ABSTRACT
The study of
superconductors, it concept and the various theories are still a mystery in the
field of Solid State Physics. Although a few theories tries to explain the
working principle (i.e. how and why it works) of super-conductors scientists
believed that a full acknowledgment of its energy gap; is dependence on
temperature and pressure and the effect of doping may finally unlock the door
to a vast acknowledge of superconductivity.
This project work brings all in one piece, the various
principle and theories as derived by some renowned scientist working to ensure
full understanding in this area of physics. It is believed that High
Temperature Superconductors (HTS) i.e. superconductors with considerable high
critical temperature hold the key to the practical application of super
conductors.
CHAPTER ONE
1.1
INTRODUCTION
Superconductivity is a fascinating and
challenging field of physics. Scientists and Engineers throughout the world
have been striving to develop it for
many years. For nearly 75 years superconductivity has been a relatively obscure
subject. Until recently, because of the cryogenic requirement of low
temperature superconductors, superconductivity at the high school level was
merely an interesting topic occasionally discussed in a Physics class. Today
however, superconductivity is being applied to many diverse areas such as:
medicine, theoretical and experimental science, the military, transportation,
power production, electronics, as well as many other areas. With the discovery
of high temperature superconductor which can operate at liquid nitrogen
temperature (77k), superconductivity is now well known within the reach of high
school student. Unique and exciting opportunities now exist today for our
student to explore and experiment with this new and important technological
field of Physics. Major advances in low-temperature refrigerator were made
during the late 19th century. (Bedornz, J and Muller, K; 1986).
1.2
PROBLEM STATEMENT
It is not practical to transmit electric energy if you need
liquid helium temperatures. The cooling costs are prohibitive. The current
state of the art are cables using thin films of BSCCO. They can operate at 77 K
without problems. The current world record for such a cable in a vacuum tube is
several kilometers but after some distance you need a small building along the
cable to cool the liquid nitrogen inside the cable again.
There is a tremendous research effort to find superconductors
with higher critical temperatures and currents but that is not so easy. The
usage for practical applications is increasing but the progress is rather slow.
In more exotic applications such a CERN or ITER you absolutely need
superconducting cables, if it is only for space reasons: Well, Is it really
possible to maintain such low temperatures required for super-conductors
(taking High-temperature superconductivity into account) over large distances? What I say is - Even if we were able to pass current
through superconductors, we need to constantly cool them for maintaining the
zero resistance. Hence to cool, we need power. Then, superconductors wouldn't
be necessary in this manner if they don't have an advantage..? Or, are there
any new approaches to overcome these disadvantages?
1.3
OBJECTIVES OF THE STUDY
The primary objective of the study is to examine the
energy gap in superconductors. Specific objectives of the study are:
1. To critically examine the various types
and properties of super conductors
2. To examine energy gaps in low
temperature super conductors.
3. To examine energy gaps in high
temperature super conductors.
1.4
SIGNIFICANCE OF THE STUDY
The study will give more
insights into the various ways superconductors can be utilised and improved.
Superconducting materials are in the forefront of current research because of
their very rich and fascinating properties and their applications in electrical
and electronics technology and energy-saving materials. Superconductivity is a
unique characteristic of certain materials that appears when the system
temperature is dropped below a specific critical value and under such
conditions the materials can carry electrical current with absolutely zero
resistance.
1.5
DISCOVERY OF SUPERCONDUCTORS
Superconductors were first discovered in
1911 by the Dutch physicist. Heike Kammerlingh Onnes.
Onnes
dedicated his scientific carriers to exploring extremely cold refrigerator He
successfully liquefied helium by cooling it to 452 degree below zero Fahrenheit
(4 Kelvin or 4K). Onnes produced only a few millilitres of liquid helium that
day, but this was to be the new beginning of his exploration. The liquid helium
enables him to cool other material closer to absolute zero (0 Kelvin)
In
1911, Onnes began to investigate the electrical properties of metal in
extremely cold temperature. It has been know for many years that the resistance
of metal fell when cooled below room temperature, but it was not know what limiting
value the resistance would approach if the temperature were reduced very close
to Ok. Onnes, found that a cold wire’s resistance would dissipate. This
suggested that there would be a steady decrease of electrical resistance
allowing for better conductor of electricity.
