SUPERCONDUCTING CRITICAL TRANSITION TEMPERATURE (Tc, Kelvin)

Below a certain critical temperature some metals, usually those that are poor conductors of electricity at normal temperatures, become superconductive, that is, their electrical resistivity falls to zero. Any electrical current induced in a superconducting ring, flows without any voltage drop across the material, and without any perceptible decay. Superconductivity was first discovered when the temperature of lead was lowered to that of liquid helium, 4.2 degrees Kelvin. Any magnetic field pervading the material before superconductivity sets in, is suddenly and totally excluded from the material (the Meissner Effect) at the critical temperature, this exclusion is powerful enough to levitate the material from a magnet placed underneath. No magnetic field can penetrate a superconductor, they are perfectly diamagnetic. Putting a magnetic near a superconductor induces a superconducting current within it generating an exactly equal but opposing magnetic field. However, if the magnetic field is above a certain critical strength, all superconductivity suddenly vanishes as the field penetrates the conductor.

In a rotating metal, the electrons are dragged around with the rotation, but, in an analogy with rotating superfluids (see Helium), the electrons in a rotating superconductor get left behind, creating a current which generates a magnetic field. This is known as the London moment, and is precisely aligned with the spin axis.

Superconductors also have a certain critical current, which if exceeded, will also destroy the superconductivity.

Superconductors fall into two categories, type I and type II superconductors, which is determined by their response to a magnetic field. Type I superconductors have just one sharp but quite low critical field. Pure elements tend to be type I superconductors. Type II superconductors tend to be alloys or transition elements with high values of normal resistivity, and are characterised by having upper and lower critical fields. In a type II superconductor, when the field exceeds the first critical value, the magnetic field penetrates and is confined within the material in narrow filaments. These filaments are normal and non-superconducting. Because the superconducting threads short out the normal threads, the material is still superconducting. As the field increases, so does the number of filaments, until the field exceeds the second critical value when the whole sample reverts to the normal non-superconducting state. Elements, like technetium, vanadium and niobium are Type II superconductors, with an upper and lower critical magnetic field (see Superconducting critical field below).

Elements like gadolinium, lanthanum and mercury, exhibit two or more superconducting critical temperatures because they exist in more than one phase. In this case, the highest temperature superconducting phase is quoted.

A new class of ceramic high temperature superconductors, the sintered metal copper oxides, variously also containing yttrium, lanthanum or strontium with barium or thallium, have been found. A mercury based cuprate, HgBa₂Ca₂Cu₃O₈, having the record Tc at 134 Kelvin, which is higher than the boiling point of liquid nitrogen of only 77 Kelvin. These high temperature superconductors are generally oxygen-deficient modifications on the perovskite structure. It appears that the greater the distance between Cooper pairing electrons, the shorter is the coherence length, the lower is the effective electron mass, and the higher is the transition temperature. The critical currents for these high temperature superconductors are generally much smaller (about 10⁴A/cm²) than for type II superconductors (10⁵A/cm²). However, the Holy Grail of room temperature superconductivity remains elusive.

Magnesium diboride, MgB₂ has the highest superconducting transition temperature of any metallic alloy known as of 2006, being 40 Kelvin. Superconductivity in metals is caused by the movement of electrons through the material setting up vibrational energy in the atomic lattice, which causes a shift in charge such as to attract a second electron to the first. The two electrons are then paired up. It is this pairing of electrons which allows the electron pair to move through the atomic lattice without bumping into any atoms in the lattice, which would then cause electrical resistance. The vibrations in the atomic lattice are phonons. Despite this record breaking superconducting temperature theoreticians calculate that in magnesium dibromide only 3% of the electrons are paired up, and if they can find a material with better matching between phonon and electron-pair vibration frequencies, the coupling electron pairing could reach 100% where it should be possible to achieve a suerconducting temperature as high as an amazing 430 Kelvin. It is just a metter of finding a material that has 100% coupling efficiency. There is no guarantee that such a material exists, after all there are only 92 odd elements from which to make any such alloy.

Another class of superconductors, called exotic superconductors, have recently been discovered where, even in the non-superconducting state, they exhibit anomalously high values of specific heat due to the effective mass of the electrons in f-orbitals being up to 1000 times higher than is normal, which is caused by the weak overlap of f-orbitals in neighbouring ions. In the superconducting state they possess properties very different from those of other superconductors, and may have non-zero angular momentum. These so-called 'heavy fermion' compounds include UBe₁₃, UPt₃, CeAl₃ and CeCu₂Si₂.

