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[Phys-l] conductivity of metals



When I speak of "conductivity", unless context requires otherwise,
I mean both thermal and electrical conductivity, in accordance with
the Wiedemann-Franz law, as previously discussed.

I neglect the small contribution to the thermal conductivity from
the underlying lattice. Also note that superconductors are a
huuuuge exception to the W-F law: the superfluid transports
charge but not entropy.

On 10/24/2006 07:21 PM, Bernard Cleyet wrote:
... I was going to suggest the the
weighted average is probably not valid.

Probably!?!?!!!!

Suppose we have a wire suitable for use as heater wire (resistance
wire), as in the application that precipitated this discussion.
It will be an alloy. It will less conductivity than any of its
components separately, probably by several orders of magnitude
(depending on temperature).

Resistivity is rooted in /scattering/ of the electrons.

For reasonably-pure metals at room temperature, the dominant
contribution is /thermal/ scattering, i.e. electrons scattering
off thermal phonons.

If you lower the temperature enough, and/or add enough impurities,
eventually you get into another regime, where the dominant
contribution is /impurity/ scattering, i.e. electrons scattering
off impurities. In this regime, electrical conductivity is (to
first order) independent of temperature, and thermal conductivity
is proportional to T.

Resistance wire, pretty much by definition, is in the impurity-
dominated regime, which makes sense because you want its electrical
conductivity to be independent of temperature.


At cryogenic temperatures, you can achieve tremendous conductivity,
if your metal is pure enough. At low temperatures, tiny amounts
of impurities can radically decrease the conductivity. Magnetic
impurities such as iron or oxygen are particularly effective
scatterers.

Once upon a time, a guy who was looking into the conductivity of
ultra-pure metals got a big surprise.
http://nobelprize.org/nobel_prizes/physics/laureates/1913/onnes-bio.html