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Super Conductors

   Posted On :  03.12.2016 07:25 pm

1 Introduction to Superconductivity 2 Properties of Superconductors 2.1 Critical magnetic field (Magnetic Property) 2.2 Diamagnetic property (Meissener effect) 2.3 SQUID (Superconducting Quantum Interference Device) 2.4 Effect of heavy Current 2.5 Persistence of Current 2.6 Effect of pressure 2.7 Isotope effect 2.8 General properties 3 Types of Super Conductors 3.1 Difference between Type I and II superconductors 3.2 Difference between High TC 4 High Temperature (High-Tc) Superconductors 5 Bcs Theory of Superconductivity 6 Applications of Superconductors 7 Engineering Applications 7.1 Cryotron 7.2 MAGLEV (MAGnetic LEVitation) 7.3 Josephson Devices

SUPER CONDUCTORS

 

1 Introduction to Superconductivity

2 Properties of Superconductors

2.1 Critical magnetic field (Magnetic Property)

2.2 Diamagnetic property (Meissener effect)

2.3 SQUID (Superconducting Quantum Interference Device)

2.4 Effect of heavy Current

2.5 Persistence of Current

2.6 Effect of pressure

2.7 Isotope effect

2.8 General properties

3 Types of Super Conductors

3.1 Difference between Type I and II superconductors

3.2 Difference between High TC

4 High Temperature (High-Tc) Superconductors

5 Bcs Theory of Superconductivity

6 Applications of Superconductors

7 Engineering Applications

7.1 Cryotron

7.2 MAGLEV (MAGnetic LEVitation)

7.3 Josephson Devices

 

1 INTRODUCTION TO SUPERCONDUCTIVITY

 

It was thought that the electrical resistance of a conductor becomes zero only at absolute zero temperature. But in 1911, H. Kammerlingh Onnes studied the properties of mercury at very low temperature using liquid helium and is found that the resistivity of mercury drops to zero at 4.2 K and changes into a superconducting material

Mathiessen’s rule:

It states that “the electrical resistivity


 

Definition

The ability of certain metals and alloys exhibit almost zero electrical resistivity when they are cooled to low temperature is known as superconducting. (ie., maximum conductivity with zero resistance at zero Kelvin)

 

Each of these parameters is very dependent on the other two properties present.

 

Critical temperature ( TC ) (or) Transition Temperature

 

The temperature at which a normal conductor loses its resistivity and becomes a superconductor is known as critical temperature (or) Transition temperature. Every superconductor has its own critical temperature at which it passes over into superconducting state. Depending on the transition temperature, superconductors are classified into two groups are

 

          Low temperature superconductors (LTS):The superconductors which have low transition temperature (below 30K) are known as low temperature superconductors.

 

Example: Tin (3.2 K), Mercury (4.15 K).

 

          High temperature superconductors (HTS): The superconductors which have high transition temperature (above 30K) is known as high temperature superconductors.

 

Example: Barium - Lanthanum - Copper - Oxide (BLCO) - 35 K

Yttrium - Barium - Copper - Oxide - (Y Ba2 Cu3 O4) - 92 K

 

Fig. 3.26 Variation of electrical resistivity with temperature

 

2  PROPERTIES OF SUPERCONDUCTORS

 

At Critical temperature, the following properties are observed.

 

          The electrical resistivity drops to zero.

 

          The magnetic flux lines are excluded (ejected out) from the superconductors.

 

          There is discontinuous change in the specific heat.

 

          There are small changes in the thermal conductivity and volume of the materials.

 

2.1 Critical magnetic field (Magnetic Property)

 

A very strong magnetic field applied to superconducting material it disappears super conducting property this is called as critical magnetic field.


Fig.3.27 Critical magnetic field

 

It is noted that when the temperature of a material increases, the value of critical magnetic field decreases. Therefore the value of critical magnetic fields are different for different materials.

 

2.2 Diamagnetic property (Meissener effect)

 

If a normal conducting material is placed in a magnetic field of flux density B, the magnetic lines penetrate through the material.

 

Now the material is cooled below its transition temperature when T TC then the magnetic lines of forces are eapelled out from the material as shown in figure.

 

We know that, a diamagnetic material have the tendency to expel the magnetic lines of force. Since the superconductor also expels tha magnetic lines of force and it behaves as a perfect diamagnet. This behaviour was first observed by meissener and hence called as meissener effect.

