Chemistry Reference
In-Depth Information
(a)
(b)
Normal impure
substance
Superconducting
state
Normal
state
Pure
substance
Temperature,
T
Temperature,
T
Figure 8.1
Schematic illustration of (a) the variation of resisitivity at low temperature
in a normal impure metal, and in a highly purified crystal of the same metal;
compared with (b) the superconducting transition at low temperature in
mercury.
8.2 Occurence of superconductivity
We consider first a normal metal, which has a DC electrical resistivity,
ρ
,
so that the current density
J
in an applied electric field
E
is given by
E
=
ρ
J
(8.1)
The resistance in such ametal has twomain components, due to (i) thermal
vibrations of the atoms, and (ii) impurities and defects in the crystal. Both
these processes scatter electrons. (Electrons are
not
scattered by a perfect
lattice.) As the temperature is decreased, the lattice vibrations decrease,
and it is consequently observed that the resisitivity also decreases. Figure
8.1(a) shows schematically the resisitivity of a normal, impure metal, and
of a highly purified single crystal of the same metal, near
T
=
0K: the
resistivity remains finite in the former case, but
ρ
→
0as
T
→
0inthe
pure sample.
In 1911, the Dutch scientist, Heike Kamerlingh Onnes, measured the
resistance of mercury at low temperature, three years after he had first
succeeded in the liquefaction of helium. He found that mercury under-
went a dramatic transition at a finite critical temperature
(
T
c
∼
4.2 K
)
from
ρ
∼
a normal to a superconducting state, with
0 below
T
c
(fig. 8.1(b)).
He was unclear because of experimental uncertainties whether
ρ
∼
0or
ρ
≡
0 exactly. The best means to determine a low resistance
R
accurately
is to observe current flow in a closed loop of self-inductance,
L
, where the
current should decay with a time constant,
R
. By observing the per-
sistent current for a year, File andMills (1963) placed a lower limit on
τ
=
L
/
in a
superconducting closed loop of 100 000 years, requiring a superconducting
resistivity
τ
m, over 10
15
times smaller than in the normal state,
thereby justifying the assumption that
10
−
26
ρ<
ρ
≡
0 in the superconducting state.
