CHAPTER-I

SUPERCONDUCTIVITY

STRUCTURE:

5.1.1) INTRODUCTION

OBJECTIVES

5.1.2) SUPER CONDUCTING TRANSITION TEMPERATURE

5.1.3) GENERAL FEATURES OF SUPERCONDUCTORS

5.1.4) GENERAL FEATURES OF SUPERCONDUCTORS

A) PERSISTENT CURRENT

B) ISOTOPIC EFFECT

C) EFFECT OF MAGNETIC FIELD

D) CRITICAL CURRENTS

E) A-C RESTIVITY

F) ENTROPY

G) THERMAL CONDUCTIVITY

H) MECHANICAL EFFECTS

1.5.5) MEISSNER EFFECT

1.5.6) TYPE OF SUPERCONDUCTORS

A) TYPE-I SUPERCONDUCTORS

B) TYPE-II SUPERCONDUCTORS

1.5.7) APPLICATION OF SUPERCONDUCTOR

SUPERCONDUCTING MAGNETS

1.5.9) SUMMARY

5.1.1) INTRODUCTION:From electron theory of metals we know that by decreasing the temperature of a perfect metal, the thermal vibrations and electron scattering of ions decreases and the electrical resistance of the substances decreases and the electrical resistance of substance may becomes zero as its temperature reaches 'O'. Based on this point experiments were conducted on many substances by scientists. This phenomena first found by kammerling Onnes in 1911.i.e, electrical resistance of pure mercury vanishes suddenly at 4.2k as shown in fig (1).This temperature is called its superconducting transition temperature, the material posses normal resistance and is said to be in the normal state .Below this temperature the resistance of the material becomes zero and its conductivity reaches infinity .This state of the material is called the superconducting state.

OBJECTIVES:

After going through this chapter you would be able to: know About the electrical resistance.

How electrical resistance can be made zero.

Why conductors are having +ve temp coefficient of resistance.

Why semi conductors has –ve temp coefficient of resistance.

Why good conductors like copper acts as bad super conductors at low Temperature.

Why insulators like ceramic materials acts as good super conductors

At low temperature.

What is the significance of paradox in super conductivity?

What is the present status of this fascinating field of super conductivity?

ELECTRICAL RESISTANCE:

We know that matter exists in three different states i.e., solids,liquids and gases.In solids again we have conductors semi conductors and insulators.In conductors ,we know that valance band and conduction band overlaps to each other as a result electrons can move freely from valance band to conduction band.Electron s existing in conduction band are called conduction electrons or free electrons .such conduction electrons are responsible to carry current when subjected for a potential difference .When free electrons moving in presence of a potential difference applied for a conductors . They frequent collisions with lattice thermal vibrations. Such lattice thermal vibrations exists in materials also called with a fancy name phonons. Therefore

electron lattice thermal vibrations interactions can also called as electron phonon interaction. Such electron- phonon interactions are responsible for the opposing force faced by free electrons we know that an opposing force faced by electrons is called electrical resistance.

What are lattice thermal vibrations .How they existing in conductors?

For conductors as a we increase the temperature amplitudes of phonons will increase and hence electron- phonon interaction will increase. Such increase in electron-phonon interaction increases resistance in conductors. For this reason conductors are said to having positive temperature coefficient of resistance. The behavior of semiconductors is completely opposite to that of conductors .i.e. semiconductors are having negative temperature coefficient of resistance. The resistance of semiconductors will decrease with increase in temperature.

For conductors as we increase the temperature amplitudes of phonons will increase and hence electron-phonon interaction will increase. Such increase in electron-phonon interaction increases resistance in conductors. For this reason conductors are said to having positive temperature coefficient of resistance.

The behavior of semiconductors is completely opposite to that of conductors.

i.e. semiconductors are having negative temperature of coefficient ,the resistance of semiconductors will decrease with increase in temperature.

