This includes : 1) Superconductivity 2) Superconductor 3) Critical Temperature 4) Properties of superconductor

1. SUPERCONDUCTING
MATERIALS - 1
BY DARSHAN, RAHIL , DHIREN

2. SUPERCONDUCTIVITY
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Superconductivity is a phenomenon in which certain metals, alloys and
ceramics conduct electricity without resistance when it is cooled below a
certain temperature called the critical temperature.
Superconductivity was discovered by Dutch physicist, Heike
Kammerlingh Onnes, in 1911. This new state was first discovered in
mercury when cooled below 4.2K.

3. SUPERCONDUCTOR
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A superconductor is a material that loses all its
resistance to the flow of electric current when it
is cooled below a certain temperature called the
critical temperature or transition temperature Tc.
Example] Mercury(Hg), Zinc(Zn) etc.

4. CRITICAL OR TRANSITION TEMPRATURE
TC :
 The temperature at which materials electrical resistivity
drops to absolute zero is called the critical temperature or
transition temperature TC .
 At and below TC , the material is said to be in the
superconducting state and above this temperature , the
material is said to be in the normal state.
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Temperature in Kelvin
Resistivity in ohm*m
Tc
p0
• Above figure shows the variation of electrical resistivity of a normal metal silver (Ag) and superconducting
metal mercury (Hg) versus temperature .
• From above figure it can be seen that electrical resistivity of normal metal decreases steadily as the temperature
is decreased and reaches a low value at 0K called the residual resistivity po. But in contrast , the electrical
resistivity of mercury suddenly drops to 0 at critical temperature Tc and is 4.2 K for Hg.
• Below the critical temperature not only does the superconductor suddenly achieves zero resistance, it also
exhibits a variety of several astonishing magnetic and electrical properties.

6. PROPERTIES OF SUPERCONDUCTOR
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1) ELECTRICAL RESISTANCE :
The electrical resistance of a superconducting material is very low and is of the
order of 10-7 ohm*m.
2) EFFECT OF IMPURITIES :
When impurities are added to superconducting elements, the superconducting
property is not lost , but the Tc value is lowered.
3) EFFECT OF PRESSURE AND STRESS :
Certain materials are found to exhibit the superconductivity phenomena
on increasing the pressure over them. For example , Cesium is found to exhibit superconductivity phenomena at
Tc = 1.5 K on applying a pressure of 110 bar .
In superconductors, the increase in stress results in increase of the Tc value .

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4) ISOTOPE EFFECTS :
The critical or transition temperature value of a superconductor is found to vary with isotopic
mass. This variation of Tc with its isotopic mass is given by,
i.e. the transition temperature is
inversely proportional to the square root of the isotopic mass of a single superconductor .
5) MAGNETIC FIELD EFFECT :
If a sufficiently strong magnetic field is applied to a superconductor at any
temperature below its critical temperature Tc , the superconductor is found to undergo a transition from the
superconducting state to the normal state.
The minimum magnetic field required to destroy the superconducting state is called the critical magnetic field
(Hc).The critical magnetic field of a superconductor is a function of temperature. The variation of Hc with temperature
is given by,
H = Hc[1 – (T/ Tc)2]
Where is H0 is the critical field at T=0K. The critical field decreases with increase in temperature and becoming zero
at T= Tc

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Below given figure shows variation of critical field Hc as a function of temperature. The material
said to be in the superconducting state within the curve and is non – superconducting in the
region outside the curve.
6) CRITICAL CURRENT DENSITY J AND CRITICAL CURRENT IC :
When the current density
through a superconducting sample exceeds a critical value Jc, the superconducting state is found
to disappear in the sample. This happens because the current through the superconductor itself
generates a magnetic field, and at a sufficiently high current density the magnetic field will start
exceeding the critical magnetic field Hc, thereby making the superconducting state to disappear
in the material.

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Hence , the critical current density can be defined as the maximum current that can be permitted in
a superconducting material without destroying its superconductivity state. The critical current
density is a function of temperature i.e. colder the temperature for superconductor the more is the
current it can carry.
For a thin long cylindrical superconducting wire of radius r , the relation between critical current
and critical magnetic filed Hc is given by,
Ic = 2(pie)rHc
Simalarly the relation between critical current density Jc and critical current Ic is given by,
Jc = Ic/A
Where A is cross sectional area.
7) PERSISTENT CURRENT :
When current is made to flow through a superconducting ring which is at
temperature either equal to its Tc value or less than its Tc value , it was observed that the current
flowing through the material without any significant loss in its value. This steady flow of current in a
superconducting ring without any potential deriving it is called the persistent current.

10. 108) MEISSNER EFFECT :
The complete expulsion of all magnetic field by a superconducting
material is called the MEISSNER EFFECT.
When superconducting material is placed in a magnetic field (H<Hc) at room temperature,
magnetic field is found to peneterate normally throughout the material.
However if the temperature is lowered below Tc and with H<Hc the material is found to
reject the magnetic field penetrating through it as shown in figure,

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The above process occurs due to the development of surface current , which in turns results in
the development of magnetization M within the superconducting material . Hence as the
developed magnetization and the applied field are equal in magnitude and opposite in direction
, they cancel each other everywhere inside the material . Thus below Tc a superconductor is a
perfectly diamagnetic substance (Xm = -1)
The Meissner effect is a distinct characterstic of a superconductor from a normal perfect
conductor . In addition this effect is exhibited by superconducting materials only when the
applied field is less than critical field Hc.

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