Superconductivity is a quantum phenomenon, the current within superconductors is quantised. Superconductivity occurs when electrons (half-spin fermions) pair up in Cooper pairs, forming spinless bosons, and co-operatively avoid being scattered by the crystal lattice, which causes electrical resistivity.

Certain alloys of metals have much higher superconducting temperatures than for pure elements; Nb₃Sn has a critical temperature of 18.45K, a far stronger critical field of 24,500 mTesla, and a critical current of 500,000 amps/cm². Main uses are in superconducting coil electromagnets to generate extremely high magnetic fields in NMR medical scanners, magnetic levitation trains and fundamental particle accelerators. Although the d.c. resistance drops to zero below the critical field, the ac resistance is not zero, and rises with frequency. Above a certain critical frequency, given by fc=4KTc/h, the metal becomes normal and not superconductive. The superconducting critical temperature for an isotope of any one element is proportional to the square root of its isotopic mass. See superconducting critical field. See Helium for discussion on superfluidity.

Generally, poor conductors of electricity are superconductors whereas good conductors are not. The alkali metals sodium, potassium, etc are good conductors and do not exhibit any superconductivity even when cooled to absolute zero. For a long time it was thought that the excellent conductors of electricity, the noble metals (gold, silver and copper) and the platinum metals (such as platinum and palladium) would not become superconducting even at absolute zero temperature. It is now known, however, that the superconducting critical temperatures of gold and platinum cannot be higher than 0.1 milli Kelvin, and that minuscule concentrations (0.01 ppm) of contaminants like chromium or manganese in the gold will completely suppress any superconductivity. Even when pure, the superconductivity in these metals is not observable unless external magnetic fields are carefully shielded, because the superconducting critical field is extremely low. Rhodium holds the record low with a Tc of only 325 microKelvin, and a Bc of just 4.9 microTesla.

Of the elements, niobium has the highest superconducting transition temperature of 9.2 Kelvin, and Nb₃Ge the highest known of the metallic alloys of 23.3 Kelvin. Alkali-metal doped fullerenes, an allotropic form of carbon possessing a football shaped molecule, have even higher transition temperatures, the record being 33 Kelvin for Cs₂RbC₆₀ (see Carbon).

At the other end of the scale, very low transition temperature superconductors are going to be very useful for making extremely sensitive real-time light detectors for use in astronomy. In a Superconducting Tunnel Junction device, a single photon incident upon the detector disrupts a Cooper pair causing a current to tunnel across the junction which in doing so generates a larger current which is proportional to the wavelength of the incident photon. The lower the superconducting transition temperature, the easier it is for a photon of lower energy (longer wavelength) to disrupt a Cooper pair and so the greater the resolution of wavelength. It is thought that hafnium, with a Tc of just 0.1 Kelvin, will offer a wavelength discrimination of 1nm. When these detectors are miniaturised and combined into a two dimensional imaging array this will be the first light detector which cam simultaneously measure the photons direction, arrival time and wavelength; the only parameter it cannot measure is polarisation.

A Josephson junction consist of two superconductors sandwiching a very thin insulator (normally a metal oxide film less than 2nm thick). When a small voltage is applied across the junction, a small current proportional to the applied voltage will tunnel at the speed of light across the insulator. Superimposed on this dc current is an oscillating component whose frequency (f) is an exact and fundamental function of the applied voltage (V) according to the formula f=483.5979×V (in THz) to an accuracy of ±0.4ppm. Because frequency can be measured very precisely, this enables a new and highly accurate voltage standard to be derived based on frequency.
A micro-chip with 6000 Superconducting Josephson junctions has been constructed that operates at cryogenic temperatures.

SQUIDS, superconducting quantum interference devices, are exquisitely sensitive to minute changes in magnetic fields, and are used in MRI, magnetic resonance imagers, in medical body scanners, and other devices. A SQUID consists of two superconducting Josephson junctions in parallel, with the magnetic field to be measured arranged so as to pass through the loop so formed. The interference between the voltages generated by the two junctions enables the device to measure changes in magnetic field as small as 10^-13 Tesla (10^-9 Gauss). [The Earths magnetic field is of order 1 Gauss]. SQUIDS exhibit the best signal to noise ratio of any detector because they generate no random noise.