1.6
BCS THEORY OF SUPERCONDUCTIVITY
The properties of type-1 superconductor
were modelled successfully by the effort of John Bardeen, Leon Cooper, and
Robert Schrieffer in what is commonly called the BCS theory(Bardeen et al;1957).
A key conceptual element in this theory is the pairing of electron close to the
Fermi level into cooper pairs through interaction with the crystal lattices.
The pairing result from a slight attraction between the electrons related to
lattice vibration. The coupling of this lattice is called Phonon. Interaction
pair of electron can behave very differently from single electron which one
fermions and must obey the Pauli Exclusion Principle. The pair of electron acts
more like Boson which can condense into the same energy level. The electron
pair has a slightly lower energy and leave an energy gap above them on the
order to 0.001 eV, which inhibit the kind of collision interaction which lead
to ordinary resistivity. For temperature such that the thermal energy is less than
the band gap, the material exhibit zero resistivity (Wu,J; 2002).
1.7
COOPER PAIRS
The behaviour
of superconductors suggest that electron pairs are coupling over a range of
hundred of nanometres, there orders of magnitude larger that the lattice spacing
called cooper pairs. This coupled electron can take the character of a boson
and condense into the ground state.
Cooper
pairs are the pairing caused by the attractive forces between electronic from
the exchanges of phonons.
Figure: 1.1 Cooper pairs
1.4 ANALYTICS OF SUPERCONDUCTIVITY
Materials that have no resistance to the flow of
electricity are one of the last great frontiers of scientific discoveries. Not
only have the limits of superconductivity not yet reached but the theories that
explain superconductivity behaviours seem to be constantly under review.(Betil,S; 2007).
In
general, superconductors become superconducting only below a certain transition
temperature Tc, which is usually within a few degree of absolute zero. Currently,
in a ringed shape superconducting
material, electric current has been observed to flow for years in the absence
of a potential difference with no measurable decrease. Measurement show that
the resistivity superconductors is less than 4x10-25Ωm, which is over 1016
times smaller than that for copper (cu) and is considered to be zero in
practice.
Figure 1.2 - A superconducting material
A superconducting materials has zero resistivity
when it is below its critical temperature (Tc). At Tc, the resistivities jump
to neither ‘normal’ nor zero value and increase with temperature as most
material do
ρT = ρo [1+∞ (T-T0)] (1.1)
Much
research has been done on superconductivity to try and understand why it
occurs. And to find materials that super conduct as higher more accessible
temperature to reduce the cost and inconvenience of refrigerator at the require
very low temperature. Before 1986, the highest temperature at which a material
was found to super conduct was 23K, and this required liquid helium to keep the
material cold(Charles, J; 2003).
In
1987, a compound of Yttrium, barium, copper and oxygen (YBCO) was developed
that can be superconducting at 90K. Since this is above the boiling temperature
of liquid nitrogen, 77K which is sufficiently cold to keep the material
superconducting.
This is
an important break through since liquid Nitrogen was much more easily and
cheaply obtained than the liquid helium needed for conventional super
conductors. Since the superconductivity at temperature as high as 160 or 16K has
been reported, through the fragile compound considerable research is being done
to develop high Tc superconductors as wires that can carry current strong
enough to be practical. Most application today use a Bismuth-Strontium-Calcium-Copper
Oxide (BSCCO) known how to make a useable bendable wire out of it, which is of
course very brittle. One solution is to embed tiny filaments of high Tc
superconductor in a metal alloy matrix with the superconducting wire wrapped
around a tube carrying liquid nitrogen to keep the BSCCO below Tc. The wire
cannot be resistance less, because of the silver connections, but the
resistance is much less than that of the conventional copper cable. (Gracho,D.C; 2005).