Prof. Vilas Shamrao patil

1. 4.5 CRITICAL FIELD AND CRITICAL TEMPERATURE
In 1913, Kamerlingh Onnes observed that a
superconductor regains its normal state below the critical
temperature if it is placed in a sufficiently strong magnetic
field. The value of the magnetic field at which the
superconductivity vanishes is called the threshold or the
critical field, Hc, and is of the order of a few hundred
oersteds for most of the pure superconductors. This field
changes with temperature. Thus we find that the
superconducting state is stable only in some definite
ranges of magnetic fields and higher temperature.
Fig. 4.3. Variation of penetration depth with temperatures
for Tin.

2. For higher temperature fields and temperatures, the
normal state is more stable. A typical plot of critical
magnetic field versus temperature for lead is shown in Fig.
4.4. Such a plot is also referred to as the magnetic phase
diagram. These types of curves are almost parabolic and
can be expressed by the relation
Hc = Hc(0)[1 −
T2
Tc
2]
where Hc(0) is the critical field at 0 K. Thus, at the critical
temperature, the critical field becomes zero,
i.e.𝐻𝑐( 𝑇𝑐) = 0
Fig. 4.4. Variation of I Hc with T for Pb.
4.6 TYPE I AND TYPE II SUPERCONDUCTORS

3. The London electromagnetic theory, theory proposed
by Gorter, Casimir and BCS showed that, more than 24
elements and many alloys and compounds possess the
superconducting properties, and now new
superconductors are being discovered continually, as new
structures and degree of purity of crystalline material
becomes available. No particular type of crystal lattice
seems to be necessary for superconductivity, since nearly
all types of metals containing tight but not very tight
packing of atoms, can possess the property of
superconductivity. The exception for this is, silver, gold
and copper metals which are good conductors at normal
temperature. The only difference in respect of this is that,
different metals will possess the property of
superconductivity at different critical temperatures. The
critical temperature is that temperature at which the
resistivity of the metal drops to zero. It is denoted by Tc.
It is also called as a "transition temperature", since at this
temperature the transition of the metal takes place from
normal to superconducting state Transition or critical
temperature is different for different metals. It depends
upon the lattice structure of the metal. viz. Tc = 7.22° K for

4. Lead, Tc =4.152°K for Mercury, Tc = 2.38°K for Thallium,
Tc= 14.7°K for Niobium nitrate and Tc = 8.0°K for Niobium.
The superconducting properties of the metals can be
changed by varying (i) temperature, (ii) magnetic field, (iii)
magnetic stress, (iv) impurity, (v) atomic structure, (vi)
size, (vii) frequency of excitation of applied electric field
and (viii) isotopic mass.
Superconductors have been classified as type I and
type II depending upon their behaviour in an external
magnetic field, i.e., how strictly they follow the Meissner
effect. We describe below these two types of
superconductors.
4.6.1. TYPE I OR SOFT SUPERCONDUCTORS
In the superconducting state, the complete and abrupt
loss of resistance must be a consequence of some
fundamental change in the electronic or atomic structure
of the metal. Because of this change some other physical
properties may also change. Depending upon the nature
of these changes, there are two types of superconductors.
Type I : The superconductors in which only loss of

5. resistance takes place at transition temperature while
other following physical properties remain unchanged.
(i)The x-ray diffraction pattern is the same both above and
below the transition temperature Tc which shows that no
change of crystal (metal) lattice is involved. The absence
of any appreciable change in the intensity distribution also
shows that the change in electronic structure must be very
slight.
(ii) There is no appreciable change in reflectivity of the
metal either in visible or in the infrared region, although
the optical properties are usually closely connected with
the electrical conductivity.
(iii) There is no change in the absorption of fast or slow
electrons. The photoelectric properties are also
unchanged.
(iv) In the absence of the magnetic field there is no latent
heat and no change of volume at the transition.
(v) The elastic properties and thermal expansion do not
change in the transition. This is probably due to
inadequate sensitivity of the experimental methods

