In this article we will discuss about the superconductivity of metals.
General Aspects Relating to Superconductivity of Metals:
Equation Rt = R[1 + α(t – 20)] holds for temperature below 20°C. But at very low temperature, some metals acquire zero electrical resistance and zero magnetic induction, the property known as superconductivity.
Some of the important superconducting elements are- Aluminium, Zinc, Cadmium, Mercury, and Lead. Typical superconducting compounds and alloys are- PbAu, PbTl2, SnSb, CuS, NbN, NbB and NrC.
The characteristic temperature at which a metal becomes superconducting depends on:
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(i) The strength of magnetic field;
(ii) Whether the field is applied externally or is the result of current used to measure the resistance.
An interesting feature to note is that metals such as copper, silver and gold which are very good conductors do not show superconducting properties whilst metals and compounds which are superconducting are rather bad conductors at room temperature. Further monovalent metals and ferromagnetic and antiferromagnetic metals are not superconducting.
Superconductivity was discovered in 1911 by Kamerlingh Onnes in Lwden when he observed that the electrical resistivity of mercury disappeared completely at temperatures below approximately 4.2°K. Fig. 7.10 shows the resistance of mercury as a function of temperature. The temperature at which there is a transition from “normal” state to “superconducting” state is called “transition temperature”, Tc, Table 7.13 gives superconducting elements and compounds and their transition temperatures.
The fact, that a superconductor has zero resistance, is often doubted. However it has already been, firmly established experimentally that the resistance is zero. Thus it has been seen experimentally that an inducted current of several hundred amperes continues to flow unreduced in a superconductor ring for over a year.
Superconductivity—The Free Electron Model:
The resistivity of the metals, according to free electron model of metals is given by:
It is evident from eqn. (7.6) that resistivity decreases as the temperature is lowered because as temperature decreases the lattice vibrations begin to “freeze” and hence the scattering of the electrons diminishes. This result in a large ‘I’ and hence a smaller r. If average time of collision becomes infinite at sufficiently low temperature, the resistivity r vanishes entirely which is observed in case of superconducting materials.
Critical Magnetic Field and Critical Temperature:
The transition temperature of a superconductor can be reduced by the application of magnetic field. Refer to Fig. 7.11, suppose a superconductor has a temperature T < Tc. If a magnetic field H is applied; the material is superconducting until a critical field Hc is reached such that H > Hc, the material is in the normal state.
The curve in Fig. 7.11 represents schematically the functional relationship between the critical field Hc and the temperature of the superconductor. The transition from the superconducting to the normal state under the influence of a magnetic field is reversible.
The function HC(T) follows with good accuracy the relation given below:
Where H0 and Tc are the constant characteristics of the material. The order of Hc for most of the superconducting materials is a few 10-4 A/m.
The magnetic field which cause a superconductor to become normal is not necessarily an externally applied field; it may also arise as a result of electric current flow I in a conductor. Thus consider a long circular wire of radius r carrying a current I. Then the superconductivity in this ring gets destroyed if the current I exceeds a certain critical value Ic which will produce the critical magnetic field Hc at the surface of the wire.
Obviously this critical current Ic is given by:
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Ic = 2r Hc, …(7.8)
This is known as Silsbee rule. This rule prohibits the use of superconductor in the coil form for the purpose of producing strong magnetic field.
Persistent Current:
In a superconducting material, current will continue to flow in a closed loop as long as the loop is held below the critical temperature Tc, such a steady current which flows with undiminishing strength is called a persistent current.
Critical Current:
The minimum current that can be passed in a sample without destroying its superconductivity is called critical current (IC).
The critical temperature is different for different materials as it depends on their isotropic mass.
Both the above quantities are related as-
Tc . √M = Constant …(7.9)
where M is the isotropic mass. It is therefore, clear that critical temperature decreases with the increasing isotropic mass.
The following points about superconductivity are worth noting:
1. The superconductivity will disappear if:
(i) The temperature of the material is raised above its critical temperature, or,
(ii) A sufficiently strong magnetic field or current density is employed. This critical magnetic field or the field at which superconductivity vanishes and the critical current density are a function of temperature and are low for high temperatures.
2. The transition from the superconducting state to conducting state is reversible.
3. Regarding design of electrical machines it may be stated that with the introduction of superconducting materials, much higher current densities are possible and practical machines working at low temperatures (below) the transition temperatures of the materials used) may be developed.
Supercooled coils can produce flux densities of 10 Wb/ m2 or higher. In comparison, it is only possible (with great difficulty) to produce a flux density 0.1 Wb/m2 in the absence of iron parts by using normal coils at room temperature. Thus from above it is clear that the machine sizes can be considerably reduced with the development of superconductors.
Meissner Effect:
It was observed by Meissner and Ochsenfield that when a superconductor is cooled in a magnetic field to below the critical temperature Tc, then at transition, the lines of induction are pushed out.
Thus:
“The expulsion of magnetic flux from the interior of a piece of superconducting material as the material undergoes the transition to the superconducting phase is known as Meissner effect”.
Meissner effect is reversible. When T > Tc the substance is in normal state.
We know that, B = μ0 (H + M) … (i)
where, B = Magnetic flux density,
H = Applied magnetic field, and
M = Magnetisation.
c. Owing to diamagnetic nature, superconducting materials strongly repel external magnets; it leads to a levitation effect.
Cryotron:
Cryotron is based on the fact of disappearance of superconductivity for fields above the critical field. Refer to Fig. 7.15. Consider a wire made of a superconducting material SA. inside a coil of a superconducting material SB. Let the temperature of the system be below the transition temperature of the two materials, so that both are superconducting.
The current (I1) in the central wire A can then be controlled by current in the coil because the magnetic field produced by the latter may exceed the critical field of the core material at the operating temperature. The control current (I2) required to make the core “normal” depends on the D.C. current flowing through the core because this current also produces a magnetic field.
A metal such as tantalum is useful as a core material if the operating temperature is that of a liquid helium bath (4.2°K). The coil material must be chosen so that it remains superconducting even if the control current flows; niobium or lead are thus suitable coil materials. The single cryotron represented in Fig. 7.15 may be used as an element in a more complicated device such as a flip-flop.
Since the elements are superconductors, the power consumption is very low. A large digital computer using cryotrons may require extremely small power of the order of only half a watt (excluding of course the terminal equipment and the helium crystal). Further the size of such a computer will be extremely small (occupying only about cubic foot).