Super Conducting Materials

SUPER CONDUCTING MATERIALS

1 Introduction

2 Super conducting phenomena

2.1 General Features

3 Properties of Superconductor

4 Types of superconductors

4.1 Type-I superconductor

4.2 Type-II superconductor

5 Difference between Type I & Type-II superconductors

6 BCS theory of superconductivity

7 High Tc Superconductivity

7.1 Properties of high Tc superconductors

7.2 Preparation and crystal structure of high Tc ceramic superconductor  (YBa2 Cu3 O9.X)

8 Application of superconducting materials engineering applications

8.1 Electric Generator

8.2 Low Loss transmission & Transformer

8.3 Cryotron

8.4 Josephson Devices

8.5 SQUID

8.6 Magnetic Levitated Train

8.7 Engineering Applications

8.8 Medical Applications

1. INTRODUCTION

Super conductivity is one of the most existing phenomena in physics. It was discovered by Dutch physicist H.K Onnes in the year 1905.

Before the discovery of super conductivity, it was though that the electrical resistance is zero only at absolute zero. But, it was found that in some material the electrical resistance becomes zero, when they are cooled to very low temperature.

2 SUPERCONDUCTING PHENOMENA

Super conducting materials have extraordinary electrical and magnetic characteristics. These materials have many important applications in the field of engineering and technology. Many electronic and magnetic devices have been fabricated with super conducting materials.

Definition

The phenomenon of sudden disappearance of electrical resistance in a material, when it is cooled blow a certain temperature is known as super conductivity.

Transition temperature or critical temperature:

The temperature at which a material at normal conducting state changes into superconducting state is known as transition temperature or critical temperature (Tc).

The transition temperature depends on the property of the material. It is found that the super conducting transition is reversible, i.e, above critical temperature (Tc) a super conductor becomes a normal conductor.

It is to note that the metals which are normally very good conductors of heat and electricity (e.g. Cu. Ag, Au) are not super conductors.

2.1GENERAL FEATURES

1.     Superconductivity is found to occur in metallic elements in which the number of valence electron lies between 2 and 4.

2.     Materials having high normal resistivities exhibit superconductivity.

3.     Superconductivity is also favoured by small atomic volume accompanied by a small atomic mass.

4.     The transition temperature(T_c) is different for different substances.

5.     Ferromagnetic and antiferromagnetic materials are not superconductors.

6.     The electrical resistivity drops to zero.

7.     The magnetic flux lines are expelled from the material.

8.     There is a discontinuous change in the specific heat.

9.     Further, there is some small changes in the thermal conductivity and the volume of the materials.

3 PROPERTIES OF SUPER CONDUCTORS

Zero electrical resistance

The first characteristic property of a super conductor is its electrical resistance. The electrical resistance of the super conductor is zero below a transition temperature. This property of zero electrical resistance is known as defining property of a superconductor.

The variation of electrical resistivity of a normal conducting metal and a superconducting metal as a function of temperature is shown in fig

Effect of magnetic field

Below the transition temperature of a material, its superconductivity can be destroyed by the application of a strong magnetic field.

The minimum magnetic field strength required to destroy the superconducting property at any temperature is known as critical magnetic field (Hc).

The critical magnetic field (Hc) depends upon the temperature of the superconducting material. The relation between critical magnetic field and temperature is given by

Hc = Ho [1- (T / Tc)²]

Where, Ho- is critical magnetic field at absolute zero temperature.

Tc- is superconducting transition temperature of a material

T –is the temperature below Tc of the superconducting material.

Effect electric current

The application of very high electrical current to superconducting material destroys its superconducting property.

The critical current i_c required to destroy the superconducting property is given by I_c = 2πrHc

Where Hc –is the critical magnetic field

r - is the radius of the superconducting wire

Persistent current

A steady current which flows through a superconducting ring without any decrease in its strength as long as the material is in superconducting state is called persistent current. The current persists even after the removal of the magnetic field.

Meissner effect

When a superconducting material is p the magnetic lines of force penetrates through the material as shown in fig.

Now, when the material is cooled below its transition temperature then the magnetic lines of force are ejected out from the material as shown in fig.

We know that diamagnetic material have the tendency to expel the magnetic lines of force. Since the super conductor also expels the magnetic lines of forces it behaves as a perfect diamagnet. This behaviour is first observed by Meissner and hence called as Meissner effect.

