free electron gas mode. Lorentz theory€¦ · MVJCE Engineering Physics Module II 1 MODULE II...
Transcript of free electron gas mode. Lorentz theory€¦ · MVJCE Engineering Physics Module II 1 MODULE II...
MVJCE Engineering Physics Module II
1
MODULE II
Electrical Conductivity of Metals notes complied Dr. Ramdas Balan
Classical free electron theory of metal was proposed by Drude and Lorentz to account electrical
conduction in metals.
Drude postulated that the metals consist of positive ion core with the valence electrons
moving freely among the core. These electrons are however, bound to move within the metal due
to electrostatic attraction between the positive ion core and the electron. The behavior of free
electron moving inside the metal is considered to be similar to that of atoms or molecules in the
perfect gas. These free electrons are therefore, also called as free electron gas and the theory is
accordingly named as free electron gas mode.
Based on the Drude considerations that the electron gas behaves as a perfect gas, Lorentz
postulated that the electrons constituting the electron gas obeys Maxwell Boltzmann statistics
under equilibrium conditions. The combined idea of Drude and Lorentz is known as Drude and
Lorentz theory.
CLASSICAL FREE ELECTRON THEORY - ASSUMPTIONS
1. The valence electron of the atom is loosely bound to their respective atom. In metals they
become the free electrons. These electrons are free to move throughout the metal and are
hence termed as free electrons. Since electrical conductivity is due to these free electrons,
these are also termed as conduction electrons.
2. These free electrons move in the metal according to Kinetic theory of gases.
3. Like the molecules of gas in a container, free electrons in these metals move randomly (in
the absence of electric field) with a velocity, which is the average velocity or rms (root
mean square) velocity. In the absence of externally applied potential difference there are
on an average as many electrons wandering through a given cross section of the
conductor in a given direction as there are in the opposite direction. Hence the net current
is zero.
4. However on application of electrical field, the random motion gets slightly affected and
the electrons experience a drift velocity in the direction of the applied field. This drift
velocity is less than the rms velocity by several orders of magnitude.
MVJCE Engineering Physics Module II
2
DRIFT VELOCITY, MEAN COLLISION TIME AND MEAN FREE PATH, RELAXATION
TIME
Since, free electrons in the metals behave like molecules/atoms in the gas. So, it is
assumed that classical kinetic theory of gases can be applied to a free electron gas. Thus the
electron can be assigned with mean free path (), mean collision time () and average speed ( c ).
MEAN FREE PATH
The distance travelled by an electron between two successive collisions is called as free
path and its mean distance is called as mean free path.
The mean free path is the average distance travelled by an electron between two successive
collisions with other free electrons.
= c
MEAN COLLISION TIME
The average duration of time that elapses between two successive collisions is called
mean collision time.
= c
DRIFT VELOCITY
Drift velocity is defined as the average velocity acquired by the free electron in a
particular direction during the presence of electric field.
When an electric field is applied on an electron of charge e, then it moves in opposite direction to
field with a velocity vd. This velocity is known as drift velocity.
Lorentz force acting on the electron:
F= - e E (1)
where, E is the electronic field and e is the electronic charge.
The opposing force can be expressed as
F’ = mvd /
When the system in steady state the driving force is equal and opposite to the opposite force
i.e, equation (1) & (2) are equal F = F’
mvd /eE
i,e
m
eEvd
MVJCE Engineering Physics Module II
3
EXPRESSION FOR ELECTRICAL CONDUCTIVITY IN METALS
The drift velocity of the electron is
vd = (em) E (1)
From ohm’s law
J = E or J/E (2)
where, J – current density and - electrical conductivity of electrons
But, the current density in terms of drift velocity can be stated as
J= nevd (3)
substituting vd from (1) in (3)
J = ne (em) E or J/E = ne2m (4)
But, J/E so, comparing the (2) and (4)
(5)
Thus eqn. (5) gives the expression for electrical conductivity
EFFECT OF IMPURITY AND TEMPERATURE ON ELECTRICAL RESISTIVITY OF
METALS
The two factors that effects the electrical resistivity (or electrical conductivity) of metals are
1. Temperature
2. Impurity
The resistivity of metals is attributed to the scattering of conduction electrons. The
scattering of electrons takes place because of two reasons: one due collision of conduction
electrons with the vibrating lattice ions and the other is caused by scattering of electrons by the
impurities present in the metal.
