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

[Vishesh Jain]

Hey folks

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

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.

Thanks ... any help is appreciated

 

[Borek]

Have you you tried to follow the geometry? Often it is enough to find right right triangles and use Pythagorean theorem.

 

[mjc123]

I think those numbers are wrong. They're not what I get (with quick mental arithmetic).

 

[Vishesh Jain]

yes i did pythogarus & got it ... thanks ...