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I know conductivity increases, but what happens to the electrons on the inside?

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  • $\begingroup$ Related: physics.stackexchange.com/q/257600 $\endgroup$
    – jng224
    Commented Oct 29, 2020 at 9:39
  • $\begingroup$ @Jonas That link is about thermal conductivity. I would assume that the question is about electrical conductivity. $\endgroup$
    – user137289
    Commented Oct 29, 2020 at 10:26
  • $\begingroup$ @Pieter Maybe it was too much to call it "related", but I thought that some of the mechanisms described in the linked question and answers might also be important in answering this question (e.g. increasing temperature --> increased oscillations of atoms) $\endgroup$
    – jng224
    Commented Oct 29, 2020 at 11:13

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Electrical conductivity is the product of the number of conduction electrons and their mobility. In metals, the number of electrons does not depend on temperature.

The mobility increases at lower temperature. That means the drift velocity of the electrons increases in an applied field. In the Drude model, this is because there is less scattering, the relaxation time (the time during which the electrons accelerate) is longer, the mean free path is longer.

At very low temperatures in very pure metals, the mean free path can be very long, like on the order of a millimeter. The electrons then move in a very regular lattice.

At higher temperatures, vibrational modes get excited. The lattice becomes less regular. There is more scattering, the mean free path is shorter, the mobility goes down, the resistivity goes up.

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The picture I've been taught was that the atoms start vibrating less en thus the electron sees a more regular periodic crystal structure and has less chance to 'collide' with an atom and slow down. How free an electron can move is essentially how good the material conducts electricity and because the electrons can move more freely the conductivity thus increases.

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