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If a metal is a Fermi sea, what makes different metals better conductors?

Clearly, one valance electron dominates.

All things being equal, I would have assumed that the bigger atoms, with more electrons and more distance between the valence electron and the nucleus, would conduct the best. That would imply gold, then silver, then copper. But silver conducts best, followed by copper, then gold. Why?

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Several things contribute to conductivity. I think two are particularly relevant to the question. First concerns band structure. Metals can conduct easily because there are empty states very close in energy to the Fermi surface, so that it is easy to promote an electron to a higher-energy level. In an electric field, the newly-occupied states all (loosely speaking) have momenta in the direction of the field, so there is net movement of the electrons in the direction of the field. How well this works depends on the density of states at the Fermi level. The more states available, the better the conductivity. I've looked for these data for the noble metals but haven't located them.

The second concerns the dominant loss mechanism at room temperature, the interaction of the electrons with the lattice. In a simple model of a solid the positions of the ion cores are taken to be fixed. In reality they are not, and a passing electron will excite lattice excitations (phonons) and lose energy. How well this works depends on the strength of the electron-phonon coupling in the solid, and that's complicated business.

Having said all that, I don't have data at hand to make an argument about the noble metals. But I think it should be clear that your picture of conductivity needs to be augmented, and that might be enough to answer your question.

Update I found data on density of states, and the order of densities of states is Ag, Cu, Au, from highest to lowest.

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  • $\begingroup$ Could you share the location of the data? This begs the question, what is the mechanism that makes silver have a higher density of states than gold? $\endgroup$ – Dov Mar 26 '14 at 22:31
  • $\begingroup$ I foolishly didn't record the source, but I found it in my browser history. It's here, in Fig 4.4. This appears to be a photocopy of a book chapter. Legality questionable. The title and author are not to be found. I'll try to find time to address the very good questioned that was begged. $\endgroup$ – garyp Mar 27 '14 at 19:15
  • $\begingroup$ I now see that I have misread that graph. It does not provide the data that I thought it did. I'll have to revisit my answer. $\endgroup$ – garyp Mar 27 '14 at 19:21
  • $\begingroup$ any news? would love an explanation... $\endgroup$ – Dov Apr 17 '14 at 4:56

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