When a superconducting material is placed in a magnetic field, under the condition T≤Tc and H≤Hc the flux lines are excluded diamagnetism. This phenomenon is called as Meissner effect.

Since the susceptibility is negative, this shows that superconductor is perfect diamagnet.

Isotope effect

The transition temperature varies due to presence of isotopes.

Example:

The atomic mass of mercury varies from 199.5 to 203.4, and hence the transition temperature varies from 4.185 K to 4.146 K.

Due   to   the   relationship   Tc α [1 / Mα]

M –atomic weight

α- constant (=.5)

4. TYPE-I AND TYPE-II SUPERCONDUCTORS

There are two types of super conductors based on their variation in magnetization, due to external magnetic field applied.

Type I superconductor or soft super conductor

Type II superconductor or hard superconductor

4.1. TYPE I SUPERCONDUCTOR

When the super conductor is  kept in the magnetic field and  if the field is  increased  the superconductor becomes normal conductor abruptly at critical magnetic field as shown in fig. These types of materials are termed as Type I superconductors.

Below critical field, the specimen excludes all the magnetic lines of force and exhibit perfect Meissner effect. Hence, Type I superconductors are perfect diamagnet, represented by negative sign in magnetization.

4.2.TYPE II SUPERCONDUCTORS

When the super conductor kept in the magnetic field and if the field is increased, below the lower critical field Hc1, the material exhibit perfect diamagnetism (i.e) it behaves as a super conductor and above Hc1, the magnetization decreases and hence the magnetic flux starts penetrating through the material. The specimen is said to be in a mixed state between Hc₁ and Hc₂. above Hc2 (upper critical field) it becomes normal conductor as shown in fig.

The materials which lose its superconducting property gradually due to increase on the magnetic field are called Type II superconductor.

5 DIFFERENCE BETWEEN TYPE –I AND TYPE –II SUPERCONDUCTORS

S.No  Type –I Superconductors

1.       The   material   loses   magnetization suddenly.

2.       They exhibit complete Meissner effect i.e., they are completely diamagnetic.

3.       There is only one critical magnetic field (HC).    

4.       No mixed state exists.

Type –II Superconductors

The material loses magnetization gradually.

They do not exhibit complete Meissner effect.

There  are  two  critical  magnetic  fields  i.e., lower critical field (HC1) and upper critical field (HC2).

Mixed state is present.

6 BCS THEORY

BCS theory (qualitative):

The microscopic theory of superconductivity developed by J. Bardeen, L.N. Cooper and J.R. Scriffer in 1957, successfully explained the effect like zero resistivity, Meissner effect etc. this theory is known as BCS theory.

Principle

This theory states that the electrons experience a special kind of attractive interaction, overcoming the coulomb forces of repulsion between them; as a result cooper pairs (i.e) electro pair are formed. At low temperature, these pairs move without any restriction through the lattice points and the material becomes superconductor. Here the electron-lattice-electrons interaction should be stronger than electrons-electros interaction.

Important features of BCS theory:

Electrons form pairs (called cooper pair) which propagate throughout the lattice.

The propagation of cooper pairs is without resistance because the electrons move in resonance with phonons.

Electron-lattice-electron interaction

When an electron (1st) moves through the lattice, it will be attracted by the core (+ve charge) of the lattice. Due to this attraction, ion core is disturbed and it is called as lattice distortion. The lattice vibrations are quantized in terms of phonons.

The deformation produces a region of increased positive charge. Thus if another electron (2nd) moves through this region as shown in fig. it will be attracted by the greater concentration of positive charge and hence the energy of the 2^nd electron is lowered.

Hence two electrons interact through the lattice or the phonons field resulting in lowering the energy of electrons. This lowering of energy implies that the force between the two electrons is attractive. This type of interaction is called electrons-lattice electron interaction. The interaction is strong only when the two electrons have equal and opposite momenta and spins.

