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Of all the elements in periodic table, which one has smallest nearest neighbor distance? I tried searching on net, but could not find any reference. My earlier guess was one which goes into FCC with smallest unit cell dimension should be one. But I am not sure.

In an FCC, if unit cell dimension is a, then nearest neighbor distance will be a/sqrt(2) because nearest atom to an atom on the edge of the cube will be face atom. But this is for FCC. For SC of size a, nearest atom will be at a distance of a. So, for different elements, there will be different nearest neighbor distance based on its unit cell geometry and unit cell length. I want to know which combination of these result in shortest nearest neighbor distance.

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Both FCC and HCP packings have nearest neighbours as close as possible (in nature at least, the simple cube is even closer but doesn't exist). Their nearest neighbour distances in terms of $a/R$ are $2\sqrt{2}$. Here $a$ is the length of a side of the unit cell and $R$ is the radius of the atom the cell consists of.

When you are looking for the smallest nearest neighbour distance this means that you are looking for the smallest $a$ in an FCC or HPC packing. You can translate this into: you are looking for the atom which forms an FCC or HPC packing and has the smallest value for $2\sqrt{2}R$ so for $R$.

Now, I don't know all the options but for example $\ce{Cu, Au, Ag}$ form FCC structures and $\ce{Zn}$ forms an HCP structure (see e.g. here). You can look up the atomic radii and find that Zinc has the smallest: $122$ pm and will thus have a nearest neighbour distance in the lattice of $345$ pm.

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  • $\begingroup$ An FCC face center atom touches face center of other faces so how can we prove the distances to be a/√2. $\endgroup$ – Scáthach Jul 4 '18 at 12:33

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