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Re: metal conductivity (fwd)



Regarding John Cooper's relayed question:

A contributor to the sister, Chemical Educator's list asks

Can anyone explain, on an atomic level, why copper and silver are better
conductors of heat and electricity than the other transition metals?

-- Challenge broadens the vista of capability --

John N. Cooper, Chemistry

This is a good question the answer to which I do not know. However, I
strongly suspect that the answer to the question of the high electrical
conductivities of these elements will not be found in an analysis at the
"atomic level". The reason for this is that the conductivity depends
very strongly on details of how those atoms are arranged in a lattice,
how the lattice potential determines the energy bands, and how the
lattice degrees of freedom interact with the conduction electron degrees
of freedom. The specific values of these relevant details is only found
in an analysis that involves macroscopic numbers of atoms and electrons,
not in an analysis that only looks at the properties of a single atom.

The main contributing factors (there are other non-main ones involving
interactions among the conduction electrons themselves, etc.) in the
conductivity are 1) the electron/phonon scattering rate for (single)
electron states near the Fermi surface, 2) the effective area of the
Fermi surface (in k-space) in the conduction band of states, and 3) the
average speeds of those (single) electron states near the Fermi surface.

For factor 1) the slower the electron/phonon scattering rate the greater
the conductivity. Other factors which determine the scattering rate
cross sections involve details of the interionic harmonic potential, the
band structure, and coupling terms between the electron degrees of
freedom and distortions of the lattice. Some of these interactions come
as perturbations (to the harmonic lattice and conduction electron
Hamiltonian) directly from underlying interactions, and others come from
a weak breakdown of the Born-Oppenheimer approximation.

Factor 2) is determined by the details of the periodic potential that
the conduction electrons each see as due to the background lattice and
that involves detailed knowledge of the Chemistryesque structure of the
ion core states and the valence states, as well as a knowledge of the
particular overall lattice structure. In this case the more area of
Fermi surface in the conduction band the higher the conductivity.

Factor 3) (like factor 2)) depends on the details of the band structure.
In particular, what is most relevant in this case is the structure of
the band-effective mass tensor as a function of energy near the Fermi
energy, and this is nearly determined by the actual curved shape of the
Fermi surface itself in the conduction band(s) in k-space. In this case
a flat slowly curving Fermi surface results in a high effective mass,
and this results in a slow velocity for the relevant electron states,
and this results in a lower conductivity.

And this doesn't even begin to get into electron correlation effects due
to inter-electron interactions and to anharmonic effects in the lattice.

I'd appreciate it if *anyone* could give good qualitative plausibility
arguments for the particular values of all these most relevant quantities
and properties as they distinguish elements like Cu and Ag from other
metals.

David Bowman
David_Bowman@georgetowncollege.edu