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## Homework Statement

An element crystalises in a face-centred cubic lattice with a basis group of two atoms at 000 and 1/4 1/4 1/4. The lattice constant is 3.55Angstroms.

i) what is the separation of nearest neighbor atoms

ii) how many nearest and second nearest neighbors does each atom have.

**attempt**

i) The nearest neighbor distance is just going to be from the 000 atom to the one 1/4 1/4 1/4 away from it? Which gives

[tex]\sqrt{3(\frac{1}{4}a)^3} = 1.54Angstroms[/tex]

ii) If the guess for part i is right then each atom will have one nearest neighbor. I can't get my head around the second nearest neighbors.

Any help appreciated, thanks.