Prof. Vilas Shamrao patil

1. SUPERCONDUCTIVITY
4.1. INTRODUCTION AND HISTORICAL DEVELOPMENTS:
The field of superconductivity has emerged as one of the
most exciting fields of solid state physics and solid state
chemistry during the last decade. The phenomenon was first
discovered in 1911 by Kamerlingh Onnes in Leiden while
observing the electrical resistance of mercury at very low at
temperatures close to 4.2 o
K, the melting point of helium. It was
observed that the electrical resistance of mercury decreased
continuously from its melting point (233 o
K) to 4.2 o
K and then,
within some hundredths of a degree, dropped suddenly to about
a millionth of its original value at the melting point as shown in
Fig. 4.1. Similar results were obtained by using various other
metals such as Pb, Sn and In. The phenomenon of disappearance
of electrical resistance of material below a certain temperature
was called su-perconductivity by Onnes and the material in this
state was called a superconductor.

2. Fig.4.1.Temperature dependence of the resistance of normal
metal and a superconductor like Hg
The discovery of superconductivity aroused considerable
interest in this field since the materials with no electrical
resistance, and hence negligible heat losses, could be exploited
to fabricate powerful and economical devices which consume
very little amount of electrical energy. For example, an
electromagnet made up of a superconducting metal can function
for years together even of the removal of the supply voltage.
However, due to the "requirement of very low temperature, it
was not feasible to manufacture such devices. It is both difficult
and expensive to attain the liquid helium temperature and
maintain it for a long time. Thus soon after the discovery of
superconductivity, a lot of research work was undertaken to
develop a superconducting material having as high critical

3. temperature as possible. A number of materials including
various metals. alloys, inter metallic and interstitial compounds,
and ceramics were employed for this purpose. Besides all these
efforts, the maximum critical temperature (Tc) of only 23 o
K was
achieved in Nb3Ge, an inter metallic compound of niobium and
germanium in the year 1977. Thus the scientists had almost
given up the hope of producing superconducting devices for
which it was necessary to have a superconductor with the
transition temperature equal to or higher than 77 o
K, the liquid
nitrogen temperature, if not the room tem-perature. In 1986,
Bednorz and Muller reported their discovery on the La-Ba-Cu-O
system of ceramic superconductors which showed Tc equal to 34
o
K. Thus, contrary to the previous findings, a new class of ceramic
superconductors was discovered which showed critical
temperature considerably greater than that of the metallic
superconductors. They named these materials as high-Tc
ceramic superconductors. They were awarded the Nobel Prize in
1988 for such an important discovery which created an
unprecedented, world wide interest in the field of oxide ceramic
superconductors. In 1987, a ceramic superconductor of the
composition YBa2Cu3O7 was discovered which showed Tc equal
to 90 o
K. In 1988, the value of Tc further shot up to about 125 o
K
for thallium cuprates. Table 4.1 gives some data on
superconductors in chronological order. It would be apparent
from the following discussions that the superconducting state is

4. a distinct phase of matter having characteristic electrical,
magnetic, thermodynamic and other physical properties. The
most easily observed characteristics of bulk superconductors are
the zero electrical resistance and the perfect diamagnetism. We
describe below the empirical properties of superconductors; the
relevant theory will be presented in a subsequent section.
4.2 ELECTRICAL RESISTIVITY
As described earlier, a superconductor exhibits no electrical
resistance. The resistance of a superconductor suddenly drops
to an extremely small value near the transition temperature as
shown in Fig. 4.1. The careful investigations have shown that the
resistivity of a metal in the superconducting state drops to less
than one part in 1017
of its value in the normal state.

5. TABLE 4.1. Properties of some selected superconductors in
chronological order

6. DIAMAGNETISM OR MEISSNER EFFECT:

7. Meissner and Ochsenfeld discovered in 1933 that a
superconductor expelled the magnetic flux as the former was
cooled below Tc in an external magnetic field, i.e., it behaved as
a perfect diamagnet. This phenomenon is known as the Meissner
effect. Such a flux exclusion is also observed if the
superconductor is first cooled below Tc and then placed in the
magnetic field. It thus follows that the diamagnetic behavior of
a superconductor is independent of its history as illustrated by
Fig. 4.2. It also follows from this figure that the Meissner effect
is a reversible phenomenon. Since B = 0 inside the
superconductor, we can write
B = μ0(H + M ) = 0
H = −M
Therefore, the susceptibility is given by χ =
M
H
= −1
which is true for a perfect diamagnet.

8. Fig. 4.2. A superconductor showing a perfect diamagnetism
independent of its history.
It is interesting to note that the perfect diamagnetic
behaviour of a superconductor cannot be explained simply by
considering its zero resistiviity. Such a perfect conductor would
behave differently under different conditions as illustrated by
Fig. 4.2. Since the resistivity, p, is zero for a perfect conductor,
the application of Ohm's law (E = ρJ) indicates that no electric
field can exist inside the perfect conductor. Using one of the
Max-well's equations, i.e.,
𝛻𝑋𝐸 = −
𝑑𝐵
𝑑𝑡
we obtain B = constant .

9. Thus the magnetic flux density passing through a perfect
conductor becomes constant. This means that when a perfect
conductor is cooled in the magnetic field until its resistance
becomes zero, the magnetic field in the material gets frozen in
and cannot change subsequently irrespective of the applied
field. This is in contradiction to the Meissner effect.
Thus we conclude that the behaviour of a superconductor is
different as the temperature rises until the critical temperature
is reached where it increases sharply. Thus at and above T, the
field penetrates the metal completely.