The resistivity due to scattering of electrons by the lattice vibrations called phonons is
denoted by . This increases with temperature. It arises even in a pure conductor and hence
called the ideal resistivity. Whereas, the resistivity in the metal caused due to scattering of
electrons by the impurities is denoted by i. This is independent of temperature and present even
at absolute zero of temperature and hence called residual resistivity.
Therefore, the total resistivity of a metal can be written as the sum of the two resistivities.
This is called Matthiessen’s rule. Mathematically,
i
Since 2ne
m , we can rewrite the above equation as
m
ne
2
MVJCE Engineering Physics Module II
4
pne
m
2 +
ine
m
2
where, p and i are the mean collision times of electron with phonons and impurities
respectively. At lower temperatures tends to zero as the amplitude of lattice vibrations
becomes small which essentially means that all the resistivity will be due to impurities, i.e .,
=i . At higher temperature increases with temperature however the curves of versus T at
room temperature remains linear.
FAILURE OF CLASSICAL FREE ELECTRON THEORY
Though classical free electron theory successfully explained the Electrical and Thermal
conductivity in metal but it failed to explain many other experimental facts among which the
notables are
i. Specific heat
ii. Temperature dependence of electrical conductivity
SPECIFIC HEAT
The molar specific heat of a gas at constant volume is Cv =3/2 R. But, the experimental
value of specific heat of a metal was found to be Cv = 10-4
RT
Thus the value of sp. heat predicted is higher than the experimental value and also the
theory predicted that the sp. heat is temperature independent whereas experimental results are
temperature dependent.
TEMPERATURE DEPENDENCE OF ELECTRICAL CONDUCTIVITY
From experiment results it is well known that conductivity is inversely proportional to
temperature
i.e exp1/T (1)
But according to main assumption of classical free electron theory
2
3 KT = 2
1 mvth2 ;
vthm
KT3 where,
vth - thermal velocity
therefore vth T (2)
and also vth
1 (3)
Comparing (2) and (3) T
1 (4)
but we know m
ne 2 i.e (5)
MVJCE Engineering Physics Module II
5
comparing equation (4) and (5)
T
1 (6)
comparing the experimentally derived conductivity equation (1) and the classically derived
equation (6) both are not same. Hence, it is failure.
QUANTUM FREE ELECTRON THEORY
In 1928, Sommerfeld proposed the quantum free electron theory in order to overcome the
failure of classical free electron theory base on quantum concepts.
They are,
In a metal, free electrons are fully responsible for electrical conductivity.
Free electron are free to move anywhere within the metal.
Electron acquires constant velocity known as drift velocity under the influence of electric
field.
Electrons obey quantum concepts.
Electrons are treated as wave like particles.
The velocity and energy of the electron are determined by Fermi- Dirac distribution
function.
Electrons obey Pauli’s exclusion principle.
FERMI ENERGY AND FERMI FACTOR
In a single atom there will be many allowed energy levels whereas in a solid each such
energy level will spread over a range of few eV. If there are N numbers of atom, there will be N
closely spaced energy levels in each energy band of the solid. According to Pauli’s exclusion
principle, each such energy level can accommodate two electrons. At absolute zero temperature,
two electrons with least energy with opposite spins occupy the lowest available energy level. The
next two electrons with opposite spins will occupy next energy level and so on. Thus, the top
most energy level occupied by electrons at absolute zero temperature is called Fermi energy
level. The energy corresponding to that energy level is called Fermi energy.
Fermi energy, Ef , is defined as the higher most energy occupied by an electron at
absolute 0 K. Below which all energy levels are completely occupied and above which all the
energy levels completely empty. Thus Fermi energy represents maximum energy that electrons
can have at absolute zero temperature.
FERMI DISTRIBUTION OR FERMI FACTOR
At absolute zero all energy levels below Fermi energy are completely filled and above it
are completely empty. But at any given temperature, the electrons get thermally excited and
move up to higher energy levels. As a result there will be many vacant energy levels below as
MVJCE Engineering Physics Module II
6
well as above Fermi energy level. Under thermal equilibrium, the distribution of electrons
among various energy levels is given by statistical function f(E). The function f(E) is called the
Fermi factor which gives the probability of occupation of a given energy level under thermal
equilibrium.
The distributions of energy in metals are explained by Fermi Dirac statics, since it deals
with the particles having half integral spin like electron.
The probability function f(E) of an electron occupying an energy level E is given by
f(E) = KT
EfE
e)(
1
1
where, Ef - Fermi energy, and K - Boltzmann constant
The probability functions lies between 0 and 1. Hence, there are three probabilities
Case 1: Probability of occupation at T = 0K, when E < Ef
f(E) = e1
1 =
01
1
= 1
Therefore, there is 100% probability that the electron occupy the energy level below Fermi
energy.
