Coordination in a zincblende lattice

[Beer-monster]

Homework Statement

Could someone please confirm my answers for the coordination numbers in Zincblende going from nearest to next nearest to next next nearest neighbours. I'm trying to estimate the value of the madelung constant for ZnS, but am getting too large a value. I'm fairly sure that my calculation of neighbour distances is accurate, which leaves a problem with my coordination numbers.

Homework Equations

This diagram might be helpful for reference.

http://cnx.org/content/m16927/latest/graphics17.png

The Attempt at a Solution

Nearest neighbours: CN = 4 (tetragonal site)

Next-nearest neighbours: CN= 12 (anions and cations form fcc lattice amongst themselves)

Next-next-nearest neighbours (this is the one I'm unsure about) CN=12.

I got this answer by considering each of the three major planes (001)(010)(100). Each plane forms a chessboard pattern with anions at the vertices and cations in the centre of the black squares. I counted the number of equivalent next-next nearest connections (i.e. from a corner to the centre of the second closest black square) as 4 in each plane. Therefore we have a CN=3x4=12 in total.

Is this correct?

I am also making the assumption that the value of the constant should be close to the databook value even after 3 terms (is this reasonable)?

Thanks for your help, let me know if anything above is not clear.

 

[AvroArrow]

Yes, your answer is correct. The coordination number for the next-next-nearest neighbors is indeed 12. And yes, it is reasonable to assume that the value of the madelung constant should be close to the databook value after three terms.