Lecture 1

Superconductivity and Nano materials: Temperature dependence of resistivity, Effect of magnetic field (Meissner effect), Penetration depth, Type I and Type II Superconductors, Temperature dependence of critical field, BCS theory(qualitative), High temperature superconductors, Applications of superconductors (qualitative).Introduction to Nano materials, Basic principles of Nano- science and technology, Creation and use of Bucky balls, Structure, properties and uses of carbon nanotubes, Some applications of Nano-materials

UNIT-2:

What are SUPERCONDUCTORS

• Before the discovery of the superconductors it was thought that the electrical resistance of a conductor becomes zero only at absolute zero

• But it was found that in some materials electrical resistance becomes zero when cooled to very low temperatures

• These materials are nothing but the SUPER CONDUTORS.

WHO FOUND IT?

• Superconductivity was discovered in 1911 by Heike Kammerlingh Onnes , who studied the resistance of solid mercury at cryogenic temperatures using the recently discovered liquid helium as ‘refrigerant’.

• At the temperature of 4.2 K , he observed that the resistance abruptly disappears.

• For this discovery he got the NOBEL PRIZE in PHYSICS in 1913.

• In 1913 lead was found to super conduct at 7K.• In 1941 niobium nitride was found to super conduct

at 16K

SUPERCONDUCTING MATERIALSSuperconductivity - The phenomenon of losing resistivity when sufficiently cooled to a very low temperature (below a certain critical temperature). H. Kammerlingh Onnes – 1911 – Pure Mercury (4.15K)

SUPERCONDUCTORS• Superconductivity is

a phenomenon in certain materials at extremely low temperatures characterized by exactly zero electrical resistance.

Definition

Superconductivity is the flow of electric current without resistance in certain metals, alloys, and ceramics at temperatures near absolute zero, and in some cases at temperatures hundreds of degrees above absolute zero .

Superconductors.org Only in nanotubes

Note: The best conductors & magnetic materials tend not to be superconductors (so far)

Transition Temperature or Critical Temperature (TC)

Temperature at which a normal conductor loses its resistivity and becomes a superconductor.

• Definite for a material• Superconducting transition is reversible• Very good electrical conductors are not

superconductors eg. Cu, Ag, Au• Types1. Low TC superconductors2. High TC superconductors

Superconductivity generally occurs at very low temperatures. In this state the materials have exactly zero electrical resistivity. As the material drops below its superconducting critical temperature, magnetic fields within the material are (totally or partially) expelled. Superconductivity occurs in a wide variety of materials,including simple elements like tin and aluminium, various metallic alloys and some heavily-doped semiconductors

Occurrence of Superconductivity

Superconducting Elements TC (K)

Sn (Tin) 3.72

Hg (Mercury) 4.15

Pb (Lead) 7.19

Superconducting Compounds

NbTi (Niobium Titanium) 10

Nb3Sn (Niobium Tin) 18.1

TEMPERATURE DEPENDENCE OF RESISTIVITY

• As temp decreases thermal vibrations of atoms decrease and conducting electrons are less scattered.

• The decrease in resistance is linear till one third of the Debye temprature and a few degrees above absolute zero they lose all traces of electric resistance and pass into superconducting state.

• Zero Electrical Resistance for super conductors but some residue (due to impurities) in ordinary metals.

• Defining Property • reversible• 10-5Ωcm

Temperature Dependence of Resistance

Normal phase Superconductivity phase

MEISSNER EFFECT

When a superconductor is placed in a weak external magnetic field, the field penetrates the superconductor only at a small distance, called the London penetration depth, decaying exponentially to zero within the bulk of the material. This is called the Meissner effect, and is a defining characteristic of superconductivity. For most superconductors, the London penetration depth is on the order of 100 nm.

MEISSNER EFFECT

• When the superconducting material is placed in a magnetic field under the condition when T≤TC and H ≤ HC, the flux lines are excluded from inside the material.

• Material exhibits perfect diamagnetism or flux exclusion.• Deciding property• χ = M/H = -1• Reversible (flux lines penetrate when T ↑ from TC)• Conditions for a material to be a superconductor

i. Resistivity ρ = 0ii. Magnetic Induction B = 0 when in an uniform magnetic field

• Simultaneous existence of conditions of zero resistivity and perfect diamagnetism.

The Meissner Effect• A diamagnetic property

exhibited by superconductors.

