What is the Wigner–Seitz cell of diamond?

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SUMMARY

The Wigner–Seitz cell of diamond is derived from its complex crystal structure, which consists of two face-centered cubic (FCC) lattices. The conventional unit cell of diamond is often misrepresented; it is essential to recognize that it contains two carbon atoms per lattice point. Visualizing the Wigner–Seitz cell within the diamond structure requires understanding the geometry of the primitive cell, which is not straightforward due to the dual FCC arrangement. Accurate representation involves acknowledging the tetrahedral symmetry inherent in the diamond cubic structure.

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  • Understanding of solid state physics concepts
  • Familiarity with crystal lattice structures, specifically face-centered cubic (FCC)
  • Knowledge of Wigner–Seitz cell construction techniques
  • Basic comprehension of diamond cubic crystal structure
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  • Study the construction of Wigner–Seitz cells in various crystal structures
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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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