Page 399 - Electrical Properties of Materials

Surface energy 381

specific heat has a discontinuity. This is borne out by experiments as well, as
shown in Fig. 14.9, where the specific heat of tin is plotted against temperature.
The discontinuity occurs at the critical temperature T c =3.72 K.

14.5 Surface energy
The preceding thermodynamical analysis was based on perfect diamagnetism,
that is, we assumed that our superconductor completely expelled the magnetic
field. In practice this is not so, and it can not be so. The currents that are set
up to exclude the magnetic field must occupy a finite volume, however small
that might be. Thus, the magnetic field can also penetrate the superconductor
to a small extent. But now we encounter a difficulty. If the magnetic field can
penetrate to a finite distance, the Gibbs free energy of that particular layer will
decrease, because it no longer has to perform work to exclude the magnetic
field. The magnetic field is admitted, and we get a lower Gibbs free energy.
Carrying this argument to its logical conclusion, it follows that the optimum
arrangement for minimum Gibbs free energy (of the whole solid at a given
temperature) should look like that shown in Fig. 14.10, where normal and su-
perconducting layers alternate. The width of the superconducting layers, s,is
small enough to permit penetration of the magnetic field, and the width of
the normal region is even smaller, n s. In this way the Gibbs free energy
of the superconducting domains is lower because the magnetic field can pen-
etrate, while the contribution of the normal domains to the total Gibbs free
energy remains negligible, because the volume of the normal domains is small
in comparison with the volume of the superconducting domains.
Thus, a consistent application of our theory leads to a superconductor
in which normal and superconducting layers alternate. Is this conclusion
correct? Do we find these alternating domains experimentally? For some super-
conducting materials we do; for some other superconducting materials we
do not. Incidentally, when the first doubts arose about the validity of the
simple thermodynamical treatment, all the experimental evidence available at
the time suggested that no break-up could occur. We shall restrict the argu-
ment to this historically authentic case for the moment. Theory suggests that

S N S N S N S N S N S N S N

Fig. 14.10
Alternating superconducting and
s n normal layers.