Superconductors

Mathiessen’ s rule : It states that “ the electrical resistivity [ ρ ] of the material is the sum of the residual resistivity due to scattering by impurities [ ρo ] and the ideal resistivity due to scattering by phonons [ ρT ] ie., ρ = ρo + ρT

The ability of certain metals and alloys exhibit almost zero electrical resistivity, when they are cooled to low temperature.

Critical temperature (Tc )

Critical magnetic field (Hc )

Critical current density (Jc)

Normal conductor ρ (Ag ) superconductor

(Tin)

0 TC T

the temperature at which the resistivity falls to zero is called transition temperature or Critical temperature

The temperature at which the normal conductor becomes a superconductor is known as critical temperature

The electrical resistivity drops to zero at Tc.

The magnetic flux lines are excluded (ejected out)

from the superconductor.

There is a discontinuous change in the specific

heat.

There are small changes in the thermal

conductivity and volume of the material.

an electron pair called cooper pair is formed at low temperature by overcoming the repulsive forceThe cooper pair moves without scattering (without any resistance) in the lattice structure. Now the material becomes a super conductorsuitable only for low temperature superconductors

Cooper pair- -2 1

The electrical resistivity drops to zero at Tc.The magnetic flux lines are excluded (ejected out) from the superconductor.There is a discontinuous change in the specific heat.There are small changes in the thermal conductivity and volume of the material

Based on the value of Hc

(1) Type I (or) Soft superconductors

(2) Type II (or) Hard superconductors

Based on the value of Tc

(1) High temperature superconductors

(2) Low temperature superconductors

Sl.

No.

TYPE I (OR) SOFT SUPERCONDUCTORS TYPE II (OR) HARD SUPERCONDUCTORS

1. It exhibits a complete Meissner Effect It does not exhibit a complete Meissner effect.2. They are completely diamagnetic They are not complete diamagnetic3. Eg: Tin, Lead, Mercury, etc., Eg: Nb - Zr, Nb -Ti, - Ga, etc.,

4. Hb

SCS NCS

Hc Ha

Ha → Applied magnetic fieldHb → Induced magnetic field

Hb

NCS

SCS mixed state

Hc1 Hc Hc2

5. The value of Hc is always too low.

It is about 0.1 teslaThe values of Hc is high and it is about 30 tesla

6. They have only one critical magnetic field value They have two critical magnetic field values . Lower critical magnetic filed [ Hc1 ] and Higher critical magnetic field [ Hc2 ] .

7. No mixed state exists Mixed state is present 8. These are called soft superconductors These are called hard Superconductors9. It requires low magnetic filed to destroy the

superconductivityIt requires large magnetic filed to destroy the superconductivity

10 .

It loses its magnetization suddenly It loses its magnetization gradually

High Tc superconductors Low Tc superconductors

1) It has high Tc ( >100K). 1) It has low Tc (< 20K).

2) Superconduction is due to hole

states.

2) Super conduction is due to

cooper

pairs.

3) Explained by RVB theory. 3) Explained by BCS theory.

4) Very useful for commercial and

Engineering applications.

4) It is not so useful due to its low

temperature maintenance.

5) It is called as P – type

superconductors

5) It is called as n – type

superconductors

Bednorz and Muller in 1986 having critical temperature greater than 30Kcritical temperature greater than 100 K are known as high TC Superconductors or ceramic or oxide superconductors The Super conduction is due to hole states and it is explained by RVB theory proposed by AndersonIt is very useful for commercial and Engineering applications and it is called as P – type superconductors .

High Tc Superconductors have high transition temperatures.They have a modified perovskite crystal structure.In which 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

HIGH TC SUPERCONDUCTORS Tc

1. (La Ba)2 CuO4 (214 system) 40K

2. (La Sr)2 CuO4 40K

3. Pb2 Y Sr2 Cu3O 8 77K

4. (PbCu) (SrBa)2 (CaY)Cu2O7 80K

5. YBa2Cu3O7 (123 system ) 90K

6. Bi2 Sr2 Can-1 Cun O2n+4 10K to 110K

7. Tl2 Ba2 Ca2 Cu3O10 125K

8. Hg Ba2 Ca2 Cu3O8 150K

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

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

3. Superconducting transformers are available.4. Superconductors can be used in switching

Devices.5. The superconductors can be used in sensitive

electrical instruments.6. It can be used as a mercury or storage element

in computers.7. These are used to design Cryotron , Maglev ,

Josephson Devices and SQUID

8. D.C. Superconducting motors used in ship propulsion and in large mills.

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

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

11.These are used in NMR (Nuclear magnetic Resonance) imaging equipments for scanning.

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

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

A

B

When the critical magnetic field of wire B exceed or less than that of 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

When the magnetic field is applied perpendicular to the plane of the ring, current is induced at the two Josephson junctions and produces interference pattern

The induced current flows around the ring, so that the magnetic flux in the ring can have quantum values of flux, which corresponds to the value of magnetic field applied.

SQUIDs are used to detect the variation in very minute magnetic signals

SQUIDs are also used in the study of earth quakes, removing paramagnetic impurities, detection of magnetic signals from the brain, heart, etc.,

V

DC - Josephson effect

When two superconducting materials are separated by a thin layer of insulating material,There is a DC current flows through the circuit in the absence of electric field or magnetic field.The gap is in the order of 50 Ao – 100 Ao.

Tin Zn

AC - Josephson effectmicrowaves

When two superconducting materials are separated by a thin layer of insulating material, there is a microwave generated when it is connected with DC external voltage.Josephson devices are used to produce microwaves.

Guiding system

TRAIN

When a magnet is placed over a superconductor, the magnet floats, this phenomenon is known as magnetic levitation. This is based on diamagnetic property of a superconductor. A diamagnetic material rejects the magnetic flux lines. Maglev is a magnetic levitated train.Electromagnetic induction principle is used here.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 the train, and there is guiding system consisting of ‘ 8 ’ shaped coils on each side. Due to actions of these magnets the train moves faster by levitation principle .

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 ‘ 8’ 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 ‘ 8’ shaped coli 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 wheels and floats in the air.

Now , by alternatively changing the poles of the superconducting magnet in the train alternating currents can be induced in ‘8’ 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

Hence the train is further moved. This can travel a speed of 500 km per hour