 

Meissener effect.

When the superconducting material is subjected to a uniform magnetic field, under the condition T TC and H HC, the magnetic flux lines are excluded from the material. Thus the material exhibits perefect diamagnetism. This phenomenon is called as meissner effect.


 

2.3 SQUID (Superconducting Quantum Interference Device)

 

(We know that a small charge in magnetic field produces variation in the flux quantum.)

 

It consists of a superconducting ring which can have the magnetic field of quantum values (1,2,3,....) of flux placed in between two Josephson junctions as shown in figure.


Fig. 3.29 SQUID

 

When the magnetic field is applied perpendicular to the plane of the ring, the current is induced at the two Josephon junctions.

 

The induced current current produces the intereference pattern and if flows around the ring so that the magnetic flux in the ring can have the quantum value of magnetic field applied.

 

Applications

 

          SQUID can be used to defect the variation of very minute magnetic signals in terms of quantum flux.

 

          It is used as a storage device for magnetic flux.

 

          It is used to study earth qurkes and to remove paramagnetic impurities.

 

Application of Meissner effect

 

          It is a standard test to prove whether the material is a perfect superconductor or not.

          This effect is used for magnetic levitated train.

2.4 Effect of heavy Current

 

The superconducting property disappears when a heavy current flows, since current flow will set up a magnetic field.

 

According to Silsbee’s rule, for a superconducting wire, the induced current to destroy the superconducting property is given by,

 


2.5 Persistence of Current

 

Persistence current is one of the most important properties of a superconductor. When a current of large magnitude is induced in a superconducting ring, the current persisted in the ring even after the removal of the field at the temperature below the critical temperature below the critical temperature, such a current flows without reducing its strength is known is persistent current.


Fig. 3.30 Persistent Current

 

The superconducting coil with persistent current acts as a magnet. It does not require power supply to maintain its magnetic field.

 

2.6 Effect of pressure

 

If pressure increases, the critical temperature also increases. Therefore certain materials are brought into the superconducting state by increasing the pressure. Research is going on to get the superconducting state at room temperature by applying heavy pressure.

 

2. 7 Isotope effect

 

The presence of isotopes in superconductor change the transition temperature of the superconductor. The transition temperature is found to be inversely proportional to the square root of the atomic weight of the isotope (M).


The transition temperature of the heavier isotope is less than that of the lighter isotope.

 

2.8 General properties

 

          There is no change in elastic properties, photo electric properties and crystal structure.

 

          The transition temperature is unchanged with the frequency variation.

 

3 TYPES OF SUPER CONDUCTORS

 

Superconductors are classified as follows

 

Based on the value of HC we have,

 

          Type I (or) Soft superconductors

 

          Type II (or) Hard superconductors

 

Based on the value of TC we have,

 

          High temperature superconductors

 

          Low temperature superconductors

 

Type I Superconductor

 

In type I superconductor, the magnetic field is completely excluded from the material below the critical magnetic field and the material loses its superconducting property abruptly at.


Fig.3.31 Type I Superconductor

 

Characteristics

 

          They exhibit complete Meissner Effect.

 

          They have only one critical magnetic field value.

 

          Below the material behaves as superconductor and above the material behaves as normal conductor.

 

          These are called as Soft superconductors.

 

Type II Superconductor

 

In type II superconductor, the magnetic field is excluded from the material and the material loses its superconducting property gradually rather than abruptly.


Fig. 3.32 Type II Superconductor

 

Characteristics

 

          They do not exhibit a complete Meissner Effect.

 

          They have two critical magnetic field values. Lower critical magnetic filed [HCl] and Higher critical magnetic field [HC2].

          Below HC1 the material behaves as superconductor and above the material behaves as normal conductor. The region in between [HCl] and [HC2] is called mixed state or vortex region.

 

          These are called as Hard superconductors.

 

Low TC Superconductors

 

          The superconductors having the critical temperature less than 20 K are known as low TC Superconductors or elemental superconductors.

          The Superconductors by BCS theory.

 

          It is explained by BCS theory.

 

          It is not so useful due to its low temperature maintenance.

 

          It is called as N-type superconductor.

 

High TC Superconductors

 

          The superconductors having the critical temperature greater than 100 K are known as high TC Superconductors or ceramic or oxide superconductors.

          The Superconductors is due to hole states.

 

          It is explained by RVB theory proposed by Anderson.