Case 2: Probability of occupation at T= 0K, when E > Ef
f(E) = e1
1 =
1
1 = 0
the energy levels above Fermi energy level Ef are unoccupied at 0K. Therefore, there is 0 %
probability for the electron to occupy the energy level above the Fermi level
Case 3: Probability of occupation at T = 0 and E = Ef
f(E) = 01
1
e =
11
1
=
2
1
This shows at T = 0K, there is a 50% probability for the electron to occupy the Fermi
energy.
DENSITY OF STATES
Fermi level divides the occupied states from the unoccupied states i.e it is the highest
energy state for the electrons to occupy at absolute zero temperature. To know the actual number
of electrons with a given energy one must know the no. of states in the system, multiplying the
no. of states by the probability of occupation we get the actual no. of electron in the system.
The energy distribution of electron in a metal is determined by Fermi-Dirac statistics. The
ability of a metal to conduct electricity depends upon the no. of quantum states and the
availability energy levels for the electrons. Therefore determination of energy states for the
MVJCE Engineering Physics Module II
7
electron is essential. The number of states at each energy level that are available to be
occupied by the electrons, we introduce the concept of the density of states of a system.
The density of states, g(E), is defined as the number of energy levels available per unit volume
per unit energy centered at E. The number of states per unit volume between the energy level E
and E+dE is denoted by g (E)dE.
Density of states = No. of quantum states present between E and E+dE
Volume of the specimen
Density of states expression
EXPRESSION FOR ELECTRICAL RESISTIVITY BASED ON QUANTUM FREE
ELECTRON
Using the concepts of density of states and Fermi-Dirac statistics Sommerfeld arrived at
the following expression for electrical conductivity in metals,
fvm
ne*
2
where, is the mean free path; m* is the effective mass and vf is called the Fermi velocity. The
Fermi velocity can be found out by equating the Fermi energy to the kinetic energy of the
electrons in a metal.
That is , 2
2
1fmv = Ef vf =
m
E f2
The resistivity of the metal is given by
1
therefore
MERITS OF QUANTUM FREE ELECTRON THEORY
Temperature dependence resistivity of metal
The experimental results of electrical conductivity is inversely proportional to temperature.
The expression for electrical conductivity is
m
ne 2
Here as per quantum free electron theory
g(E)dE =3
23
)(28
h
m 21E dE
2
*
ne
vm f
MVJCE Engineering Physics Module II
8
fv
, therefore fmv
ne 2
i.e (1)
As the conduction electron transverse in the metal, they are subjected to scattering by the
vibrating ions of the lattice. The vibration occurs such that the displacement of ions takes place
equally in all directions. If the r is the amplitude of the vibrations, then the ions can be
considered to present effectively a circular cross section of area, r2 that blocks the path of the
electrons irrespective of the direction of approach. Since the vibrations of larger area of cross
section should scatter more effectively, it results in a reduction in the value of mean free path of
the electrons.
therefore2
1
r (2)
The amplitude of vibration varies with the temperature i.e the radius of increase with increase in
temperature
hence r2 T (3)
therefore, from (2) and (3) T
1 (4)
comparing eqn (1) and (4 ) we have , T
1
Thus, quantum free electron theory derived temperature dependent conductivity and
experimental values are same.
SPECIFIC HEAT CAPACITY
The quantum theory of free electrons solves the flaws of the classical theory which is discussed
below. Specific heat of free electrons: From quantum theory of free electrons, the specific heat of
free electrons is given by
Cv = fE
k2 RT
For a typical value of Ef = 5eV, we get
Cv = 10-4
RT
which is agreement with the experimental results.
Dependence of electrical conductivity on electron concentration: The electrical conductivity in
metals is given by
fvm
ne*
2
It is clear from this above equation that the electrical conductivity depends both the electron
concentration (n).
MVJCE Engineering Physics Module II
9
SEMICONDUCTORS
Materials are classified based on their electrical conductivity as conductor, semiconductor and
Insulators. Using band gap (which is also called as forbidden gap i,e. a gap between conduction
band and valence band) the classification of the materials can be explained. If materials posses
band gap of the order of 1 eV then it is called Semiconductors.
Figure 1: Band gap of semiconductor
Semiconductors are broadly classified in to two types i) Intrinsic semiconductors and
ii) Extrinsic semiconductors.
Semiconductor which does not have any kind of impurities, behaves as an Insulator at 0 K and
behaves as a conductor at higher temperature is known as Intrinsic Semiconductor or Pure
Semiconductors. e.g Silicon (Si), Germanium (Ge).
Figure 2: Electronic structures of fourth group element - Si, Ge (example for Intrinsic
semiconductor)
Extrinsic semiconductors are those in which presence of impurities of large quantity present.
Usually, the impurities can be either 3rd
group elements or 5th
group elements.
Based on the impurities present in the extrinsic semiconductors which introduce either majorly
holes or electrons, upon these they are classified into,
i) n-type semiconductors - electron are majority charge carriers
ii) p-type semiconductors - holes are majority charge carriers
MVJCE Engineering Physics Module II
10
Figure 3 : a) n-type semiconductors b) p-type semiconductors
CARRIER CONCENTRATION IN INTRINSIC SEMICONDUCTORS
In semiconductor, two types of charge carrier that is electron and hole can contribute to a current.
Since the current in a semiconductors is determined largely by the number of electrons in the
conduction band and number of holes in the valence band. Under thermal equilibrium condition
number electron in the conduction(ne) is equal to number of holes in the valence band (np).
The distribution of electrons in the conduction band is given by the density of states, g(E) times
the probability that a state is occupied by the electrons, f(E).
Let ‘ne’ be the number of electrons available between energy interval ‘E and E+ dE’ in the
conduction band, then,
(1)
where, g(E) is density of states in the conduction band,
f(E) is the fermi dirac statistics
density of states, dEEmh
dEEg e2
3
3)(
28)(
(2)
Probability of occupancy
Hence,
(3)
band theof top
)()(
cE
e dEEfEgn
)exp(
1)(
res temperatupossible allFor
)exp(1
1)(
kT
EEEf
kTEE
kT
EEEf
f
F
f
)exp()(
)(exp)(
kT
EEEf
kT
EEEf
F
F
MVJCE Engineering Physics Module II
11
Substituting equation (2 ) and (3 ) in (1)
(4)
or where ,
Let ‘np’ be the number of holes or vacancies in the energy interval ‘E and E + dE’ in the valence
band.
(5)
density of state , (6)
Probability of un-occupancy
(7)
substituting equation (6) and (7) in (5)
or
where
FERMI LEVEL IN INTRINSIC SEMICONDUCTORS
For Intrinsic semiconductor, number of electrons in the conduction band (ne) is equal to number
of holes in the valence band (np). i,e ne = np
)exp()(24
2
3
3 kT
EEkTm
hn cF
ee
Ev
p dEEFEgnband theof bottom
)}(1){(
)exp(kT
EENn cF
ce
2
3
3)(
24kTm
hN ec
kTEE
kT
EEEf
kT
EEEf
F
f
f
res temperatupossible allFor
)exp(1
1)(1
)exp(1
11)(1
)exp()(24
)exp()(24
2
3
32
3
3 kT
EEkTm
hkT
EEkTm
h
Fve
cFe
)exp(
1)(1
kT
EEEf
f
dEEmh
dEEg e2
3
3)(
28)(
2
3
3)(
24kTm
hN hh
)exp()(24
2
3
3 kT
EEkTm
hn Fv
hp
)exp(
kT
EENn Fv
hp
MVJCE Engineering Physics Module II
12
i,e
Taking natural logarithm on both side on above equation
where, Ev +Ec = Eg
Thus, fermi level is in the middle of the band gap for intrinsic semiconductors.
EXPRESSION FOR CONDUCITIVITY IN INTRINSIC SEMICONDUCTORS
Consider an intrinsic semiconductor of area of cross section A, in which a current 'I' flows. let 'v'
be the velocity of electrons, Ne is the number of electron per unit volume and 'e' is the magnitude
of electric charge on the electron.
