How to prove there is no primitive cell of diamond structure with only one atom?

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Discussion Overview

The discussion revolves around the question of whether a primitive cell of the diamond structure can exist with only one atom. Participants explore the definitions and implications of primitive cells in the context of the diamond crystal structure, which is related to face-centered cubic (fcc) lattices.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant asks how to prove that there is no primitive cell of the diamond structure with only one atom.
  • Another participant questions the definition of a primitive cell and suggests that if the fcc structure is not a primitive cell, then the diamond structure cannot be either.
  • It is stated that the carbon atoms in diamond do not form a primitive lattice, implying that the elementary cell must contain more than one atom. A translation mapping one carbon atom to its neighbor does not map the entire lattice onto itself.
  • One participant proposes that replacing a cell containing two neighboring atoms with a point could yield a primitive lattice, suggesting that the smallest unit cell must contain two atoms.
  • A later reply agrees with the notion that diamond is not a primitive cell but suggests that a primitive cell of diamond can be constructed.

Areas of Agreement / Disagreement

Participants express differing views on the existence of a primitive cell with one atom in the diamond structure. Some argue that it cannot exist, while others suggest that a primitive cell can be constructed, indicating unresolved disagreement.

Contextual Notes

The discussion includes assumptions about the definitions of primitive cells and the nature of the diamond structure, which may not be fully articulated. The implications of translations and lattice mappings are also under consideration but remain unresolved.

dudu1
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How to prove there is no primitive cell of diamond structure with only one atom?

Thanks in advance!
 
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What is primitive cell?

I know that you know the definition of primitive cell. Diamond is the fcc structured crystal. So can you think that is there any primitive cell in diamond structure??

First think that if fcc is not a primitive cell then how would diamond?
 
The C atoms in a diamond do not form a primitive lattice, hence the elementary cell has to contain more than one atom. Specifically, a translation which maps a selected C atom onto its neighbour does not map the whole crystal lattice onto itself.
On the other hand, replacing a cell containing two neighbouring atoms by a point will yield a primitive lattice, hence the smallest unit cell possible has to contain two atoms.
 
Yeah,
That was I meant too.
Diamond itself is not a primitive cell but a primitive of diamond can be constructed.
 

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