 

          It is very useful for commercial and engineering purposes.

 

          It is called as P-type superconductor.

 

3.1 Difference between Type I and II superconductors.


 

3.2 Difference between High TC and Low TC superconductors


High TC Superconductors

 

1. It has high TC (>100 K).

2. Super conduction is due to hole states.

3. Explained by RVB theory.

4. Very useful for commercial and engineering purposes.

5. It is called as P-type superconductor.

 

Low TC Superconductors

1. It has low TC (<20 K)

2. Super conduction is due to cooper pairs.

3. Explained by BCS theory.

4. It is not so useful due to its low maintenance temperature.

5. It is called as N-type superconductor.

4 HIGH TEMPERATURE (HIGH-TC) SUPERCONDUCTORS

 

Superconductors with high values of critical temperature are called high temperature superconductors (HTSC). The discovery of copper oxide based ceramic materials by Bednorz and Muller in 1986 having critical temperature greater than 30 K made a new era in the field of superconductivity.

 

The superconductors have the critical temperature greater than 100 K are known as high Superconductors or ceramic or oxide superconductors.

 

The Superconductors is due to hole states and it is explained by RVB theory proposed by Anderson. It is very useful for commercial and engineering applications and it is called as P-type superconductors.

 

Characteristics

 

          High TC Superconductors have high temperatures.

 

          They have a modified perovskite crystal structure.

 

          Superconducting state is direction dependent.

 

          These are oxides of copper with other elements.

 

          These are reactive, brittle, and cannot be easily modified or joined.

 

          For high TC superconductors, liquid Nitrogen is used instead of liquid helium.

 

5  BCS THEORY OF SUPERCONDUCTIVITY

 

The properties of Type I superconductors were modeled successfully by the efforts of John Bardeen, Leon Cooper, and Robert Schrieffer in what is commonly called the BCS theory. 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 lattice. This pairing results form a slight attraction between the electrons related to lattice vibrations, the coupling to the lattice is called a phonon interaction.

 

Pairs of electrons can behave very differently from single electrons which are fermions and must obey the Pauli Exclusion Principle. The pairs of electrons act more like bosons which can condense into the same energy level.

 

The electron pairs have a slightly lower energy and leave an energy gap above them on the order of 0.001 eV which inhibits the kind of collision interactions which lead to ordinary resistivity. For temperatures such that the thermal energy is less than the band gap, the material exhibits zero resistivity.

 

Bardeen, Cooper, and Schrieffer received the Nobel Prize in 1972 for the development of the theory of superconductivity.

 

Cooper Pairs

 

The transition of a metal from the normal to the superconducting state has the nature of a condensation of the electrons into a state which leaves a band gap above them, this kind of condensation is seen with superfluid helium, but helium is made up of bosons-multiple electrons can’t collect into a single state because of the Pauli Exclusion Principle.

 

Froehlich was first to suggest that the electrons act as pairs coupled by lattice vibrations in the material. This coupling is viewed as an exchange of phonons, phonons being the quanta of lattice vibration energy. Experimental corroboration of an interaction with the lattice was provided by the isotopic effect on the superconducting transition temperature.

 

The boson-like of such electron pairs was further investigated by Cooper and they are called “Cooper pairs”. The condensation of Cooper pairs is the foundation of the BCS theory of superconductivity.

 

A model of Cooper pair attraction


Fig.3.33 Cooper pair attraction


Fig .3.34 Cooper pair repulsion


Fig. 3.35 Model of pair attraction

 

Ideas Leading to the BCS Theory

 

The BCS theory of superconductivity has successfully described the measured properties of Type I superconductors. It envisions resistance-free conduction of coupled pairs of electrons called Cooper pairs. This theory is remarkable enough that it is interesting to look at the chain of ideas which led to it.


Fig. 3.36 Cooper pair (interaction)

 

          One of the first steps toward a theory of superconductivity was the realization that there must be a band gap separating the charge carriers from the state of normal conduction.

 

          A band gap was implied by the very fact that the resistance is precisely zero. If charge carriers can move through a crystal lattice without interacting at all, it must be because their energies are quantized such that they do not have any available energy levels within reach of the energies of interaction with the lattice.

 

          A band gap is suggested by specific heats of materials like vanadium. The fact that there is an exponentially increasing specific hear as the temperature approaches the critical temperature from below implies that thermal energy is being used to bridge some kind of gap in energy. As the temperature increases, there is an exponential increase in the number of particles which would have enough energy to cross the gap.

