Relative atomic coordinates

The relative atomic coordinates of a structure always correspond to a definition of the unit cell, respectively, i.e. they are specified by the setting of the given space-group type. The coordinates are free of choice and not limited on the interval between 0 and 1. PowderCell automatically translates all atoms within the unit cell, but in principle that's really not necessary for the calculation of the structure factor. The necessity of this translation into the unit cell is caused by the procedure for identification of the Wyckoff positions and the generation of all symmetry-equivalent atomic positions using a specific generator sequence. In connection with the identification of the Wyckoff position it is necessary that the coordinates of a given atom must be brought into the line with the defined Wyckoff-position types.

example:

In the space-group type P bca (61) the Wyckoff-position type 4a corresponds to the coordinates (0,0,0). The symmmetry-equivalent positions are (½,0,½), (0,½,½) and (½,½,0). One can use all of them as input in the worksheet structure data but PowderCell will transform these always in (0,0,0), automatically.

Caused by the enlargement using several group-subgroup relations, PowderCell fits a given atomic position to a special position of this space-group type, if the deviation is smaller than 0.0005.
The atomic coordinates can be entered in structure data as decimal numbers as well as decimal fractions, i.e. it is possible to use 0.3333, 1.3333, 1/3 or -2.6667 for the same atomic position. We recommend to input a four-figure number or better, a decimal fraction.
Within the procedure of identification of the Wyckoff position the program brings the coordinates into the line with the characteristic of the Wyckoff-position type (e.g. for (x,x,½) only the x-coordinate can be varied, whereas the y-coordinate is set automatically as copy of x). This makes the input of atomic coordinates more comfortable.
But you can also input only the Wyckoff letters. In the special case of no degree of freedom in the atomic position it is enough to input the letter. PowderCell completes the entry by the multiplicity of this position and by all coordinates. In this moment when you input the letter in the (correct) column in the table the characteristic of the Wyckoff-position type will be inserted. That means that it is not necessary to know this for the given space-group type. If the entered Wyckoff letter doesn't exist in the defined space-group type a short hint will be inserted, where the latest Wyckoff letter will be given.

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