Engineering Physics 3(2+1)

LESSON 21. Basic Concept of Superconductor

Phenomena

• Metal are good conductors of electricity as they contain large number of free electrons. As a result low resistance offered by them to the flow current is attributed to the scattering of the free electrons by vibrating ions of the lattice. As temperature increases, the amplitude of the lattice vibrations increases and causes more scattering of electrons leading to more resistance. 

• Even at 0 K (-273), metals offers finite resistance is called residual resistance. It is attributed to scattering of electrons by impurities and crystal defects present in the material.

• The variation of resistivity of normal metals with temperature is shown in  Fig.

• It indicates the existence of residual resistance (ρr).

• H Onne was explained the behavior of metals at very low temperature.

• The electrical resistance of highly purified H_g dropped suddenly to zero at a temperature of 4.2K.

• This transition is reversible, when the metal heated above the transition temperature of 4.2K, the H_g regained its resistivity.

• H Onne named the phenomenon as superconductivity.

• Superconductivity was a strictly low temperature phenomena; some ceramic were found to exhibit superconductivity at high temperature of about 120K.

• It was discovered for Lead, Zink, Aluminum and other metals and number of alloys.

• Superconductor is the phenomenon in which the electrical resistance of materials suddenly disappears below a certain temperature.

• The materials that exhibit superconductivity and which are in the superconducting state are called superconductors.

Transition Temperature

The temperature at which a normal material suddenly changes into a superconductor is called transition temperature T_c .

It is also called as critical temperature.

Critical Magnetic Field

• Superconducting state depends on the strength of the magnetic field in which the material is placed Fig.

  

• It is vanishes if a sufficiently strong magnetic field is applied.

• The minimum magnetic field, which is essential to regain the normal resistivity, is called critical magnetic field H_c   .

• When the applied magnetic field exceeds the critical value H_c , the superconducting state is destroyed and the material goes into normal state.

• The value of  H_c varies with the temperatures.

• It shows the dependence of  H_c on temperature in a typical semiconductor.

• At temperature below T_c  in absence of magnetic field, the material is in super conducting state.

• When magnetic field is applied and as its strength reaches the critical value material is in super conducting state.

• When magnetic field is applied and as its strength reaches the critical value H_c, the superconductivity in the material will be disappears.

• At any temperature   T < T_c    , the material remains superconducting until a corresponding critical magnetic field  H_c is applied.

• When the magnetic field is exceed than critical magnetic field  H_c, the material goes into normal state.

• The relation between magnetic field and temperature for the superconducting phenomena is

\[{H_c}\left( T \right)\] = \[{H_c}\left( 0 \right)\] \[\left[ {1 - {{\left( {{T \over {{T_c}}}} \right)}^2}} \right]\]

\[{H_c}\left( T \right)\] - Critical magnetic field at temperature K

\[{H_c}\left( 0 \right)\] - Critical magnetic field at 0K

T - Temperature in K

T_c - Critical temperature at magnetic zero field

Meissner Effect

In 1933, W Hans Meissner found that when superconductors are cooled below the critical temperature in presence of a magnetic field, the magnetic flux is expelled from the interior of the specimen and a super conductor becomes a perfect diamagnetic in nature.

This phenomena is known as Meissner Effect Fig.

Meissner found that as the temperature of the specimen is lowered to T_c, the magnetic flex is suddenly and completely expelled from it.

The flux expulsion continues for  T <  T_c .

The effect is reversible, when the temperature is raised from below T_c  , the flux suddenly penetrates the specimen at T = T_c   and material returns to the normal state.

The magnetic induction inside the sample is

 B = \[{\mu _o}\left( {H + M} \right)\]

H  Applied magnetic field

M Magnetization produced in the sample

 At  T <  T_c  ,B  = 0

0 = \[{\mu _o}\left( {H + M} \right)\]

H = -M

The susceptibility of the material

\[{M \over H}\] = χ = -1

The sample is diamagnetic and the state in which magnetization cancels the external magnetic field completely is referred to as perfect diamagnetic.