Silicon FCC -- Why are so many atoms shown in the lattice?

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Discussion Overview

The discussion revolves around the crystallographic structure of silicon, specifically its face-centered cubic (FCC) lattice and the implications of atomic arrangement and bonding. Participants explore the relationship between silicon's valence electrons, the representation of atoms in the lattice, and the significance of different colored atoms in the model.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant questions why many atoms are shown in the silicon lattice despite each silicon atom having four valence electrons and needing four more to complete its outer shell.
  • Another participant clarifies that the lattice representation is not about compounds but rather the smallest repeatable unit cell, emphasizing that each atom is connected to four others.
  • Some participants discuss the distinction between blue and grey atoms, noting that blue atoms are entirely within the unit cell while grey atoms are shared with neighboring cells and do not count as whole atoms in the unit cell count.
  • There is a contention regarding the minimal cell structure, with one participant asserting that the cell shown is not minimal and contains inequivalent positions of atoms.
  • One participant seeks further clarification on the relationship between the number of atoms in the cell and the completeness of the outer electron layer, questioning if two silicon atoms could suffice by sharing electrons.
  • Another participant states that the number of atoms in a cell is not directly related to the number of bonds, as bonds can exist between atoms in different cells.

Areas of Agreement / Disagreement

Participants express differing views on the minimal cell structure and the relationship between atomic arrangement and bonding. There is no consensus on the implications of the lattice representation regarding silicon's valence electrons and bonding requirements.

Contextual Notes

Participants highlight limitations in understanding the representation of atoms in the lattice and the implications of atomic bonding, indicating a need for clarity on definitions and assumptions related to the silicon structure.

pj33
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TL;DR
Explanation of lattice
https://www.researchgate.net/figure/1-Silicon-crystallographic-structure-It-has-the-diamond-structure-which-is-two-fcc_fig4_34172659 the fcc silicon lattice is shown.
My question is:
Since the silicon atom has 4 valence electrons and requires 4 more to be completed, why are so many atoms shown in the lattice. There are 8 electrons shown as nodes and each of it, is connected to a neighbouring node, thus each silison requires one more to be complete.
Also, what is the difference between the blue-ish and grey atoms?
Sorry for this silly question, but I didnt study chemistry extensively in the past and I find some concepts hard to understand.

Thank you in advance
 

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It is not about a compound (in which case electrons/bonds would matter), it is about a lattice - so it has to show the smallest repeatable cell. Note that each atom is connected to four other (just like you expected).

Also: I am not sure what you mean by "electrons shown as nodes".

Blue atoms are those completely inside the cell, grey ones are on the walls and they are shared with neighboring cells, they don't count as whole when counting cell atoms.
 
The cell shown is not a minimal cell, which would contain only two atoms, one black and the other blue. The black and blue positions cannot be mapped upon each other by a simple shift of the whole lattice, therefore, they are inequivalent. Each Si has 4 covalent bonds to 4 neighbouring atoms.
 
Last edited:
Borek said:
It is not about a compound (in which case electrons/bonds would matter), it is about a lattice - so it has to show the smallest repeatable cell. Note that each atom is connected to four other (just like you expected).

Also: I am not sure what you mean by "electrons shown as nodes".

Blue atoms are those completely inside the cell, grey ones are on the walls and they are shared with neighboring cells, they don't count as whole when counting cell atoms.
I see, I got it wrong, by "electrons shwon as nodes" I meant the spheres that form the cube, so those are the Si atoms.
 
DrDu said:
The cell shown is not a minimal cell, which would contain only two atoms, one black and the other blue. The black and blue positions cannot be mapped upon each other by a simple shift of the whole lattice, therefore, they are inequivalent. Each Si has 4 covalent bonds to 4 neighbouring atoms.
Can you explain this in a bit more detail please.
I though this correspond to the configuration of the minimum number of atoms thus all of the to have a complete outer layer.
Correct me if I am wrong, but since the Si atom has 4valence electrons and it needs 4 more to be complete, doesn't this mean that it needs at least 4 more atoms thus the most efficient shape possible is the one shown above. Can 2 Si atoms be suffiecient by sharing 8 electrons simultaneously?
If this is true, then what does the above shape mean/ porpuse?
 
The number of atoms in a cell is not directly related to the number of bonds, as bonds may exist between atoms in different cells.
 

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