What is the Wigner–Seitz cell of diamond?

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Discussion Overview

The discussion revolves around the Wigner–Seitz cell of the diamond crystal structure, specifically addressing the complexities of visualizing this cell within the context of the diamond's conventional unit cell, which is described as composed of two face-centered cubic (FCC) lattices.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant expresses difficulty in visualizing the Wigner–Seitz cell of the diamond structure and questions whether it can be represented as an FCC with a basis of two carbon atoms.
  • Another participant points to external resources, including Wikipedia articles on diamond cubic structures and Wigner–Seitz cells, suggesting they may provide helpful information.
  • A participant notes that the Wigner–Seitz cell for diamond is not trivial and references a specific geometry related to it.
  • Further inquiry is made about how to visualize the Wigner–Seitz cell within the conventional diamond cell and whether the lattice point in a diamond-like cell consists of one or two atoms.
  • Another participant mentions that while Wikipedia states the tetrahedral cell is the unit cell of diamond, this may not be entirely accurate, and they seek clarification on the primitive cell's representation and the number of atoms considered per lattice point.

Areas of Agreement / Disagreement

Participants appear to have differing views on the representation of the Wigner–Seitz cell and the unit cell of diamond, with no consensus reached regarding the correct visualization or the number of atoms per lattice point.

Contextual Notes

There are unresolved questions regarding the visualization of the Wigner–Seitz cell within the diamond structure and the definitions of lattice points in this context, which may depend on specific interpretations of the crystal structure.

Urza_tron
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Hi everybody,
I'm struggling with some solid state physics topics. I am dealing with the Carbon diamond crystal structure, which is basically made of 2 FCC compenetrated. I really cannot visualize the Wigner–Seitz cell of this structure, is it possible to do it? I was thinking about visualizing the diamond conventional cell as an FCC where each basis is made of two C atoms, but I don't know if it's correct.
Is there someone who could help me to visualize it?
 
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TeethWhitener said:
https://en.m.wikipedia.org/wiki/Triakis_truncated_tetrahedral_honeycomb
The Wigner Seitz cell for diamond isn’t trivial.
This is the geometry of the weigner seitz cell for crystal, but how can I visualize it inside of the conventional diamond cell? I can't see how is it shaped inside the conventional cell in order to obtain a cell that contain only one lattice point. And further more, when we consider the lattice point of a diamond like cell, are we considering a lattice point made of 1 or 2 atoms?
 
Baluncore said:
Welcome to PF.

https://en.wikipedia.org/wiki/Diamond_cubic
https://en.wikipedia.org/wiki/Wigner–Seitz_cell
Okay but Wikipedia says that the tetrahedral cell is the unit cell of diamond, but it's not completely accurate. The unit cell one usually refers to is the 2 FCC compenetrated structure. What I'm trying to understand is the drawing of the primitive cell inside of a diamond crystal, how many atoms are we considering per lattice point and how can it contain only one lattice point in a so complex structure.
 

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