhombohedral axis)
LMonoclinic (unique axis a)
MMonoclinic (unique axis b)
NMonoclinic (unique axis c)
AAnortic (Triclinic)
*complement for displacive modulation
Holohedral 0if the group is not holohedral (eg 3 or 4/m)
1if the group is holohedral
SymCenter 0the group has no symmetry center at the origin.
1the group is centrosymmetric at the origin, in this case, only the operations belonging to the factor group G/I have to be declared.
NSymOpsIntegernumber of symmetry operations to be read

Comment on hexagonal and trigonal systems

In case of this ternary symmetry there is often some problems with xnd encoding. In the pattern we can distinguish to things : one is related to the metric.

symmetry operations

The NSymOps symmetry operations are entered as The symmetry operations are separated by a semicolumn or by a linefeed. The only valid translation are given using simple ratio (up to 12).


 P21/C  #13 axe b
 M 1 1 2
 x,y,z; -x,1/2+y,1/2-z;

 FD3M_E  #227 Fd-3m  orig -3m (wickoff sites : a, b, c, d, and e only)
 C 1 1 4
 x, y, z;  x, 1/4-y, 1/4-z;  
 1/4-x, y, 1/4-z; 1/4-x, 1/4-y, z;

Tables generation

It is possible to generate all the symmetry tables using the software sginfo as shown in the following example by doing some cut and paste.
sginfo can be found at http://www.csb.yale.edu/sginfo
$ sginfo -xyz P2/c
# sginfo -xyz P2/c
Space Group  13:b1  C2h^4  P2/c:b1 = P12/c1  -P 2yc
Point Group  2/m
Laue  Group  2/m
Unique Axis  y

Order     4
Order P   4

s.i.Vector  Modulus
  1  0  0   2
  0  1  0   2
  0  0  1   2

#List     2

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

$ sginfo -xyz Pm-3m
# sginfo -xyz Pm-3m
Space Group  221  Oh^1  Pm-3m  -P 4 2 3
Point Group  m-3m
Laue  Group  m-3m

Order    48
Order P  48

s.i.Vector  Modulus
  1  1  1   2

#List    24

x, y, z
-y, x, z
-x, -y, z
y, -x, z
x, -z, y
x, -y, -z
x, z, -y
z, y, -x
-x, y, -z
-z, y, x

Complement for modulated structure

The complement for modulated structure need to give 4D symetry operations, but the classical part can be separated from the complementary part which is only concern by the 4th dimension. In this case 2 groups have to be read, the first contains all the classical operation and the second the complementary part for each operation. In this case after the header we found the 4D part of the symmetry operation writen like a 3D operation where only the first coordinate x is used instead of its classical name t. Then the complement of the operations on the fourth dimension are writen like x; x+1/4; -x

Example of modulated structure

# input for spacegroup
 O 1 1 4
  X, Y, Z;  -X, -Y+1/2, Z;  -X, Y+1/2, -Z;  X, -Y, -Z

 *_CMMA #complement 
 * 1 0 4
  X+1/2;  -X+1/2;  X+1/2;  -X+1/2


This Symmetry tables module has to be repeated for each symmetry group needed in the refinement when the module is not defined in xnd_sym.d.
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JFB Aug, 25th 99