My teacher told us that there are 18 4th nearest neighbors in an hcp lattice, at a distance of √3a . I have only been able to identify 12.
Can you help me find all the 4th nearest neighbors?
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Sign up to join this communityWith HCP, things get hairy pretty quickly.
This is the first coordination sphere, with 12 atoms at the distance $a$ from the origin:
These are the second nearest neighbors, i.e. the 6 atoms at $\sqrt{2}a$ from the origin, each touching 4 atoms of the first sphere:
These are the third nearest neighbors, which are the 2 atoms at $\sqrt{8\over3}a$ from the origin, each touching 3 atoms of the first sphere:
And finally, here are your 18 atoms which are the $4^{th}$ nearest neighbors of the atom at the origin. Each touches 2 atoms of the first sphere: