Unit – I (Conducting and Superconducting Materials)
Free Electron Theory of Metals
Electrical Conductivity of Metals
Thermal Conductivity of Metals
Wiedemann-Franz Law and Merits –Demerits of Classical Theory
Quantum Free Electron Theory and Fermi Function
Density of States
Electron Concentration and Average Energy of an Electron in a Metal
Superconductors (Properties and Types of Superconductors)
Superconductors (High Tc Superconductors)
Superconductors – Applications
General Objective
To understand the basic concepts of superconductivity and
their properties
Specific Objectives
1. Define superconductivity (S)
2. Define critical temperature (S)
3. List the superconducting materials with their critical temperature(S)
4. State Meissner Effect (S)
5. Define critical magnetic field (S)
6. Mention the properties of superconducting materials (S)
Superconductivity
Superconductivity is an unusual
property of certain metals, alloys &
ceramics, in which electrical
resistance drops to zero (perfect
conductivity) when the temperature is
reduced below a critical value called
critical temperature (Tc) or transition
temperature
In normal metals, the electrical resistance decreases as the
temperature is lowered but does not disappear completely
Superconductivity
Superconductivity was first discovered
by Kamerling Onnes (from Holland) in
1911
Kamerling Onnes observed that when
a sample of mercury is cooled below
4.2 K, its resistivity totally vanishes
and the material behaves as a
superconductor
Critical Temperature (Tc) or Transition
Temperature
The temperature at which a material at
normal conducting state changes into
superconducting state (Critical or
Transition temperature)
Transition (critical) temperature depends
on the property of the material
Above critical temperature, a
superconductor becomes a normal
material)
Superconducting Materials
S.No Element Critical
. Temperature
Superconductivity occurs in TC (K)
1 Indium (In) 3.40
2 Tin (Sn) 3.72
Metallic elements
3 Mercury (Hg) 4.2
Alloys 4 Tantalum (Ta) 4.48
Intermetallic 5 Vanadium (V) 5.38
compounds 6 Lead (Pb) 7.19
7 Niobium (Nb) 9.50
Semiconductors
There are many conductors (silver, gold, copper) that do not exhibit
superconductivity
Superconducting Materials
S.No. Alloy Critical Temperature
TC (K)
1 Niobium Titanium (NbTi) 10.0
2 Vanadium Gallium (V3Ga) 16.5
3 Vanadium Silicon (V3Si) 17.1
4 Niobium Aluminium 17.5
(Nb3Al)
5 Niobium Tin (Nb3Sn) 18.1
6 Niobium Germanium 23.2
(Nb3Ge)
7 Niobium (Nb) 9.50
Superconductors Critical Temperature (Tc)
Lead (Pb) 7.2 K
Nb3Ge 23 K
La–Ba–Cu–O 35 K (Nobel prize-winning discovery)
J. Georg Bednorz, K. Alex Müller
(1987)
Y–Ba–Cu–O 95 K - above the boiling point of N (77 K)
Hg–Ba–Ca–Cu–O 130 K
Meissner Effect
Consider a superconducting material
The superconductor is placed in a
magnetic field above Tc When the superconductor is
The magnetic lines will penetrate cooled below Tc, it rejects all
the sample the magnetic lines of force
Meissner Effect
The expulsion of magnetic lines of force
from a superconducting material when it
is cooled below the critical temperature
(behave like a perfect diamagnetic
material)
A superconductor
(cooled below TC) in
a magnetic field
The magnetic field
is rejected
(Meissner Effect)
Perfect conductor
(cooled below TC) in
a magnetic field
The magnetic field is
not rejected
(No Meissner Effect)
Critical Magnetic Field
Superconducting state of a metal depends on
Temperature
Strength of the magnetic field in which the metal is placed
Critical Magnetic Field
Magnetic field required to convert
a superconductor into a conductor
Critical Magnetic Field
Superconducting state cannot exist in
the presence of a magnetic field
greater than a critical value even at
T=0K
Superconductivity disappears if either
the temperature of the sample is
increased above Tc or strong enough
magnetic field (> Hc) is applied
Effect of Magnetic Field
At T = TC, Hc = 0
At temperatures below Tc, Hc increases
The dependence of the critical field on the
temperature is given by
T
2
H c (T ) H c( 0 ) 1
Tc
HC (0) is the critical field at T = 0 K
HC (0) and Tc are constants and material characteristics
Example Problem
A superconducting tin has a critical temperature of 3.7 K at zero magnetic
field and a critical field of 0.0306 Tesla at 0 K. Find the critical field at 2 K.