Then, current (charge flow per second ) I =Ne eAv (1)
Current density J = I/A = Ne e (2)
Mobility of electron , e = /E i,e = e E (3)
substituting (3) in (2) (4)
As per Ohms law J = eE (5)
From equation (4) and (5)
Similarly, contribution of hole in electrical conductivity,
2
3
)(
)exp(
)exp(
e
h
Fv
cF
m
m
kT
EEkT
EE
2
3
)()exp(
e
hFvCF
m
m
kT
EEEE
2
3
)()2
exp(
e
hgF
m
m
kT
EE
EeJ eeN
ee e eN
hh e hN
)exp()()exp()( 2
3
2
3
kT
EEm
kT
EEm Fv
hcF
e
)2
(
that know tor wesemiconduc intrinsicIn
)2
()log(4
3
)()log(2
32
2
3
cvF
he
cv
e
hF
cv
e
hF
EEE
mm
EE
m
mkTE
kT
EE
m
m
kT
E
2
g
F
EE
MVJCE Engineering Physics Module II
13
Total conductivity of semiconductors is given by sum of e and h
i.e
For Intrinsic semiconductors, Nh = Ne = ni therefore,
HALL EFFECT
When magnetic field is applied perpendicular to a current carrying conductor or semiconductor,
voltage is developed across the specimen in a direction perpendicular to both the current and the
magnetic field. This phenomenon is called the Hall effect and voltage developed is called the
Hall voltage (VH).
Consider a rectangular bar of n-type semiconductor material in which a current 'I' flows in the
positive 'x' direction. It means that electron move in negative 'x' direction. Let a magnetic field
'B' be applied along the negative 'z' direction. Under the influence of magnetic field, the electrons
experience the Lorentz force, )( BveF d , (1)
where B - applied magnetic field,
e - magnitude on charge of electron and d - drift velocity of the electron.
Figure 4 : Schematic diagram of Hall effect
As a result, the density of the electrons increases in the lower end of the material, due to which
its bottom edge becomes negatively charged. Hence, top edge of the material become positively
charged. This result with potential called Hall voltage (VH). And electric field, EH is established
between upper and lower surface of the material. This field exert an upward forces (F') on the
electron.
F' = e EH (2)
eh ee eh NN
)(n i ehe
Left hand rule : Hall effect
fore finger - represent the
direction of current
middle finger - represent the
direction of applied magnetic
field
thumb finger - direction of the
drift electron
MVJCE Engineering Physics Module II
14
When an equilibrium is reached, the magnetic deflecting force on the electrons are balanced by
the electric forces due to electric field.
Hd eEBve )( i,e )( BvE dH (3)
The relation between current density and drift velocity is J = ne dv , we know that I = ne dv A
where A is area i,e d x w i,e )(dwne
Ivd
therefore equation (3) becomes, (4)
If 'd' is the distance between the upper and lower surfaces of the slab, then d
VE H
H (5)
where, charge density = n e From equation (4) and (5)
Hence,
For p- type semiconductors, the positively charged holes will be deflected to the bottom so that
electron will be maintained at the top of the semiconductor, when similar direction of current and
magnetic field is applied to that above. Hence, negative Hall voltage is maintained.
Based on the polarity of the VH, type of semiconductors can be identified.
Hall co-efficient
For a given semiconductor , the Hall field EH depends upon the current density J and applied
field B,
i,e EH J B or EH =RH J B where RH is called Hall co-efficient
therefore
where from eqution (3) that is EH =B Vd and J =neVd substituting with above equation
)((
dwne
BIEH
new
BIVH
w
BIVH
JB
ER H
H
neBnev
BvR
d
dH
1
MVJCE Engineering Physics Module II
15
Superconductivity
Metals show positive temperature co-efficient (PTC) as resistivity
increases with increase in temperature. They are directly
proportional to each other, T . As per Matthensien rule,
resistivity in metal are mainly due to two main factors
i) temperature and ii) impurity. Lowering the temperature,
resistivity decreases for metals as shown in the figure 1.
Figure 1 Temperature Vs Resistivity for metals
In 1908, Dutch physicist Kamerlingh Onnes liquefied Helium at the
standard pressure to obtain 4.2K (i.e -268.6 oC). He has studied
number of metals' electrical resistivity lowering the temperature up to
liquefied helium temperature. Onnes observed abrupt drop in
resistivity to zero at 4.3K for mercury (Hg), as shown in figure 2.
Figure 2 Temperature Vs Electrical resistivity plot of mercury
Electrical resistivity completely vanishes at low temperature is called Superconductivity. And the
materials which shows superconductivity are called Superconductors.
CRITICAL TEMPERATURE (Tc)
The temperature at which the material shows transition from normal state to superconductivity
state (i,e material shows zero resistivity) is called critical temperature. Above the critical
temperature material will be in normal state.
MEISSNER EFFECT
When a superconductor in superconducting state (maintained below
critical temperature) kept in the magnetic field, it is observed to
expel the magnetic flux and the phenomenon is called Meissner
effect. It is similar characteristics like diamagnetism. Hence
superconductors exhibit diamagnetic property.
