Interpret Wyckoff Positions: Crystal Class Coordinates

  • Thread starter tirrel
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In summary, the Wyckoff positions in the international table of crystallography consist of three coordinates (x,y,z) that are normalized to the lattice parameters. This can be observed in special, high symmetry Wyckoff positions that often have coordinates such as 1/2, 1/3, or 1/4.
  • #1
tirrel
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Hello, maybe this is a silly question. I wanted to ask how to interpret the Wyckoff positions in the international table of crystallography (I am new to them). In particular, I see three coordinates (x,y,z). I wanted to be sure that these are the (normalized) coordinates with respect to the axes of the conventional unit cell given by the respective crystal class, usually called a, b,c.

Maybe it's trivial but I could not find the answer till now.

Thanks a lot,
Tirrel
 
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  • #3
Yes, (xyz) are normalized to the lattice parameters. You can easily see that when you look at special, high symmetry Wyckoff positions that usually have coordinates like 1/2, 1/3 or 1/4.
 

What is the purpose of interpreting Wyckoff positions in crystal class coordinates?

The purpose of interpreting Wyckoff positions in crystal class coordinates is to describe the symmetry and arrangement of atoms in a crystal structure. This information can be used to identify the crystal system, space group, and lattice parameters of a crystal.

What are Wyckoff positions and how are they determined?

Wyckoff positions are specific locations within a crystal structure where atoms of the same element are found. They are determined by considering the symmetry elements present in the crystal lattice and the arrangement of atoms within the unit cell.

How do crystal class coordinates differ from Cartesian coordinates?

Crystal class coordinates are based on the symmetry of the crystal, while Cartesian coordinates are based on a fixed reference frame. Crystal class coordinates use lattice parameters and symmetry operations to describe the position of atoms, while Cartesian coordinates use x, y, and z coordinates.

What is the relationship between Wyckoff positions and space groups?

Wyckoff positions are closely related to space groups, as they are used to describe the symmetry of a crystal structure. Each space group has a unique set of Wyckoff positions, which can be used to identify the space group of a crystal.

How can interpreting Wyckoff positions help in studying crystal structures?

Interpreting Wyckoff positions can provide valuable information about the symmetry, arrangement, and packing of atoms in a crystal structure. This can help in understanding the physical and chemical properties of the crystal, as well as predicting its behavior under different conditions.

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