Explanation

Consider the 1^st electron with wave vector k distorts the lattice, here by emitting phonons of wave vector q. This results in the wave vector k-q for the 1^st electron. now if the 2^nd electron with wave

vector k’, seeks the lattice it takes up the shown in fig. two electrons with wave vectors k-q and k’+qknownformascooperpair.pair

Cooper pair

The pair of electrons formed due to electron-lattice (phonons)-electron interaction (force of attraction) by overcoming the electron-electron interaction (force of repulsion), with equal and opposite momentum and spins (i.e) with wave vector k-q and k’+q, are called coo

Coherence length

In the electron-lattice-electron interaction, the electrons will not be fixed, they move in opposite directions and their co-relations may persist over lengths of maximum 10-⁶m. This length is called coherence length.

Note: BCS theory hold good only for low temperature superconductivity.

7. HIGH TEMPERATURE SUPERCONDUCTOR

In a superconductor if the transition temperature is high ie., greater than 20K, then it is called as high temperature superconductor.

Earlier it was believed that the superconductivity was only in metals. Surprisingly in 1986, Muller and Bednorz discovered high temperature superconductor in ceramics.

They made a particular type of ceramic material from a compound of barium, lanthanum, copper and oxygen (Ba-La-Cu-O). This compound superconductor showed superconductivity even at a temperature as high as 30K.

The oxide Y Ba₂ Cu₃ O₇ with a Tc of 90K was the most extensively studied high temperature superconductor.

7.1. CHARACTERISTICS OF HIGH TEMPERATURE SUPERCONDUCTOR

They have high transition temperature.

They have a modified perovskite crystal structure.

Formation of the superconducting state is direction dependent.

They are oxides of copper in combination with other elements.

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

7.2. PREPARATION OF HIGH TC CERAMIC SUPERCONDUCTOR Y BA₂ CU₃ O_9-X

The oxide (Y Ba₂ Cu₃ O_9-x) is prepared from compacted powder mixture of Y₂O₃, BaCO₃ and CuO in the right proportion and heating them in temperature between 900°C and 1100°C. BaCO₃ decomposes at this temperature to BaO and CO₂. This is followed by another annealing treatment at 800°C in an atmosphere of oxygen.

Crystal structure of Y Ba₂ Cu₃ O_9-x

Here, the primitive cell is developed by three body centered cubic unit cells stacked one above the the other to form a tetragonal (a=b≠c) perovskite structure tripled along the C axis.

Yttrium atoms:

Each yttrium atom is shared by one unit cell.

1 / 1^th of the atom is shared by that unit cell.

Number of yttrium atoms per unit cell = 1 / 1 X total number of yttrium atoms

= 1 / 1 X 1 = 1

Barium atoms

Each barium atom is one unit cell

1 / 1^th of the atom is shared by that unit cell.

Number barium atoms per unit cell = 1 / 1 X total number of yttrium atoms

= 1 / 1 X 2 = 2 atoms per unit cell.

Copper atoms

Each yttrium atom is shared by 8 unit cells [since copper is the corner atoms].

1 / 8 ^th of the atom is shared by one unit cell.

Number copper atoms per unit cell = 1 / 8 X total number of yttrium atoms

X number of unit cells

= 1 / 8 X 8 X 3 =3 atoms per unit cell.

Oxygen atoms

Each yttrium atom is shared by 4unit cells [since oxygen atoms are situated at mid points between two corner atoms].

1 / 4^th of the atom is shared by one unit cell.

Number copper atoms per unit cell = 1 / 4 X total number of yttrium atoms

X number of unit cells

= 1 / 4 X 12 X 3 =9 atoms per unit cell.

8 APPLICATION OF SUPERCONDUCTORS:

8.1.ELECTRIC GENERATORS

Superconducting generators are very small in size and light weight when compared with conventional generators. The low loss superconducting coil is rotated in extremely strong magnetic field. Motors with very high powers as large as 2500 kw could be constructed at very low as 450 V. This is the basis of new generation of energy saving power systems.

8.2 LOW LOSS TRANSMISSION LINE AND TRANSFORMERS

Since, the resistance is almost zero at superconducting phase, the power loss during transmission is negligible. Hence, electric cables are designed with superconducting wires. If superconductors are used for winding the transformers, the power loss will be very small. Using superconductor, 2000-3000 MW portable transformers have been manufactured.

8.3. CRYOTRON

Cryotron is a magnetically operated current switch.

Principle

We know that the superconducting property of a material disappears when the applied magnetic field is greater than the critical magnetic field.

