Page 392 - Electrical Properties of Materials

374 Superconductivity

Table 14.1 The critical temperature and critical magnetic field of a number
of superconducting elements

–4
–4
Element T c (K) H 0 ×10 Am –1 Element T c (K) H 0 ×10 Am –1
Al 1.19 0.8 Pb 7.18 6.5
Ga 1.09 0.4 Sn 3.72 2.5
Hg α 4.15 3.3 Ta 4.48 6.7
Hg β 3.95 2.7 Th 1.37 1.3
In 3.41 2.3 V 5.30 10.5
Nb 9.46 15.6 Zn 0.92 0.4

H the dependence of the critical magnetic field on temperature is well described
by the formula,
H
0
Normal state
2
T
H c = H 0 1– . (14.1)
T c
Superconducting
state
C D This relationship is plotted in Fig. 14.4. It can be seen that the material is
normal above the curve and superconducting below the curve. H 0 is defined as
0 B T c A T the magnetic field that destroys superconductivity at absolute zero temperature.
The values of H 0 and T c for a number of superconducting elements are given
Fig. 14.4 in Table 14.1. Alloys could have both much higher critical temperatures and
The critical magnetic field as a much higher critical magnetic fields. They will come later.
function of temperature.
14.2.2 The Meissner effect

We have seen that below a certain temperature and magnetic field a number
(a)
of materials lose their electrical resistivity completely. How would we expect
these materials to behave if taken from point A to C in Fig. 14.4 by the paths
ABC and ADC respectively? At point A there is no applied magnetic field and
A B C the temperature is higher than the critical one [Fig. 14.5(a)]. From A to B the
T > T T < T T < T
c c c temperature is reduced below the critical temperature; so the material loses its
H = 0 H = 0 0 < H < H
c resistivity, but nothing else happens. Going from B to C means switching on the
magnetic field. The changing flux creates an electric field that sets up a current
opposing the applied magnetic field. This is just Lenz’s law, and in the past
(b)
we have referred to such currents as eddy currents. The essential difference
now is the absence of resistivity. The eddy currents do not decay; they produce
a magnetic field that completely cancels the applied magnetic field inside the
A D C material. Thus, we may regard our superconductor as a perfect diamagnet.
T > T T > T T < T Starting again at A with no magnetic field [Fig. 14.5(b)] and proceeding
c c c
H = 0 0 < H < H 0 < H < H to D puts the material into a magnetic field at a constant temperature. As-
c c
suming that our material is non-magnetic (superconductors are in fact slightly
Fig. 14.5 paramagnetic above their critical temperature, as follows from their metallic
The magnetic states of a
nature), the magnetic field will penetrate. Going from D to C means reducing
superconductor while tracing the (a)
the temperature at constant magnetic field. The material becomes supercon-
ABC and (b) ADC paths in Fig. 14.4.
ducting at some point, but there is no reason why this should imply any change
in the magnetic field distribution. At C the magnetic field should penetrate just