For conductors as we increase in temperature the resistance will increase, the converse effect is also observed. i.e for conductors the resistance will decrease with decrease in temperature. This phenomenon was practically verified by a Dutch physicist Kammerlingis Onnes when he is working in his laborite ties . he found that resistance of mercury decreasing with temperature and falls to zero at 4.2k with in a temperature range of 0.05c.Below 4.2k resistance is zero and above 4.2k material will regain resistance again.

According to ohm’s law V=iR

If R=0 i

Such material in which R=0

According to ohms law current tends to ‘ ’ Theoretically

And practically said to be very high.In such situations the current flowing through conductors are said to be super and the conductors are called super conductors.

5.1.2) SUPER CONDUCTING TRANSITION TEMPERATURE:

It is defined as the temperature at which the material changes from normal state to superconducting state it is cooled .The total disappearance of electrical resistance of the few substances is called superconductivity and the materials which exhibits this property are called superconductors. The electrical resistivity of materials due to temperature impurities and crystal defects.

Fig:

5.1.3) GENERAL FEATURES OF SUPERCONDUCTORS:

The theory of superconductors has been developed by Bardeen Cooper and Schrieffer (BCS) theory in1957.They showed that superconductivity occurs when a special state of affairs exists between the conduction electrons. Two electrons in free space will be mutually repelled by coulomb forces between but in the solid state, the force between the two electrons will be modified by the interaction of electrons with the crystal lattice ions. In certain crystals lattice interaction is so great that simple repulsive forces becomes modified into an attractive force finding certain electrons called cooper-pair. This type of interaction can only at low temperatures.

5.1.4) SOME GENERAL FEATURES OF SUPERCONDUCTORS:

A) PERSISTENT CURRENT:

The electrical current in a superconductor in superconducting state remains for very long time .This can be proved by placing a superconducting loop of a material in magnetic field and lowering its temperature below its superconducting transition temperature (Tc) and the magnetic field is removed .This causes D.C in the

superconductor loop and the current remains for a very long period without attenuation.

File and mills determine in time taken by a super current to reduce to 1/e of its initial value is more than 1,00,000 years .This indicates that D.C current in a super conducting is persistent (Persistent means continuing for a long period of time without interruption ) . Normally superconductivity has been observed in metals having valance electrons between 2to 8 and not 1. Transition metals having odd number of valance electrons are favorable to ex bit superconductivity while metals having even number of valance electrons are in favorable. Generally in electrical conductors are not good super conductors examples: copper, gold, sodium cry staling iron At the same time the good super conducting metals are known good conductors at room temperature example: Zinc, led.

B) ISOTOPIC EFFECT:

Transition temperature of a superconducting substance varies with isotopic mass for example the transition temperature of three isotopes of mercury in shown below.Isotopic mass Transition temperature (Tc in kelvin)199 4.161200 4.153204 4.126 Maxwell found that transition temperatures are inversely proportion to square root of atomic weights.i.e, Tc α M- β or Tc *M β is equal to constant . β ≈+0.5

C) EFFECT OF MAGNETIC FIELD:

By applying sufficient strength of magnetic field to the superconductors, the superconductivity of material can be destroy the minimum magnetic field strength required to destroy superconductivity of substance below Tc is called critical magnetic field Hc at that temperature. Hc varies with temperature it is shown in fig. From the graph we concluded that critical magnetic field for different elements will be different at different temperatures and Hc increases with decrease of temperature below Tc.

At transition temperature no magnetic field is required to change the material from superconducting state to normal state .Maximum magnetic field is required to destroy superconductivity at zero kelvin the critical magnetic field at zero kelvin is Ho. The critical magnetic field at any temperature t below Tc can be given as

Hc=Ho (1-(TTc)2)

D) CRITICAL CURRENTS:

Suppose a material carries electrical current in superconducting state, this current produces magnetic field if this magnetic field greater than critical magnetic field at that temperature T is less Than Tc then normal resistance will be included in the material and it will be in the normal state hence it is not possible to pass large current through a superconductor.The maximum current passing through the superconductor is called critical current and it is denoted with Ic according to silsbee's rule for superconducting wire,Ic=2πrHc.

