Deriving fractional atomic coordination numbers

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Discussion Overview

The discussion revolves around the derivation of coordination numbers and atomic positions in crystal structures, specifically focusing on NaCl and ZnS. Participants explore the fractional coordinates of atoms within these structures and the underlying principles that dictate their positions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification

Main Points Raised

  • One participant questions how the coordination numbers for NaCl are derived, specifically why Na is at (0,0,0) and Cl at (1/2,1/2,1/2) instead of (0,0,0) and (1/4,1/4,1/4).
  • Another participant mentions that NaCl has a halite structure and confirms the fractional coordinates of Na and Cl in the unit cell.
  • A participant notes that the ZnS unit cell is based on a face-centered cubic (FCC) lattice but has different atomic positions, with Zn at (0,0,0) and S at (1/4,1/4,1/4), leading to tetrahedral coordination.
  • There is a request for clarification on the significance of units in the context of fractional coordinates.
  • One participant expresses uncertainty about how the positions of atoms in an FCC structure are determined, acknowledging that lattice parameters are experimentally derived but seeking insight into the determination of atomic positions.

Areas of Agreement / Disagreement

Participants express varying levels of understanding regarding the determination of atomic positions in crystal structures, with no consensus reached on the fundamental principles governing these positions.

Contextual Notes

Participants highlight the dependence on lattice parameters and the potential need for further clarification on the terminology related to fractional coordinates and unit cells.

SSJ2
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hi guys

i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived

...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not
(0,0,0) and (1/4,1/4,1/4)

of course this is in fractional coordinates
 
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SSJ2 said:
hi guys

i was wondering how the coordination numbers for the atomic positions of atoms in crystals such as NaCl are derived

...more specifically why is Na at (0,0,0) and Cl at (1/2,1/2,1/2) and not
(0,0,0) and (1/4,1/4,1/4)

of course this is in fractional coordinates
What are the units?
 
why do the units matter...NaCl has at halite structure...or the atomic positions of (0,0,0) and(.5,.5,.5) in fractional coordinates for the unit cell

maybe i didnt explain clearly enough... let me try again

So I know that the NaCl unit cell is based on a FCC lattice with a basis of Na Cl atoms at fractional coordinates (0,0,0) and (1/2,1/2,1/2) respectively

the zincblend (ZnS) unit cell (specifically the sphalerite not wurtzite) i know is also based on a fcc lattice but instead has a basis of Zn at (0,0,0) and S at (1/4,1/4,1/4) respectively which makes it tetrahedraly coordinated instead

i was wondering fundamentally why the S is at 1/4,1/4,1/4 and not 1/2,1/2,1/2 like Cl

i.e. the atomic positions...i was wondering if there was a way to derive this based on the lattice parameters.
 
I am not familiar with the terminology here. You talk about fractions of unit cells. Could you be more specific.
 
hmm, i guess in the end i was wondering how the position of the atoms in a fcc structure are determined. i know the lattice parameters are determined experimentally. But how are the positions of the atoms determined
 

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