How do I know which is the asymmetric unit of a unit cell?

Question

I need the number of independent atoms in the asymmetric unit I have to introduce them in this form:

# [atom type] [number] [WP] [x] [y] [z]
Pb  1   4e  0.0000  0.0000  0.7500
Pb  2   8f  0.0000  0.0000  0.8563
P   1   8f  0.0000  0.0000  0.9511
O   1   8f  0.0000  0.0000  0.9145
O   2   8f  0.2715  0.7285  0.8885
O   3   8f  0.9570  0.5000  0.1170
O   4   8f  0.7285  0.2715  0.6115 

(this is just an example) I only have data given like this:

a,b,c, alpha, beta, gamma
 5.801  5.801  7.906 90.00 90.00 90.00 Sym.group:  131
          occ      x             y           z
Ca1        1.0     0.500000      0.500000     0.25000
Ca1        1.0     0.500000      0.500000     0.74999
Ca1        1.0     0.500000      1.000000     0.24999
Ca1        1.0     1.000000      0.500000     0.75000
Si1        1.0     1.000000     0.500000     0.250000
Si1        1.0     0.500000     0.000000     0.750000
O1         1.0     0.000000     0.227421     0.250001
O1         1.0     1.000000     0.772579     0.250001
O1         1.0     0.227420     1.000000     0.749999
O1         1.0     0.772580     1.000000     0.749999
O1         1.0     0.000000     1.000000     0.000000
O1         1.0     0.000000     1.000000     0.500000
O1         1.0     0.500000     0.500000     0.000000
O1         1.0     0.500000     0.500000     0.500000

How can I extract which are the independent atoms in the asymmetric unit and the Wyckoff positions? I thought that if you knew the space group, then someone you could determine which atoms were within the asymmetric unit, but I've nothing about it. The same goes for the Wyckoff positions. I have tried with VESTA without success.

Thanks!

Answer 1

I recommend you to take a look at the Bilbao Crystallographic Server. There are several tools can help you.

One of them is inside the Space-group symmetry section. Specifically the Wyckoff Positions of Space Groups (WYCKPOS) where you input the space group and it returns a list of the positions AND, at the end, a section where you enter a position and it return which is the corresponding Wyckoff position:

Input:

Output:

Also, you can use the Structure Data Converter & Editor tool (in the Structure Utilities section) where you can convert between the following file formats:

BCS: The Bilbao Crystallographic Server (BCS) file format is the standard format used throughout the server's tools. It contains the space-group, lattice and sites information (for the asymmetric unit shell) assumed to be given in standard setting (one can use our SETSTRU tool to convert to other settings). As of the moment, the occupational and magnetic information are not supported.

CIF: The Crystallographic Information File format is developed by the International Union of Crystallography and is a widely used, standard-assumed file format. Although it has many supported tags for defining additional structural information, unfortunately a consensus on the representation of magnetic information hasn't been reached yet.

mCIF: As the ISOCIF program, developed by Harold T. Stokes and Branton J. Campbell started supporting magnetic space groups and magnetic moment information, Stokes and Campbell extended the CIF dictionaries by adding magnetic related tags such as "_magnetic_space_group_BNS_number", "_magnetic_space_group_symop_operation_timereversal", "_magnetic_atom_site_moment_crystalaxis_mx", etc.. To discern this extended CIF file, they also relabeled the existing tags like "_magnetic_cell_length_a", "_magnetic_space_group_symop_operation_xyz" and thus the mCIF format came into being. Although one can store all magnetic related information to a mCIF file, its -for the moment- incompatibility with most of the crystallographic software makes it difficult to import the magnetic data contained within.

VESTA: Developed by Koichi Momma, VESTA is a highly advanced, yet simple to use 3D visualization program for structural data. Even though it has no direct support for magnetic space groups / magnetic moments, nevertheless they can be represented by assigning vectors to atomic sites.

VASP: The Vienna Ab initio Simulation Package, developed by Jürgen Hafner, Georg Kresse, Doris Vogtenhuber & Martijn Marsman, is mainly an ab-initio calculation software, accepting its structure input data in P1. Currently our Structure Data Converter & Editor tool only supports the POSCAR/CONTCAR files with "Direct/Fractional" atomic coordinates.