• End result is the exclusion of magnetic field from the interior of a superconductor. Below its critical temperature (Tc) a superconductor does not allow any magnetic field to enter it.

• What is diamagnetism?

meissner effect Maxwell's equations could explain

the superconductivity phenomenon.

superconductors 0 0

0 tan .

This means that the magnetic flux de

Before the

JJ E E J

for E

B BAs XE B cons t

t t

nsity in the interior of the

superconductor cannot change on cooling at or below the

transition tempr

Re

at

si

ure.

stiv

But this

ity and

contradicts the

perfect Diamagne

mei

tism

ssners effec

tw

t.

o ar pe indeof the

endent

superproper conduc sties tor

Meissner effect shows that magnetic flux is ejected

outward of the specimen

4 ( )

superconductors 0

10 4 ( )

4 behave as d

0 de t

iamagne

specim n

.

e

ts

m

B insi he

B H I M

for B

IH I M

HSC

• Circulating currents on the surface of the superconductor induce microscopic magnetic dipoles that oppose the applied field.

• The induced field repels the applied field, and the magnet associated with it.

• If a magnet is on top of a superconductor as it is cooled below its Tc, it would exclude the magnetic field of the magnet.

The Result

Applications of Meissner Effect

• Standard test – proof for a superconductor

• Repulsion of external magnets - levitationMagnet

Superconductor

Yamanashi MLX01 MagLev train

Temprature dependance of critical field/Effect of external magnetic

field on superconductorsSuperconductivity will dissapear if

temp of specimen is raised above Tc or if a sufficiently strong magnetic field is applied

Critical magnetic field (HC) – Minimum magnetic field required to destroy the superconducting property at any temperature

H0 – Critical field at 0K

T - Temperature below TC

TC - Transition TemperatureSuperconducting

Normal

T (K) TC

H0

Element HC at 0K(mT)

Nb 198

Pb 80.3

Sn 30.9

2

0 1CC

TH H

T

HC

A superconducting Sn has a critical temprature

of 3.7K in zero magnetic field and a critical

field of 0.0306T at 0K. find the critical field

at 2K.

0

22

0 2

T =3.7K , H =

H =H

=

0.0306T (at 0K)

2(1 ) 0.0306(1 )

3.7

0.02166Tesla

c

cc

T

T

5

5The critical field of niobium is 1x10 A/m

at 8K and 2x10 A/m at 0K. calculate the

critical temprature of the material

2 2

0 2 20

1/ 2

1/ 20

0

HH =H =

H

H

HHH

=

(1 ) 1

(1 ) or (1 )

11.31K

cc

c c

cc

cc

T T

T T

T TT

T

The Science….• The understanding of superconductivity was advanced in 1957 by

three American physicists-John Bardeen, Leon Cooper, and John Schrieffer, through their Theories of Superconductivity, know as the BCS Theory.

• Pictures of Bardeen, Cooper, and Schrieffer, respectively.

• The BCS theory explains superconductivity at temperatures close to absolute zero.

• Cooper realized that atomic lattice vibrations were directly responsible for unifying the entire current.

• They forced the electrons to pair up into teams that could pass all of the obstacles which caused resistance in the conductor.

In many superconductors, the attractive interaction between electrons (necessary for pairing) is brought about indirectly by the interaction between the electrons and the vibrating crystal lattice (the phonons).

Roughly speaking the picture is the following:

An electron moving through a conductor will attract nearby positive charges in the lattice.

This deformation of the lattice causes another electron, with opposite spin, to move into the region of higher positive charge density.

The two electrons then become correlated. There are a lot of such electron pairs in a superconductor, so that they overlap very strongly, forming a highly collective condensate.

The electron pairing is favorable because it has the effect of putting the material into a lower energy state.

When electrons are linked together in pairs, they move through the superconductor in an orderly fashion.

Best conductors best ‘free-electrons’ no e- – lattice interaction not superconducting

The Science….• The BCS theory successfully shows that electrons can be

attracted to one another through interactions with the crystalline lattice. This occurs despite the fact that electrons have the same charge.

• When the atoms of the lattice oscillate as positive and negative regions, the electron pair is alternatively pulled together and pushed apart without a collision.

The Science….• One can imagine a metal as a lattice of positive ions, which can

move as if attached by stiff springs. Single electrons moving through the lattice constitute an electric current.

