In the figure for second nearest atom, there are 18 atoms linked by the black lines. However, there are only 6 second nearest neighbors. Similarly, in the the figure for 4th nearest neighbors, there are more than 18 atoms linked by the black lines. In the figure for 1st and 3rd nearest neighbors, I can make out the required atoms. Could you please clarify the required neighbor in the 2nd and 4th one.More
With 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:
With 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:
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