Consider a superconducting material A surrounded by another superconducting material B as shown in fig. let the critical magnetic field of material A be less than the critical magnetic field of material B. Initially, let the temperature of the whole system blow the transition temperature of two materials.

Now at the operating temperature, the magnetic field produced by material B may exceed the critical

magnetic field of material A. Hence, material A becomes a normal conductor because the critical magnetic field of A is less than that of B.

Moreover, B not become a normal conductor at the critical magnetic field of A because Hc_B > Hc_A. Therefore the current in the material A can be controlled by the current in the material B. hence this system can act as a relay or switching element.

8.4. JOSEPHSON DEVICES Principle

A steady and undiminishing current (Persistent of current) influenced by d.c. voltage is the principle used in Josephson devices.

Josephson Effect

Josephson effect happens by virtue of quantum tunnelling of Cooper pairs. According to Josephson effect, the tunnelling cooper pairs would take place between two superconductors separated by an insulator even in the absence of applied voltage. Pairs of electrons move through the potential barrier induce the superconducting current. This effect is know as Josephson effect.

Explanation

It consists of a thin layer of oxide material placed in between tow supeconducting materials as shown in. Here, the Oxide layer acts as a barrier to the flow of conduction electrons from one superconductor to the other.

When the battery is switched ON, the voltage V is applied across the super conductors. Due to applied voltage, the electrons in the super conductor –1 is tunnel across the insulator into the super conductor –2. This tunneling effect produce the current between the superconductors. The increase in voltage produce more and more electrons and hence increases the current. This current has two components.

8.5. SQUID:

QUID  stands  for  Superconducting  Quantum  Interference  Device.  It  is  an  ultra-sensitive instrument used to measure very weak magnetic field in the order of 10-14 tesla.

Principle

We know that small change in magnetic field produces in the flux quantum

Description and working

A SQUID consist of superconducting wire which can have the magnetic field of quantum values (1, 2, 3…) of flux placed in between two Josephson junctions as shown in fig.

Then magnetic field if applied perpendicular to the plane of the ring, the current is produced at the two Josephson junctions. The induced  current produces the  interference  pattern and  it  flows through the ring so that the magnetic flux in the ring can have the quantum value of magnetic field applied.

Application

It can be used to detect the variation of very minute magnetic signals in terms of quantum flux. It can also be used as storage device for magnetic flux.

It is useful in the study of earthquakes, removing paramagnetic impurities, detection of magnetic signals from the brain, heart.

8.6. Magnetic levitated train (MAG LEV)

Magnetic levitated train is the train which cannot move over the rail, rather it floats above the rail, under the condition, when it moves faster.

Principle

Electromagnetic induction is used as the principle. (i.e) when there is a relative motion of a conductor across the magnetic field, current is induced in the conductor and vice versa.

Direction of magnetic force

Explanation

This train consists of superconducting magnets placed on each side of the train. The train can run in a guidance system which consists of a series of 8 shaped coils as shown in fig.

Initially when the train starts, they slide on the rails. Now, when the train moves faster, the superconducting magnets on each side of th kept in the guidance system.

This induced current generates a magnetic force in the coils in such a way that the lower half of the 8-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 hence the train is levitated (or) raised above the wheels (i.e) the train now floats above the air.

Now, by alternatively changing the poles of the superconducting magnet in the train alternating current can be induced in the “8” shaped c

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.

The magnetic levitated train can travel a speed 500 km/hour, which is double the speed of existing fastest train

Note: The train is supposed to move always at the centre. Suppose if it moves away from the centre, say for example right side, an attractive force is given at the left side, and a repulsive force is given at the right side and is made to come at the centre.

8.7. ENGINEERING APPLICATIONS

1.           They are used to construct very sensitive electrical measuring instruments such as galvanometers because they requires very small voltages.

2.           They are used to transmit power over very long distance without any power loss.

3.           They are used as storae devices in computers.

4.           Superconductors are used to design rectifiers, logic gates, modulators etc.

8.8. MEDICAL APPLICATIONS

1.     They are used to study tiny magnetic signals from brain and heart.

2.     They are used in NMR imaging systems.

3.     They are used to detect brain tumours and clots using superconductingsolenoids.

4.     They are used in magneto-cardiography, magneto –encephalography.

5.     They are used to study the amount of iron held in the lever of the body accurately.