• Normally, the electrons repel each other and are scattered by the lattice, creating resistance.

• A second electron passing by is attracted toward this positive region and in a superconductor it follows the first electron and they travel bond together through the lattice.

• Electrons in the lattice form Cooper pairs which allow for current to flow without resistance.

• The electron-phonon interaction leads to a new ground state of electron pairs (Cooper pairs) which shows all the desired properties.

Classification of superconductors

The SC may be classified into two categories, depending On their magnetization behavior ie the way in which the transition from the normal state to SC state proceeds in external magnetic field.

1. TYPE I (soft SC)2. TYPE II (hard SC)

TYPE I (soft SC)The SC in which the the magnetic field is totally excludedFrom the interior of the SC ie it exhibits complete meissner effect. Above a certain magnetic field Hc the SC loses Superconductivity and magnetic field penetrates fully.

The transition from normal to SC state in the presence of magnetic field occurs sharply at Hc

TYPE II (hard SC)Have two critical fields a lower Hc1 and Hc2 an upper. State of specimen between Hc1 and Hc2 is termed as the intermediate state magnetically but electrically it is a SC.Alloys and transition metals with high value of resistivity in normal stateThey exhibit incomplete meissner effect.

Superconductor Classifications• Type I

– tend to be pure elements or simple alloys

– r = 0 at T < Tcrit

–Internal B = 0 (Meissner Effect)–At Bext > Bcrit, no superconductivity–Well explained by BCS theory

Type IItend to be ceramic compoundsCan carry higher current densities ~ 1010

A/m2

Mechanically harder compoundsHigher Hc critical fieldsAbove Hext > Hc, some superconductivity

High Temperature Superconductors

CHARACTERISTICS• High TC

• 1-2-3 Compounds: they are neither metals nor inter-metallic compounds , they are oxides. their unit cell contains 1 atom of rare earth(yttrium), 2 barium atoms ,3 cu atoms and 7 oxygen atoms.

• Perovskite crystal structure:form as layers of Cu and O2 atoms sandwitched between layers containing other lements in the compounds.

• Direction dependent(anisotropic)• Reactive, brittle

Applications of high Tc SCs• Large distance power transmission (ρ = 0)• Switching device (easy destruction of

superconductivity)• Sensitive electrical equipment (small V

variation large constant current)• Memory / Storage element (persistent

current)• Highly efficient small sized electrical generator

and transformer

PENETRATION DEPTHIt is defined as the effective depth to which a magnetic field penetrates the superconductor.Depends strongly on temperature and becomes muchLarger as T approaches Tc.

14 2

0

0

( ) [1 ( ) ]

and are penetration depths at

TK and 0K respectively.

T

c

T

T

T

The penetration depth of Hg at 3.5K is about

750A and n

(superconducting electron density) as T 0

. Estimate the values of o

s

14 2

0

14 02

0

10 2

0 020

28 3

( ) [1 ( ) ]

[1 ( ) ] 528.7 also

[ ] electron,

e charge, of super electrons

1.0x10

T

c

Tc

Ts

s

s

T

T

TA

T

mm mass of

n e

n number

n m

Applications of Superconductors• magnetic shielding devices• medical imaging systems, e.g. MRI’s • superconducting quantum interference

devices (SQUIDS) used to detect extremely small changes in magnetic fields, electric currents, and voltages.

• infrared sensors• analog signal processing devices• microwave devices

SQUIDS

Source: Superconductors.org

Flux-Pinning:

• The phenomenon where a magnet's lines of force (called flux) become trapped or "pinned" inside a superconducting material. This pinning binds the superconductor to the magnet at a fixed distance.

Picture of Flux-Pinning:

Source: Superconductors.org

Emerging Applications

• power transmission• superconducting magnets in generators• energy storage devices• particle accelerators• levitated vehicle transportation• rotating machinery• magnetic separators

What Types of Superconducting Power Systems Equipment Can Help Us?

• Underground transmission cables• Fault current limiters• Transformers• Motors • SMES, Generators, etc.

Cable – transmits 3 to 5 times more energy than copper wire

Source: Southwire

Transformer- 2 times overload capacity without insulation damage and environmentally friendly due to lack of oil used in operation.

Source: Waukesha Electric Systems

HTS Motor – requires half the space of copper based motors

Source: Rockwell

SMES (Superconducting Magnetic Energy Storage)

Source: American Superconductor

THE END