SUPERCONDUCTIVITY

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                                                   SUPERCONDUCTIVITY
Some Definitions:

1. Superconductivity and superconductors:  

The phenomenon in which the electrical  resistivity of many metals and
alloys drops suddenly to zero when the specimen is cooled to a sufficient
low temperature is called superconductivity and the materials are called
superconductors.

2. Transition Temperature:

The temperature at which the specimen undergoes a phase transition from
the state of normal resistance to a superconducting state ( i.e. sudden
disappearance of resistance ), is called superconducting transition
temperature  or critical temperature   Tc .

3. Transition width :

The transition from the normal state to the superconducting state occurs over
a very small temperature range of about  0.05K. This temperature range is
known as transition width.
An Idea about the highest critical temperature
(Historical Survey):

 (i).  Till 1973, the highest critical temperature attained as 23.2K for  Nb Ge alloy.

(ii) .In 1986 Muller and Bendorz of IBM reported possible
superconductivity at 35 K in a mixture of crystalline phases in LaBa-Cu-O system. This opened the era of high  c
T superconductivity.
  (iii).      Till date the new superconducting systems have been found for  
which   c
T > 100 K. Experimental Survey:
The complete and abrupt disappearance of resistance is considered as a
consequence of some fundamental change in electronic and atomic structure
of the metal. Thus various experiments were performed to discuss the nature
of this change. The experimental observations indicated that  in the
superconducting transition
1. crystal lattice structure remains same
2. there is no appreciable change in the reflectivity of the metal either in
the visible or infrared region
3. elastic properties and thermal expansion do not change
4. photoelectric properties also remain unchanged.

                                                    
                                        HOWEVER 




1. The magnetic properties undergo change in the same way as electrical
properties. In pure superconducting state practically no magnetic flux
is able to penetrate the metal ( Meissner effect)
2. The specific heat changes discontinuously at transition temperature.
3. All thermo electric effects disappear  in the superconducting state.
4. The  thermal conductivity changes discontinuously

Effect of external factors on Superconductivity:

The superconducting properties of materials can change by varying (i).
temperature  (ii). magnetic field  (iii). Stress  (iv). Impurity (v). atomic
structure  (vi). Isotope mass  (vii).  Frequency of excitation of applied
electric field. The most important among  are the effect of magnetic field
and of isotope mass. So we shall first have a look at them.
Effect of magnetic field on superconductivity:
Suppose that a specimen (superconducting wire) is in a superconducting
state. If we now apply a magnetic field  of certain strength then the
resistance of the wire is suddenly restored i.e. the superconductivity
disappears. The field at which the superconductivity disappears is called
the critical magnetic field   H (T )c
 and it depends on temperature. It is to be noted that the restoration of resistance is  abrupt only if the metal is
perfectly pure and free from strain. At critical temperature , the magnetic field is zero i.e.   Hc (Tc
) = 0 . The variation of the critical field  with  temperature is nearly parabolic and is expressed by the relation
                            
Critical  Current Strength :

An important consequence of  the existence  of critical magnetic field is
that there is also a critical strength   c
I of the current flowing in a
superconductor.  If the  current  I exceeds the critical current  c
I then
superconductivity is destroyed.
“ Critical current is that current which can flow in a sample without
destroying the superconductivity”.
Consider a wire of radius ‘r’ of a soft superconductor.

H > H then there will be a transition from the superconducting state
to the normal state and the specimen will become normal. Now if we
apply an additional transverse magnetic field  H to the specimen, the
condition for the transition from superconducting state to the normal state
is that at the surface of the wire

Isotope effect:  
It has been observed that the Critical temperature is inversely
proportional to the square root of isotopic mass, i.e.                   Tc ∝ M        

This  equations indicate that the superconducting transition must
depend on the mass of the lattice ions ( called phonons ), a concept which
formed  electron – phonon interaction as the basic mechanism for the
occurrence  of superconductivity.

Meissner Effect :

This is one of the most important effects of superconducting state of a
specimen. It states that
“If a superconducting material is placed in a magnetic field and then
cooled below its critical temperature, it expels all the originally present
magnetic lines of force from its interior”.
It is to be noted that

1. Meissner effect is a reversible process which means that if the
material is cooled first below its critical temperature and then is
placed in a magnetic field, the magnetic flux will not penetrate the
material.

2. Meissner effect shows that a bulk superconductor in a weak magnetic
field behaves like a perfect diamagnet, with zero magnetic induction
in its interior (B=0). To see this, recall the equation    B = H + 4πM
which gives us   H = −4πM .

3. Meissner effect gives an extended definition of superconductivity in
the sense that for a material to be in a superconducting state it is
necessary ( and also sufficient) that the following two conditions should be satisfied : (i),   ρ = 0 , i.e. the zero resistivity state which is
equivalent to saying that the electric field  E=0 because  E= ρ J. and

(ii).  B=0 (Meissner Effect).
The expulsion of magnetic flux during the transition from the normal to the
superconducting state is called the Meissner effect.  This effect shows that in
the superconductor not only
dt
dB= 0, but also B = 0, thus from equation
           B = H + 4πM
           0 = H + 4πM
           H = −4πM
  This is the maximum value for the  susceptibility of a diamagnet.  In
this sense a superconductor is a perfect diamagnet. “Ideal diamagnet”,
 From ohm’s law
            E =  ρJ, if resistivity  ρ goes to zero while J is held
finite then E must be zero

  Thus the conditions defining superconducting state are
            E = 0 (absence of resistivity)
           B = 0 (Meissner effect)

Theoretical Explanation of Meissner Effect :


It is to be noted that the Maxwell’s equations were unable to explain the
electrodynamics of a superconductor ( according to Maxwell’s equations
the magnetic flux in the interior of a superconductor is not necessarily
zero but has a constant value which contradicts the Meissner’s
observations). London equations  which are based on a two fluid model
of conduction electrons, came as a modification to Maxwell’s equations
and could explain the electrodynamics of a superconductor. So we shall
first discuss the two fluid model which serves as basic assumption in
London’s equations.



 APPLICATION OF SUPERCONDUCTIVITY 


1. Superconductors are used for making very strong electromagnets.
2. Superconductors are used for the transmission of electric power.
3. Super conductivity is used to produce very high speed computers.
4. Super conductivity is playing an important role in material science
research and high energy particle physics.
5. Medical diagnostics e.g. MRI and NMR.
6. Superconductors are used in construction of very sensitive electrical
measuring instrument like galvanometers.
7. They are employed in switching devices.
8. Using superconducting materials as the core of the electromegnet very
intense magnetic fields can be produced.  It is also possible to design
low temperature devices like master.
9. Superconducting ceases when temperature rises above +c and the
magnetic induction goes beyond Hc.  In superconducting state the
magnetic field does not penetrate into superconductor i.e. a super
conductor behaves like a substance  with zero magnetic permeability.
Therefore, external magnetic field and super conductor repel each other.
This characteristic can be utilized  in developing friction less bearing
with magnetic lubrication for use in gyroscopes and electric machines.
10.Superconductors are used to multiply very small direct current and
voltages.
11.A new technology called cryogenics has been developed to utilize super
conductivity.