Figure 3 Meissner effect
Temperature in K
Res
isti
vit
y
()
normal conductor Superconductor
MVJCE Engineering Physics Module II
16
CRITICAL FIELD (Hc)
It is studied that apply of high magnetic fields destroy the superconductivity and restores the
normal conducting state. The magnetic field at which the superconducting state is destroyed is
called Critical field.
TYPE SUPERCONDUCTORS
Depending on the characteristics of transition from superconducting state to normal state when it
is exposed to external magnetic field, superconductors are classified in to two types 1) type I and
type II superconductors.
TYPE I SUPERCONDUCTORS
Superconducors that undergo abrupt transition from superconducting state to normal state at
critical magnetic field are known as type Type I superconductors .
Type I superconductors exhibit complete Meissner effect i,e completely expels the magnetic flux
(B) when it is superconducting state (figure 4b). When the applied magnetic field (H) is greater
than the critical field Hc, the entire material becomes normal by losing it superconducting
property completely and the magnetic flux (B) penetrates through the body.
In the presence of an external magnetic field H < Hc, the materials in superconducting state is a
perfect diamagnetic. Since it is a diamagnetic, it possesses negative magnetic moment ( - 4M),
shown in figure 4a.
Figure 4 Type I superconductors
The critical field value for Type I superconductors are found to be very low.
a
b
superconducting state
superconducting
state
normal state
MVJCE Engineering Physics Module II
17
TYPE II SUPERCONDUCTORS
Type II superconductor has two critical magnetic fields Hc1 and Hc2. When the applied magnetic
field (H) is lesser than the Hc1, superconductor completely expels the magnetic field and
behaves as a perfect diamagnetic. For the applied field between Hc1 and Hc2 , magnetic flux
partially penetrates the superconductor (shown in figure 5b), where Meissner effect is
incomplete.
Figure 5 Type II superconductors
This partial penetration is in the form of a regular array of
normal conducting regions. These normal regions allow the
penetration of the magnetic field in the form of thin
filament, called vortex. The material surrounding this
normal can have zero resistance. Vortex region are
essentially filaments of normal conductor that run through the
material when an external magnetic field increases , the number of vortex increases. The number
of vortex increase until the field reaches the upper critical field Hc2, the vortex crowd and join up
so that the entire materials become normal.
BCS THEORY
According to classical physics , part of the resistance of a metal is due to collisions between free
electrons and lattice vibration known as phonons. And part of resistance is due to scattering of
electrons from impurities. In 1957 John Bardeen , Cooper and Schrieffer developed a theory of
superconductivity called BCS theory which explains the loss of electrical resistance due to
electron pairing called Copper pair.
In normal metal, the electrical current are carried by electrons which are scattered giving rise to
resistance. since electrons each carry negative electric charge, they repel each other. In a
superconductor, there is an attractive force between electrons of opposite momentum and
a b
super conducting
state, no magnetic
flux penetrate Mixed state,
partially magnetic
flux penetrate
normal conducting
region , which allow
the magnetic flux to
penetrate through
MVJCE Engineering Physics Module II
18
opposite spin that overcomes this repulsion enabling them to form a pairs. These pairs are able to
move through the material effectively without being scattered.
An electron passes through the lattice and positive ions are attracted to it, causing a distortion in
their nominal positions. The second electron come along attracted by the displaced ions since
having high positive charge. Hence the electron forms a pair through the phonon interaction.
HIGH TEMPERATURE SUPERCONDUCTOR
High temperature superconductors are which shows transition at higher temperature greater than
the boiling temperature of liquid nitrogen (77K). Until 1986, transition temperature for
superconductors was recorded with 23K. Bednorz and Muller discovered new class of material,
La2CuO4 which has transition at 30K. Soon after other superconducting cuprates materials were
discovered with even high transition temperature. YBa2Cu3O7 which shown superconductivity at
critical temperature of 135K. These temperature could be achieved with liquid nitrogen (77K) to
cool them.
APPLICATION OF SUPERCONDUCTOR
MAGLEV VEHICLES
Magnetically levitated vehicles are called Maglev vehicles.
The phenomenon on which the magnetic levitation is based on
Meissner effect. The Levitating vehicle consist of powerful
electromagnet made from superconductors built on its base.
Normal electromagnets on a guideway repel the superconducting electromagnets to levitate the
vehicle. During motion of the vehicle , the absence of contact between the moving and
stationary systems, the friction is eliminated. Hence great speed could be achieved with very low
energy consumption.