Ques. on high symm points of a crystal

In summary, a user on the forum is wondering if there is a high symmetry point in a crystal that can be used as a central point for all point operations. They are asking for suggestions on how to show this for any complex crystal in order to write a program that can test all 48 possible operations. However, it is not possible as there are crystals, such as the diamond structure, that have a center of symmetry but also have diads perpendicular to each cube face that cannot be placed through the center of symmetry. A more general answer is not available.
  • #1
sam_bell
67
0
Hi! I'm new to these forums.

To get right to it, My head'z been spinning wondering ..

Is there a high symmetry point in a crystal about which *all* point operations can be re-centered? I can show this for a simple lattice.

Does anyone know if this is true for any complex crystal as well? And maybe how to show it? I'm asking because I want to write a program that sets the origin of coordinates at such a point and then tests all 48 possible operations about it. I know some good candidates would be at the atom centers and the midpoint between atoms.

Any knowledge/suggestions is appreciated. Thanks.
 
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  • #2
No, that's not possible. Think about the diamond structure for example. The center of symmetry is at 1/8 1/8 1/8, so this would be your only option for such a point. But the crystal has a diad perpendicular to each cube face, which cannot be placed so that it runs through the center of symmetry.

I can't give a more general answer unfortunately.
 

Related to Ques. on high symm points of a crystal

1. What are high symmetry points in a crystal?

High symmetry points in a crystal refer to the points in the Brillouin zone (BZ) where the symmetry of the crystal lattice is most pronounced. These points occur at the corners, center, and faces of the BZ and represent the highest degree of symmetry in the crystal structure.

2. How are high symmetry points labeled in a crystal?

High symmetry points are typically labeled using a combination of letters and numbers, such as Γ, X, M, and R. These labels correspond to specific points in the BZ and are based on the crystal's symmetry elements.

3. Why are high symmetry points important in crystallography?

High symmetry points are important in crystallography because they provide a convenient reference for describing the symmetry of a crystal lattice. They also help to simplify calculations and analysis of the crystal's properties, such as its electronic band structure.

4. How do high symmetry points affect the properties of a crystal?

High symmetry points can have a significant impact on the properties of a crystal. For example, they can determine the crystal's electronic band structure, which in turn affects its electrical and optical properties. High symmetry points can also influence the crystal's mechanical and thermal properties.

5. Can high symmetry points be manipulated or controlled in a crystal?

High symmetry points cannot be directly manipulated or controlled in a crystal. However, they can be indirectly affected by changing the crystal's lattice parameters or composition. This can alter the symmetry of the crystal and potentially lead to different high symmetry points in the BZ.

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