6. Fig. 4.5. Magnetization curve of pure lead at 4.2 K.
The superconductors which strictly follow the
Meissner effect are called type I superconductors. The
typical magnetic behaviour of lead, a type I
superconductor, is shown in Fig. 4.5. These superconduc-
tors exhibit perfect diamagnetism below a critical field He
which, for most of the cases, is of the order of 0.1 testa.
As the applied magnetic field is increased beyond He, the
field penetrates the material com-pletely and the latter
abruptly reverts to its normal resistive state. These
materials give away their superconductivity at lower field
strengths and are referred to as the soft superconductors.
Pure specimens of various metals exhibit this type of

7. behaviour. These materials have very limited technical
applications owing to the very low values of Hc.
4.6.2. TYPE II OR HARD SUPERCONDUCTORS
Type II : The superconductors in which, along with the loss
of resistance, the following physical properties also
change at transition temperature.
(i)In superconducting metals, magnetic properties
remarkably change in comparison to electrical properties.
In the superconducting state, practically no magnetic flux
is able to penetrate the metal, which thus, behaves as if it
had zero permeability or a strong diamagnetic
susceptibility. Due to this property, the shape of the
specimen plays an important role and when
superconductivity is destroyed by a magnetic field, the
magnetic behaviour becomes complicated for any shape
except that of the long cylinder parallel to the field. In such
circumstances, the specimen breaks up into a mixture of
superconducting and normal regions known as the
"Intermediate State".

8. Fig. 4.6 : Temperature Variation of Sp. heat
(ii) The specific heat of a superconductor is
discontinuously higher just below the critical temperature
as shown in Fig. 4.9 viz. For tin the sp. heat is 1.9. x 10- 4
watt.sec / (g) (°k) just above the critical temperature and
is equal to 2.79 x 10-4 Watt-sec / (g) (°k) just below the
critical temperature. In the intermediate state, the sp.
heat may be several times higher than these values. If the
superconducting transition takes place in the presence of
magnetic field, transition in latent heat and small change
in volume takes place.
(iii) All thermo-electric effects disappear in the
superconducting state.

9. (iv) The thermal conductivity changes discontinuously
when superconductivity is destroyed in a magnetic field.
The thermal conductivity of superconductors undergoes a
continuous change between two phases in the absence of
magnetic field and is usually lower in the superconducting
phase for pure metal as shown in the Fig. 4.7 viz. The
thermal conductivity of
Fig. 4.7. Magnetization curve of a lead-exceeds Ha,
I : Superconducting state
II: Vortex or mixed or intermediate state
III: Normal state

10. These superconductors do not follow the Meissner
effect strictly, i.e., the magnetic field does not penetrate
these materials abruptly at the critical-field. The typical
magnetization curve for Pb-Bi alloy shown in Fig. 4.7
illustrates the magnetic behaviour of such a
superconductor. It follows from this curve that for fields
less than Ha, the material exhibits perfect diamagetism
and no flux penetration takes place. Thus for H <Hc1, the
material exists in the super-conducting state. As the field
-exceeds Hc1,the flux begins to bismuth alloy at 4.2 K.
penetrate the specimen and, for H = Hc2 the complete
penetration occurs and the material becomes a normal
conductor. The fields Hc1 and Hc2 are called the lower and
upper critical fields respectively. In the region between
the fields Hc1and Hc2, the diamagnetic behaviour of the
material vanishes gradually and the flux density B inside
the specimen remains non-zero, i.e., the Meissner effect
is not strictly followed. The specimen in this region is said
to be existing in the vortex or intermediate state which
has a complicated distribution of superconducting and
non-superconducting regions and may be regarded as a
mixture of superconducting and normal states. The type II
superconductors are also called the hard superconductors

11. because relatively large fields are needed to bring them
back to the normal state. Also, large magnetic hysteresis
can be induced in these materials by appropriate
mechanical treatment. Hence these materials can be used
to manufacture superconducting wires which can be used
to produce high magnetic fields of the order of 10 tesla.
Apart from some metals and alloys, the newly developed
copper oxide superconductors belong to this category and
have Ho of about 150 tesla.
Fig. 4.8. Entropy versus temperature for aluminium.
7. : Conclusions from the BCS theory

