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The concept of nearest neighbours

I'm having trouble understanding the concept of "nearest neighbours" and "next nearest neighbours." I understand that the number of nearest neighbours is the number of atoms per unit cell, but that's all I know (and I'm not sure why).

I'd like someone to show me how to calculate the number of nearest, second nearest, third nearest, etc. neighbours and the nearest neighbour distance for either a BCC or FCC structure.

For example, I've read that there are 6 nearest neighbours, 12 second nearest neighbours, etc. for a simple cubic lattice, with nearest neighbour distance 1, sqrt(2), etc. I don't know how this is found for SC or any other structure. Please explain thoroughly, and visually if possible.

Solution Summary

We compute the separation of nearest neighbors, next nearest neighbors, and third nearest (next next nearest) neighbors for SC, FCC, and BCC lattices.