Conductivity in a one-dimensional chain of flourine atoms

[bushman00]

If we prepare a chain of flourine atoms: F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F-F we can construct the band structure shown. I'm using flourine as an example but my question can be generalized: What do we know about the conductivity of a material (such as this 1D chain) when the fermi level lies in the conduction band, ie. above the band gap? I'm also curious how the fermi level would rise and fall if this chain would have been constructed from F- or F + ions. I imagine with the F- ion because all the bands are filled, the structure is most certainly insulating but where would F+ lie?

BM

 

[Modulated]

The idea of a band gap normally refers to the difference in energy between an entirely full (valence) band and an entirely empty (conduction) band. Here, since you have a half-filled band, the system would be metallic if you believe the simplified band structure diagram you’ve attached. (In fact, one-dimensional metals will spontaneously undergo a distortion that makes them insulating – google “Peierls distortion” for more on this if you’re interested.)

As for your second questions: where do you think the Fermi level would fall in a hypothetical chain of F+ ions? (Note of course that this would be unstable in real life since it would carry an infinite amount of charge!)

 

[bushman00]

Thanks for the response, I'm under the impression that the band gap exists in a region whereby bands don't overlap or in other words where the density of states is 0. So to some degree what you're saying must be an extension of this principle?

Considering the fermi level for a chain of F+ I would presume it would lie slightly below its placement for the F chain, at the level of the degenerate pi orbitals. But what does this imply about its conductivity? It still overlaps the pz sigma character band (that is now unoccupied) so doesn't this make it a metal?

To extend this concept a bit further, wouldn't F2+ (ignoring infinite charge) also lie in the same place as F+ because there would still exist one fully occupied pi degenerate orbital? I believe that S would also share a similar chain band structure as F+ as well but without the infinite charge to make the theory a little less fictitious. Thanks,

BM

 

[DrDu]

Even if the chain of fluorine (not flourine) atoms were stable against Peierls distortion, it would probably not be a conductor but a Mott insulator. A one-electron band structure does not allow you to decide whether a substance will be a conductor when there are strong electronic correlation effects. In the process of conduction, electrons would have to hop independently from one atom to the next, thereby creating F^+ F^- pairs, which is very awkward due to the high electronegativity of fluorine.

Instead of considering a chain of F^+ or F^- I would consider a chain of isoelectronic O or Ne atoms, respectively. Ne is certainly an insulator and O too.