E) A-C RESISTIVITY:

In normal state the current carry by normal electrons .When the materials changes normal state to super conducting state then few normal electrons are converted into cooper-pairs which carry DC currents in superconducting state without resistance but in AC fields the cooper pairs accelerated in forward and backward direction and they log behind the field due to inertia.In A.C field the normal electrons are also carried the A.C current and produce some resistance then superconductor behaves as a normal material.

F) ENTROPY:

Entropy is the measure of disorder in material by reducing a temperature of a material, it goes into superconducting state .Also thermal vibrations and entropy of the material reduce the electrons are more ordered in superconducting state than the normal state.

G) THERMAL CONDUCTIVITY:

It has been observed that the thermal conductivity in superconducting state less than in normal state by applying a sufficient magnetic field to a material then material changes from superconducting state to normal state below Tc. In normal state all free electrons participate in thermal conductivity, hence the thermal conductivity is large; where as in super conducting state the cooper-pair electrons will not participate in thermal c onductivity so thermal conductivity is less. The thermal conductivity suddenly drops then the material changes from normal state to super conducting state.

Fig

H) MECHANICAL EFFECTS:

Experimentally it is found that the super conducting transition temperature and magnetic field changes slightly by applying mechanical stress on it small changes in volume ,co-efficient of thermal expansion and sum other factors are changes when the material changes from normal state to super conducting state.

5.1.4) MEISSNER EFFECT:

In 1993, Meissner and Ochsen Feld the repel of magnetic flux by a superconductor below Tc. They reduced by the temperature of a long superconductor in a magnetic field .They observed that the superconductor pushes the magnetic force of lines out of the body some temperature below Tc is shown in figure.

A Superconductor in its superconducting state behaves like a perfect diamagnet:

Consider a specimen in the form of a sphere inserted in a magnetic field. If the temperature of the specimen is more that its transition temperature and magnetic field also more than its critical value then all the magnetic lines of forces will pass through the specimen as shown in fig (a). When both magnetic field and temperatures are reduced below the critical values of the specimen them we can see the magnetic lines of forces pushed out by the specimen as shown in fig (b).

When the material is in normal state the magnetic lines of force of lines pass through it. The magnetic induction (B) inside the material is given as

B=µ (H+M) =µ0 H (1+ Х)Where µ0 is magnetic permeability of the material.H is the intensity of applied magnetic field.M is the magnetization of the material. Х is Magnetic susceptibility. Х=MH=-1 When the temperature reaches below transition temperature (T<Tc) and it repels the magnetic force of lines .So magnetic induction inside the material B=0

From the eq B=µ0(H+M)0=µ0(H+M)

H+M=0H=-M

Х=M/H=-1 So in superconducting state inside the material magnetize on takes place which is equal in magnitude and opposite in direction to the applied field .the superconductor is a perfect diamagnetic material (since =-1.0).The repulsion magnetic force of lines from a super conductor when it is cooled below Tc in the presence of magnetic field is called Meissner effect .

5.1.6) TYPE I AND TYPE II SUPERCONDUCTORS:

Based on critical magnetic field they are two types of superconductors 1) TYPE-I(Soft) superconductors :

2) TYPE-II(Hard ) superconductors :

A) TYPE-I(SOFT) SUPERCONDUCTORS :

When the magnetic field applied two normal metal and increase the magnetic field the material magnetization takes place in opposite direction The magnetization material opposes the external applied magnetic force of lines and material converted into superconducting state and it can act as perfect diamagnetism at below Hc. In this case applied magnetic field reaches critical magnetic field Hc and above fields the force of lines passing through the material and suddenly the material changes from super conducting state to normal state it is shown in figure.

This effect was first observed by Silsbee in 1916.So this effect is also called Silsbee effect.The critical magnetic field for type 1 super conductors is the order of 0.1 Tesla.So high magnetic fields cannot produce type 1 super conductors .These are called soft super conductors .Example aluminum, zinc, cladium.