Superconducting Critical Temperature & Critical Field by Element 1-100

SUPERCONDUCTING CRITICAL MAGNETIC FIELD
Superconductors also have a certain critical current, which if exceeded, will also quench the superconductivity. The critical field is quoted at absolute zero, as it decreases at an ever increasing rate with increasing temperature, becoming zero at the critical temperature. Certain elements, like gadolinium, lanthanum and mercury, exhibit two or more superconducting critical temperatures because they exist in more than one phase. In this case, the highest temperature superconducting phase is quoted. When superconducting, heat conductivity is greatly reduced than when normal. The highest superconducting critical field is exhibited by niobium at 198 milliTeslas at zero Kelvin, this is very small by comparison with the superconducting critical fields of superconducting alloys, the alloy PbMo₆S₈ holds the record at 54 Teslas at 4.2 Kelvin (Tc=14 Kelvin).

Superconductivity is caused by the cooperative pairing up of two electrons with opposing spins (electrons are fermions, have half-integral spin, and obey Fermi-Dirac statistics) to form a pair with integral spin, called a boson, which obeys Bose-Einstein statistics. Since, by the Pauli exclusion principal, no two fermions can occupy the same energy levels, the fermionic electrons in an ordinary conductor exist in a continuum of non-zero energy levels, but in a superconductor, the bosononic electron pairs all have the same energy. This is Bose condensation, which is also responsible for the superfluid behaviour of liquid helium-II at cryogenic temperatures. The spins of the electrons pair off anti-parallel, to form a boson of zero spin. These pairs of electrons, called Cooper pairs, co-operate over largish distances, and this enables them to successfully avoid being scattered by the atoms of the crystal lattice, which would otherwise give rise to electrical resistance. Because the paired electrons behave as one, and all pairs move in a coordinated way with each other and not in a random fashion as they do when normal, the ability to transport heat (disorder) is greatly diminished: superconductors are thermally insulating. However, because the spins are paired anti-parallel (forming a spin zero pair), any magnetic field will affect the electrons differentially, increasing the energy of one whilst decreasing the energy of the other. When the electrons no longer have identical energies, the bosonic pairing falters and superconductivity ceases; this is the mechanism by which strong magnetic fields quench superconductivity at the critical field strength. But things are vastly different if the electrons pair off with spins parallel, forming a spin-1 boson. With this arrangement, any magnetic field would affect both electrons identically, and the Cooper pairing would be preserved. Superconductors of this kind, if they exist, would be unaffected by strong magnetic fields, and would be ideal for generating intensely powerful magnetic fields. Scientist already know that liquid helium-3 forms a spin-1 superfluid, they are now looking for such spin-1 superconductors. (See helium).

A superconductor with spin-1 boson Cooper pairing of the electrons (as described above) has recently (2004) been experimentally confirmed in strontium ruthenide, where the electrons are paired up with their spins parallel rather than in the usual anti-parallel alignment. Here the total spin does not cancel to zero, but is unity.

POSITIVE-ION CONDUCTING SUPERCONDUCTORS
When neutrons were fired at an alloy of niobium and palladium saturated with hydrogen gas, the neutrons sailed straight though the crystals of metal-hydride instead of scattering off the hydrogen as expected. It seems that the hydrogen nuclei (protons) were pairing up becoming de-localised, making collisions between the incoming neutrons and the protons much less likely.

This may lead the way to a novel superconducting material where it is predicted that positively-charged protons within the crystal lattice undergo Bose-Einstein condensation into the Cooper-pair state at low temperatures. (Whereas in standard superconductors it is the negatively-charged electrons that undergo Cooper pairing). It is thought that the crystal lattice would have to be permeated with hydrogen gas (to supply the free protons) at a concentration of one to one for this to work properly, which is probably an impossibly high concentration of hydrogen. However, if achieved, because the proton is much heavier than an electron, and the Cooper pairing less likely to be destroyed by higher temperatures, the superconducting transition temperature may be a lot higher, possibly as high as room temperature for these superconductors. On the other hand, the impurities are much more likely to destroy the Cooper pairing, and the superconductivity may be limited to small perfect crystals of the material.

Rhodium holds the record low with a Tc of only 325 microKelvin, and a Bc of just 4.9 microTesla.