Superconductivity - Civil Engineering (CE) PDF Download

Superconductivity
Temperature dependence of resistivity of metal
The variation of resistivity with temperature for a metal is as shown in the fig. Resistivity in the case of pure metal decreases with the decrease in temperature and becomes zero at absolute zero temperature. While in the case of impure metals the resistivity of metal will have some residual value even at absolute zero temperature. This residual resistance depends only on the amount of impurity present in the metal and is independent of the temperature. Thus net Resistivity of a metal can be written

as ρ = ρ₀ + ρ(T)

Thus net resistivity of conductor is equal to sum of temperature independent part and temperature dependent part as shown in the graph.

Superconductivity:
Kamerlingh Onnes discovered the phenomenon of superconductivity in the year 1911. When he was studying the temperature dependence of resistance of Mercury at very low temperature he found that resistance of Mercury decreases with temperature with the decrease in temperature up to a particular temperature T_c = 4.15K . Below this temperature the resistance of mercury abruptly drops to zero. Between 4.15K and Zero degree Kelvin Mercury offered no resistance for the flow of electric current. The phenomenon is reversible and material becomes normal once again when temperature was increased above 4.15K. He called this phenomenon as superconductivity and material which exhibited this property as superconductors.

Thus the phenomenon of super conductivity is defined as:

“The phenomenon in which resistance of certain metals, alloys and compounds drops to zero abruptly, below certain temperature is called superconductivity”

The temperature, below which materials exhibit superconducting property is called critical temperature, denoted by Tc. Critical temperature Tc is different for different substances. The materials, which exhibit superconducting property, are called superconductors. 
Above critical temperature material is said to be in normal state and offers resistance for the flow of electric current. Below critical temperature material is said to be in superconducting state. Thus Tc is also called as transition temperature. 

Meissner Effect 
In 1933, Meissner and Ochsenfeld showed that when a superconducting material is placed in a magnetic field, it allows magnetic lines of force to pass through, if its temperature is above T_c. If temperature is reduced below the critical temperature T_c ,it expels all the lines of force completely out of the specimen to become a perfect diamagnetic material. This is known as Meissner effect.

Since superconductor exhibits perfect diamagnetism below the critical temperature T_c, magnetic flux density inside the material is zero.

Therefore B = 0, for T < T_c Relationship between flux density and the strength of the magnetizing field is given by B = µ₀(M + H)

µ₀ = Absolute permeability of free space
M = Intensity of magnetization of the material and
H = Strength of the magnetizing field

∵ B = o

0 = µ₀(M + H)

or M = −H

Thus superconductor possesses negative magnetic moment when it is in superconducting state.

Critical field
We know that when superconductor is placed in a magnetic field it expels magnetic lines of force completely out of the body and becomes a perfect diamagnet. But if the strength of the magnetic field is further increased, it was found that for a particular value of the magnetic field, material looses its superconducting property and becomes a normal conductor. The value of the magnetic field at which superconductivity is destroyed is called the Critical magnetic field, denoted by H_c . It was found that by reducing the temperature of the material further superconducting property of the material could be restored. Thus, critical field doesnt destroy the superconducting property of the material completely but only reduces the critical temperature of the material.

Critical magnetic field H_c depends on the temperature of the material. The relationship between the two is given by