T
2
H c (T ) H c( 0 ) 1
Tc
Given 2
2
H c 0.0306 1
Tc 3.7 K 3.7
H c (0) 0.0306 Tesla
T 2 K H c 0.02166 Tesla
Definition of Superconductor
A metallic element or alloy or inter-metallic compound that will
conduct electricity without resistance below a certain
temperature (Tc), magnetic field (Hc) & applied current (Jc or Imax)
Critical current density (J c) is
the maximum current (Imax)
that a superconductor can
carry without losing its
superconductivity
Properties of Superconductors
1. Zero resistance to current
2. Diamagnetic property (Meissner effect)
3. Extremely high current carrying density (Jc or Imax)
4. Extremely low resistance at high frequencies
5. High sensitivity to magnetic field
6. Isotope effect (change in Tc for isotopes of same elements)
7. Heat Capacity effect (different heat capacity in
superconducting state than in normal conducting state)
Types of Superconductors
Based on the magnetic behavior of superconductors in an
external magnetic field, they are classified into two types
(1) Type I Superconductors
(2) Type II Superconductors
Type I Superconductors
Type I superconductors loose their superconductivity very easily or
abruptly when placed in an external magnetic field
Type I superconductors
suddenly loses its
Type I
superconductivity at critical magnetic
field (Hc)
called as soft superconductors
(loose their superconductivity
easily)
perfectly obey Meissner effect
Type I Superconductors
Critical Temperatures and Critical Magnetic Fields (at T = 0 K)
(HC)
Type II Superconductors
Type II superconductors loose their superconductivity gradually but
not easily when placed in an external magnetic field
Type II superconductors have
two critical magnetic fields
They start to loose their
superconductivity at lower
critical magnetic field (Hc1) and
completely loose their
superconductivity at upper
critical magnetic field (Hc2)
Type II Superconductors
The state between Hc1 and Hc2
is called as mixed state or
vortex state
Type II superconductors obey
Meissner effect but not
completely
They are also known as hard superconductors (loose their
superconductivity gradually not easily)
Type II Superconductors
Critical Temperatures and Upper Critical Magnetic Fields (at T = 0 K)
(HC2)
Applications of Superconductors
1. Superconducting Transmission Lines
2. Superconducting Motors and Generators
3. Superconducting Magnetic Energy Storage
4. Magnetic Levitation
5. Generation of High Magnetic Fields
6. Fast Electrical Switching
7. Computers
8. SQUID Magnetometer
Superconducting Transmission Lines
Since the resistance is almost zero at superconducting phase, the power
loss during transmission is negligible
Hence electric cables are designed with superconducting wires
Superconducting Motors and Generators
Superconducting generators and motors are very smaller in size and
weight when compared with the conventional devices
Magnetic Levitation
Diamagnetic property of a superconductor (rejection of magnetic flux
lines) is the basis of magnetic levitation
When a magnet is placed over a superconductor,
the magnet will float due to the repulsive force
from the superconductor (Magnetic Levitation)
Magnetic levitation effect can be used for
high speed (Maglev) trains
Maglev trains does not move over the rails
but it floats above the rails
Generation of High Magnetic Fields
Superconducting materials are used
for producing very high magnetic fields
of the order of 50 Tesla
Such high magnetic fields are required in Magneto Hydro Dynamic (MHD)
power generators, Magnetic Resonance Imaging (MRI) in hospitals,
Nuclear Magnetic Resonance (NMR) in physics and chemistry
laboratories to study the effect of magnetic fields in solids
Magnetic Resonance Imaging (MRI) enables to “see” inside the human
body with no harm
MRIs use the small magnets inside the
nuclei of the human body atoms to
visualize what surrounds them (brain,
muscles,. . . )
Nuclei magnets called “spin” must first be
lined up and this can be done by a
magnetic field
To produce these fields, a strong electric current is needed
Superconducting wire with no electrical resistance (no heating) can be
used for creating the magnetic field
Fast Electrical Switching (Cryotron)
Cryotron is a switch that operates using superconductivity
Superconductor possess two states (superconducting state and normal
state)
Application of magnetic field greater than Hc can initiate a change from
superconducting state to normal and the removal of the field reverses the
process (normal to superconducting)
This principle is applied in development of switching element cryotron
Josephson Effect
Josephson effects state that electrons are able to flow across an insulating
barrier placed between two superconducting materials
Josephson junctions have a thin layer of insulating materials squeezed
between superconducting material
Josephson junction require little power to operate, thus creating less heat
Superconducting Quantum Interference Devices (SQUIDs)
SQUID is a double junction quantum
interferometer
Very minute magnetic signals can be
detected by SQUID sensors
To study tiny magnetic signals from brain &
heart
To detect paramagnetic response in the liver