 

          The critical temperature for superconductivity must be a measure of the band gap, since the material could lose superconductivity if thermal energy could get charge carriers across the gap.

 

          The critical temperature was found to depend up on isotopic mass. It certainly would not if the conduction was by free electrons alone. The made it evident that the superconducting transition involved some kind of interaction with the crystal lattice.


          Single electrons could be eliminated as the charge carriers in superconductivity since with a system of fermions you don’t get energy gaps. All available levels up to the Fermi energy fill up.

 

          The needed boson behavior was consistent with having coupled pairs of electrons with opposite spins. The isotope effect described above suggested that the coupling mechanism involved the crystal lattice, so this gave rise to the phonon model of coupling envisioned with Cooper pairs.

 

6 APPLICATIONS OF SUPERCONDUCTORS

 

General Applications

 

          Electric generators can be made by using superconductors with smaller size, less weight and low energy consumption.

 

          Superconductors can be used for the transmission of power over very long distances.

 

          Superconductors can be used in switching Devices.

 

          The superconductors can be used in sensitive electrical instruments.

 

          It can be used as a memory or storage element in computers.

          These are used to design Cryotron, Maglev, Josephson Devices and SQUID.

 

          DC superconducting motors are used in ship propulsion and in large mills.

 

          Superconducting magnetic field may be used to launch satellite into orbit directly from the earth without use of rockets.

 

          Ore separation can be done by using machines made of superconducting magnets.

 

10.These are used in NMR (Nuclear Magnetic Resonance) imaging equipments which is used for scanning purposes.

 

11.Superconductors are used for the detection of brain tumor, defective cells, etc.,

 

12.Superconducting solenoids are used in magneto hydrodynamic power generation to maintain the plasma in the body.

 

7  ENGINEERING  APPLICATIONS

 

7.1 Cryotron

 

It is a magnetically operated current switch. The superconducting property disappear when the magnetic field is greater than critical field ().

 

It consists of a superconducting material [A] and it is surrounded by a super conducting coil of wire [B].


Fig. 3.38 Cryotron

 

When the critical magnetic field of wire B exceeds or less than that of a Superconducting material A, the current in A can be controlled by the current in the material B, it can act as relay or switching elements and it can be used as memory or storage element in computers.

7.2 MAGLEV (MAGnetic LEVitation)

 

Maglev is a magnetic levitated train, its works under the principal of Electromagnetic induction. This train cannot move over the rail. Instead it floats above the rails, so that it moves faster with speed of 500 Km/hr without any frictional loss. It has two superconducting magnet on each side of the train and there is guiding system consisting of ‘S” shaped coils on each side. Due to actions of these magnets the train moves faster by levitation principle.

 

Working

 

This train consists of superconducting magnets placed on each side of the train. The train can run in a guiding system, which consists of serial ‘S’ shaped coil as shown in figure.


Fig. 3.39 MGLEV

 

Initially when the train starts, they slide on the rails. Now, when the train moves faster, the superconducting magnets on each side of the train will induce a current in the ‘S’ shaped coils kept in the guiding system.

 

This induced current generates a magnetic force in the coils in such a way that the lower half of ‘S’ shaped coil has the same magnetic pole as that of the superconducting magnet in the train, while the upper half has the opposite magnetic pole. Therefore, the total upward magnetic force acts on the train and the train is levitated or raised above the rails and floats in the air.

 

Now, by alternatively changing the poles of the superconducting magnet in the train, alternating currents can be induced in ‘S’ shaped coils.

Thus, alternating series of north and south magnetic poles are produced in the coils, which pulls and pushes the superconducting magnets in the train and hence the train is further moved. This can travel a speed of 500 km per hour.

 

7.3 Josephson Devices

 

Presistence of current in an insulator which is separated by an insulator, even in the absence of an applied voltage pairs of electrons moving through the potential barrier induce the superconducting current. This effect is known as Josephson effect.


Fig. 3.40 Josephson effect

 

A thin layer of insulating material (10-50A°) is placed in between two superconducting materials as shown in figure. When the voltage is applied across the superconductors, current start flowing between the superconductors.

 

The flowing current has both a.c and d.c components. The a.c current exists only up to which the external voltage is applied whereas the d.c current exist even after the removal of applied voltage. This effect is called Josephson effect.


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