D O C U M E N T 7 6 O N S U P E R C O N D U C T I V I T Y 9 1
The theoretical scientific researcher is not to be envied, because Nature—or
more precisely put: experiment—is a merciless and not very kindly judge of his
efforts. She never says “yes” to a theory, in the best case merely “perhaps”; but in
most cases simply
“no.”[1]
If an experiment agrees with the theory, it means “per-
haps”; if it does not agree, then it means “no.” Every theory is sure to experience
its “no” someday, most theories already do so soon after their formulation. We
would here like to cast a glance at the fates of the theories of metallic conductivity
and at the revolutionary impact that the discovery of superconductivity must have
on our ideas about metallic conductivity.
After it was realized that negative electricity is embodied in subatomic carriers
of a particular mass and charge
(electrons),[2]
it made sense to assume that the
motion of electrons is the basis of metallic conductivity. Furthermore, the circum-
stance that metals conduct heat far better than nonmetals, likewise the Wiedemann-
Franz approximation
law[3]
that the ratio of electrical and thermal conductivity of
pure metals is independent of the substance (at normal temperatures), also led to
ascribing thermal conductivity mainly to electrons. These circumstances gave
occasion for an electron theory of metals following the model of the kinetic theory
of gases (Riecke, Drude, H. A.
Lorentz).[4]
This theory has assumed that electrons
in metals, disregarding collisions they undergo from time to time with the metal’s
atoms, are freely moving and, like gas molecules, should be endowed with thermal
kinetic energy of average magnitude
3/2
kT.
This theory was wonderfully successful to the extent that it was able to derive
theoretically, with admirable precision, the coefficient of the Wiedemann-Franz
law from the ratio of the electron’s mechanical and electrical
mass.[5]
It also
explained qualitatively the phenomena of thermoelectricity, the Hall effect, etc.
However the theory of electrical conduction may develop in the future, one main
support of this theory will surely always be retained, namely: the hypothesis that
electrical conductivity is based on the motion of electrons.
Drude’s formula for the specific resistance of metals
is[6]
, . . . (1)
where m signifies the mass, is the electron’s charge, u the mean velocity, n the
volume density, and l the electrons’ free length of path. Unfortunately, three
unknown temperature functions u, n, and l enter into the theory, one of which (u),
according to the kinetic theory of heat, is supposed to be connected with the abso-
lute temperature by the relation[7]
; . . . (2)
[p. 429]
[p. 430]
ω
ω
2m
ε2
-----------
u
nl
- =
ε
3mu2
kT =
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