12. 1. The electron-lattice-electron interaction is attractive
and can overcome the Coulomb repulsion between
electrons.
2. An attractive interaction between electrons can also
lead to a ground state of the entire electronic system
which is separated from excited states by an energy gap.
The critical field, thermal properties and most of the
electromagnetic properties are the consequences of
energy gap.
3. It gives the isotope effect.
4. The London penetration depth and the Pippard
coherence length are natural consequences of the BCS
ground state.
5. Several specialized effects, such as quantization of
magnetic flux through superconducting ring, have given
impressive evidence for the BCS theory.
6. Thus, superconductivity is the special state of the solid-
metal or element, which occurs in low temperature
region. When metal acquires this state, its electrical
resistance becomes zero and hence it can conduct very
large amount of electric current without any loss of

13. electrical power. Because of this property, in the
beginning it was known as "perfect conductor".
Uses of Superconductors
There are wide applications of superconductors in the
field of engineering including radioelectronics. This new
branch of electronics based on superconductivity is
known as low temperature electronics, which is
commonly known as cryogenic electronics or simply
"Cryoelectronics". In this branch of electronics, by using
superconductors, "supersensitive miniature receivers"
capable of detecting extremely weak radio signals to which
common receivers are insensitive, are manufactured.
Large scale (LSI) and Very Large Scale (VLSI) integrated
circuits are designed for a new class of electronic
computers. The superconductors are also used to
increase the frequency stability and frequency
selectivity in microwave appliances. They are also used
for the extension of radiowave bands into microwave
region.
Further, the superconductors are used in the
construction of
following equipments.
1.Microwave and far infrared frequency oscillators.

14. 2.Superconducting magnetometers capable of measuring
magnetic fields whose induction B is smaller than 10-
"
Tesla.
3.Superconducting galvanometer of extremely low
resistance and hence very high voltage sensitivity, down
to 10-11 V.
4.High-responsivity photodetectors ( bolometers) with a
threshold
response of about 10 i
's
W per hertz of the transmission
band of the detecting system.
5.Cryotron switches - the basic elements of amplifiers and
modulators. Superconductivity
6.At low frequencies, cryotron based amplifiers can
detect signals lower than 10-1
'V at a time constant of 1
second, and input resistance below 10-5
Ohm.
7.Resonators with a quality factor of about 1011
in the
microwave band. Superconducting resonators can
improve the frequency stability of common klystrons by a
factor 105
or 106
.
8.Superconducting filters - These filters offer the
possibility of increasing the selectivity in the rejection
band by a factor of 103
to 106
in comparison with
common filters.
9.Superconductivity enables to decrease the diameter of
'h f' cables from 10 cm and over to a few millimeters.

15. 10.High-current high-magnetic field solenoids. Wire
solenoids made of certain alloy superconductors can
produce magnetic fields larger than 10 Webers/m2, with
no power dissipation.
11.Electromagnets - The strong diamagnetism of
superconductors offers the possibility of supporting
heavy loads by a magnetic field.
12.Frictionless bearings for rotating equipments.
13.Computer memory cells - These are utilised in the form
of a closed superconducting circuit in which a persistence
current can be induced for the purpose of writing and
storage of information in computers.
14.By using Meissner effect, it is possible to design the
railway track on which the train can run with high speed
without friction with the railway track.
There are wide applications of superconductors in the
field of engineering including radioelectronics.
i)The superconductors are used to increase the frequency
stability and frequency selectivity in microwave appliances.
ii)They are also used for the extension of radiowave bands
into microwave region.
iii)At low frequencies, cryotron based amplifiers can detect
signals lower than 10-1'V at a time constant of 1 second,
and input resistance below 10-5
Ohm.
(vi) Resonators with a quality factor of about 1011
in the
microwave band. Superconducting resonators can

16. improve the frequency stability of common klystrons by a
factor 105
or 106
.
(vii) Superconducting filters - These filters offer the
possibility of increasing the selectivity in the rejection
band by a factor of 103
to 106
in comparison with
common filters.
(viii) Superconductivity enables to decrease the diameter of 'h
f' cables from 10 cm and over to a few millimeters.
(ix) High-current high-magnetic field solenoids. Wire
solenoids made of certain alloy superconductors can
produce magnetic fields larger than 10 Webers/m2
, with
no power dissipation.
(x) Electromagnets - The strong diamagnetism of
superconductors offers the possibility of supporting
heavy loads by a magnetic field.
(xi) Frictionless bearings for rotating equipments.
(xii) Computer memory cells - These are utilised in the form of
a closed superconducting circuit in which a persistence
current can be induced for the purpose of writing and
storage of information in computers.
By using Meissner effect, it is possible to design