# SUPERCONDUCTIVITY

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These notes have been compiled by Francisca Wheeler and Peter Freilinger during the HST 2001 and  are intended  for teachers and students in the High School. They are a brief attempt to alert them for an important property of certain materials, which has many applications, from the large accelerators used in the search for fundamental particles, to applications in medicine, in computers,  transport, etc...

What is superconductivity?

Superconductivity is a phenomenon observed in several metals and ceramic materials. When these materials are cooled to temperatures ranging from near absolute zero ( 0 degrees Kelvin, -273 degrees Celsius) to liquid nitrogen temperatures ( 77 K, -196 C), their electrical resistance  drops with a jump down to zero.

The temperature at which electrical resistance is zero is called the critical temperature (Tc)  and this temperature is a characteristic of the material as it is shown in the following table:

 Material Type Tc(K) Zinc metal 0.88 Aluminum metal 1.19 Tin metal 3.72 Mercury metal 4.15 YBa2Cu3O7 ceramic 90 TlBaCaCuO ceramic 125

The value of the critical temperature is dependent on the current density  and the magnetic field as shown in this picture

The cooling of the materials is achieved using liquid nitrogen or liquid helium for even lower temperatures.There is already in this small table a clear separation between the low and high  temperature superconductors. While superconductivity at low temperature is well understood, there is no clear explanation as yet of this phenomena at "high temperatures".

The critical temperature is known to be inversely proportional to the square root of the atomic mass. Take a look at the periodic table , to see which elements have been found to have superconducting properties.

Some background .....

Electrical resistance in metals arises because electrons moving through the metal are scattered due to deviations from translational symmetry.  These are produced either by impurities, giving raise to a temperature independent contribution to the resistance, or by the vibrations of the lattice in the metal.

In a superconductor below its critical temperature, there is no resistance because these scattering mechanisms are unable to impede the motion of the current carriers.   As a negatively-charged electron moves through the space between two rows of positively-charged atoms, it pulls inward on the atoms of the lattice. This distortion attracts a second electron to move in behind it.

An electron in the lattice can interact with another electron by exchanging an acoustic quanta called phonon.   Phonons in acoustics are analogous to photons in electromagnetic. The energy of a phonon is usually less than 0.1 eV (electron-volt) and thus is one or two orders of magnitude less than that of a photon.

The two electrons form a weak attraction, travel together in a pair and encounter less resistance overall. In a superconductor, electron pairs are constantly forming, breaking and reforming, but the overall effect is that electrons flow with little or no resistance.   The current is carried then by  electrons moving in pairs called Cooper pairs.

A Cooper Pair moving through the lattice

The second electron encounters less resistance, much like a passenger car following a truck on the motorway encounters less air resistance.

Below the critical temperature these superconducting materials have no electrical resistance  and so  they can carry large amounts of electrical current for long periods of time without loosing energy as  ohmic heat.  For example, loops of superconducting wire have been shown to carry electrical currents for several years with no measurable loss.  This property offers tremendous challenges and opportunities in the modern world.

MEISSNER EFFECT

Another property of superconducting materials is the Meissner Effect. It was observed that as a magnet is brought near a superconductor, the magnet encounters a repulsive force.  It can be said that the superconductor completely expels the magnetic field and behaves as a perfect diamagnet.

The classic demonstration of the Meissner Effect.

A superconductive disk on the bottom, cooled by liquid nitrogen, causes the magnet above to levitate. The floating magnet induces a current, and therefore a magnetic field, in the superconductor, and the two magnetic fields repel to levitate the magnet.

This property has implications for making high speed, magnetically-levitated trains, for making powerful, small, superconducting magnets for magnetic resonance imaging, etc.

JOSEPHSON  EFFECT

One other property of superconductors is that when two of them are joined by a thin, insulating layer, it is easier for the electron pairs to pass from one superconductor to another without resistance . This is called the Josephson Effect. This effect has implications for superfast electrical switches that can be used to make small, high-speed computers.

SPECIFIC HEAT

In a superconducting phase transition, the electric resistance changes with a jump, while the energy undergoes a continuous variation.  The specific heat, or the amount of heat necessary to affect its temperature, also changes with a jump.  When a substance is cooled, its specific heat typically decreases but at the critical temperature it increases suddenly.

SUPERFLUIDITY

This phenomenon was first observed in helium at a temperature below 2.17K.  Helium at these low temperatures was seen to flow quite freely, without any friction, through any gaps and even through very  thin capillary tubes.  Once set in circular motion, for example, it will keep on flowing forever - if there are no external forces acting upon it. Unlike all other chemical elements helium does not solidify when cooled down near absolute zero. Physicists explain this phenomenon by extremely weak attractive forces between the almost "perfectly round" atoms and by their rapid motion which is due to Heisenberg's Uncertainty Principle

Bulk superfluid helium has many unusual properties - it can flow up walls and through narrow pores without resistance. Helium-4 and Helium-3 become superfluid below 2.12 and 0.003 Kelvin respectively. However, only a proportion of the Helium becomes superfluid at the transition temperature.

This free movement of helium at a temperature below 2.17K looks very much like the superconductivity behaviour  mentioned above.  To explain this frictionless motion,  we can imagine that all the particles in the liquid are linked together and none of them can be separated, without violating the whole state.

CONCLUSION

Both these two special properties were described by Ziman with a very apt epigram:  "The more of us gather, the merrier we are together".

The future of superconductivity research is to find materials that can become superconductors at room temperature. Once this happens, the whole world of electronics, power and transportation will be revolutionized.

HowStuffWorks    look there for "superconductivity" . You can even find there questions for students

Making High-Temperature Superconductors

Phonon Java program  shows the influence of the lattice to the moving electron

Superconductor Modelling, GJ Barnes