B) TYPE II SUPERCONDUCTORS:

In the case of type to superconductors as we increase the applied field intensity, in the material opposing magnetization takes place up to some applied field Hc, called lower critical magnetic field. Up to this magnetic field the material completely repels the magnetic force of lines.The material is completely diamagnetic material and it is in superconducting state .If further increase of applied magnetic field slowly the magnetic force of lines pass through the material and transition superconducting state to normal state takes place gradually.The penetration of magnetic force of lines through the material increases gradually from Hc1 to Hc2 .At Hc2 the magnetic forces of lines completely penetrate through the material and material completely change into normal state. The material in mixed state in between Hc1 and Hc2 .It is shown in figure.

Type-2 superconductivity discovered by schubnicov co workers in 1930.The critical field Hc2 for type 2 superconductors’ order of 10 Tesla .Hc2 is called upper critical

field .Type II superconductors also called hard superconductors. Type 2 super conductors are alloys or transition metals with high values of electrical resistivity.

Example Zr, Nb, 60%Nb and 40%Ti alloy.

5.1.7) APPLICATION OF SUPERCONDUCTIVITY:

1) SUPERCONDUCTING MAGNETS: Super conducting magnets similar to electromagnets to obtained magnetic field from electromagnets current should be maintain in the coil ,where as in the superconducting coils ones current introduced in to coil will remain for very long time and during this period magnetic field can be obtained ,provided the temperature of the coil is maintain below its transition temperature the benefit of using superconducting magnets instead of electromagnets is the cost of the power require to maintain superconductors at low temperature will be thousand times less than the cost of power required in case of electromagnets to produce same magnetic field. The size of the superconductor is very small than the electromagnets. Super conducting magnets are made of type II superconductors because type II superconductors strong and produce high magnetic fields order of 10 to 20 Tesla.Example: Niobium titanium (Nb Ti) it is used mostly because it can be easily drawn into thin wires2) It is a basis of new generation of energy-saving power systems .Super conducting generators are smaller in size and weight and compare with conventional generators.These generators consume very low energy and so we can save more energy.3) The current in a superconducting ring will flow without any change its value, It can be used as a memory are storage element in computers.4) One can be left extremely fast and large scale computer with in a small volume using superconducting elements. The power consumed by this computer is less than half watt. 5) Superconducting cables can be used to transmit electric power over long distances without resistive losses.

6) Because superconductors are diamagnetic, they can be used to shield out unwanted magnetic flux, as in shaping the magnetic lens system of an electron microscope .7) When we apply a magnetic field whose value is greater than critical field of the superconductors, the superconducting properties will disappear. This fact is used in gating circuits or cryotrons.8) Superconducting solenoids are used in magneto hydro dynamic power generation to maintain plasma and in nuclear magnetic resonance imaging equipment which is a whole body scan equipment.9) Superconductors are used to amplifying very small direct current and voltages.10) SQUID (Superconducting Quantum Interference Devices) :- Used for measuring very small amounts of magnetic flux. It is also used to detect the presence of bacteria, for searching of explosives and examining the materials for defects etc.

Fig: Sensing element of the SQUID

5.1.7) SUMMARY:

Certain metals and alloys exhibit almost zero resistivity when they are cooled to sufficiently low temperatures. This phenomenon is called superconductivity.

The temperature at which the transition from normal state to superconducting state takes place on cooling in the absence of magnetic field is called critical temperature or transition temperature.

Superconductivity disappears if a strong enough magnetic field is applied .in the absence of any magnetic field, the material is in superconducting state. When the strength of magnetic field applied reaches a critical value the superconductivity disappears.

When a weak magnetic field is applied to a superconducting specimen at a temperature below transition temperature the magnetic lines are expelled and the specimen acts as an ideal dia magnet. This effect is called meissner effect.

There are two types of super conductors. Type-I and Type-II

In Type-I super conductors the super conducting state is destroyed at a critical magnetic field and above.

In type-II super conductors there are two critical magnetic fields. Below lower critical field the specimen is in superconducting state, above upper critical field the specimen is in normal state and in between these two critical fields it is in mixed state

The super conductors are used in electrical generators, magnetic levitation, generation of high magnetic fields. Fast electrical switching and in SQUIDS