Distance to 3rd and 5th nearest ion to S2- in ZnS structure

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Discussion Overview

The discussion revolves around determining the distances to the 3rd and 5th nearest ions to S2- in the ZnS structure, which features a cubic close-packed (ccp) arrangement of ions. Participants are exploring geometric relationships and mathematical proofs related to these distances.

Discussion Character

  • Mathematical reasoning, Technical explanation, Debate/contested

Main Points Raised

  • One participant presents the distances to the 3rd and 5th nearest ions as √11a/4 and √19a/11, respectively, and seeks assistance in proving these values.
  • Another participant suggests following the geometry and using right triangles along with the Pythagorean theorem to find the distances.
  • A different participant expresses skepticism about the proposed distances, claiming they yield different results through quick mental calculations.
  • A later reply indicates that the original poster has applied the Pythagorean theorem and achieved a result, although it does not clarify whether this aligns with the initial claims.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are competing views regarding the correctness of the proposed distances and the methods used to derive them.

Contextual Notes

There may be limitations related to the assumptions made about the geometry of the ZnS structure and the specific definitions of nearest neighbors, which are not fully explored in the discussion.

Vishesh Jain
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Please post this type of questions in the HW section using the template and showing your work.
Hey folks

ZnS has a ccp structure with S2- ions forming FCC lattice with Zn2+ ions at half the tetrahedral voids

zbcell.gif


Attached is a table showing no. of nearest neighbours and their distance for an S2- ion

'a' is edge length of the unit cell

I want to know how the distance to the 3rd & 5th nearest ion is √11a/4 & √19a/11, i.e how to prove this.
upload_2018-10-13_16-17-34.png
Thanks ... any help is appreciated
 

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Have you you tried to follow the geometry? Often it is enough to find right right triangles and use Pythagorean theorem.
 
I think those numbers are wrong. They're not what I get (with quick mental arithmetic).
 
yes i did pythogarus & got it ... thanks ...
 

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