Superconductivity



A phenomenon occurring in many electrical conductors, in which the electrons responsible for conduction undergo a collective transition into an ordered state with many unique and remarkable properties. These include the vanishing of resistance to the flow of electric current, the appearance of a large diamagnetism and other unusual magnetic effects, substantial alteration of many thermal properties, and the occurrence of quantum effects otherwise observable only at the atomic and subatomic level.

Superconductivity was discovered by H. Kamerlingh Onnes in Leiden in 1911 while studying the temperature dependence of the electrical resistance of mercury within a few degrees of absolute zero. He observed that the resistance dropped sharply to an unmeasurably small value at a temperature of 4.2 K (?452°F). The temperature at which the transition occurs is called the transition or critical temperature, Tc. The vanishingly small resistance (very high conductivity) below Tc suggested the name given the phenomenon.

In 1933 W. Meissner and R. Ochsenfeld discovered that a metal cooled into the superconducting state in a moderate magnetic field expels the field from its interior. This discovery demonstrated that superconductivity involves more than simply very high or infinite electrical conductivity, remarkable as that alone is.

In 1957, J. Bardeen, L. N. Cooper, and J. R. Schrieffer reported the first successful microscopic theory of superconductivity. The Bardeen-Cooper-Schrieffer (BCS) theory describes how the electrons in a conductor form the ordered superconducting state. The BCS theory still stands as the basic explanation of superconductivity, even though extensive theoretical work has embellished it.

There are a number of practical applications of superconductivity. Powerful superconducting electromagnets guide elementary particles in particle accelerators, and they also provide the magnetic field needed for magnetic resonance imaging. Ultrasensitive superconducting circuits are used in medical studies of the human heart and brain and for a wide variety of physical science experiments. A completely superconducting prototype computer has even been built.



Source: McGraw Hill Encyclopedia

Transition temperatures



It was realized from the start that practical applications of superconductivity could become much more widespread if a high-temperature superconductor, that is, one with a high Tc, could be found. For instance, the only practical way to cool superconductors with transition temperatures below 20 K (?424°F) is to use liquid helium, which boils at a temperature of 4.2 K (?452°F) and which is rather expensive. On the other hand, a superconductor with a transition temperature of 100 K (?280°F) could be cooled with liquid nitrogen, which boils at 77 K (?321°F) and which is roughly 500 times less expensive than liquid helium. Another advantage of a high-Tc material is that, since many of the other superconducting properties are proportional to Tc, such a material would have enhanced properties. In 1986 the discovery of transition temperatures possibly as high as 30 K (?406°F) was reported in a compound containing barium, lanthanum, copper, and oxygen. In 1987 a compound of yttrium, barium, copper, and oxygen was shown to be superconducting above 90 K (?298°F). In 1988 researchers showed that a bismuth, strontium, calcium, copper, and oxygen compound was superconducting below 110 K (?262°F), and transition temperatures as high as 135 K (?216°F) were found in a mercury, thallium, barium, calcium, copper, and oxygen compound.

__________________
||||||||||||||||||||50% Complete

Occurrence

Some 29 metallic elements are known to be superconductors in their normal form, and another 17 become superconducting under pressure or when prepared in the form of thin films. The number of known superconducting compounds and alloys runs into the thousands. Superconductivity is thus a rather common characteristic of metallic conductors. The phenomenon also spans an extremely large temperature range. Rhodium is the element with the lowest transition temperature (370 ?K), while Hg0.2 Tl0.8 Ca2 Ba2 Cu3 O is the compound with the highest (135 K or ?216°F).

Despite the existence of a successful microscopic theory of superconductivity, there are no completely reliable rules for predicting whether a metal will be a superconductor. Certain trends and correlations are apparent among the known superconductors, however—some with obvious bases in the theory—and these provide empirical guidelines in the search for new superconductors. Superconductors with relatively high transition temperatures tend to be rather poor conductors in the normal state.

The ordered superconducting state appears to be incompatible with any long-range-ordered magnetic state: Usually the ferromagnetic or antiferromagnetic metals are not superconducting. The presence of nonmagnetic impurities in a superconductor usually has very little effect on the superconductivity, but the presence of impurity atoms which have localized magnetic moments can markedly depress the transition temperature even in concentrations as low as a few parts per million.

Some semiconductors with very high densities of charge carriers are superconducting, and others such as silicon and germanium have high-pressure metallic phases which are superconducting. Many elements which are not themselves superconducting form compounds which are.

Certain organic conductors are superconducting. For instance, brominated polymeric chains of sulfur and nitrogen, known as (SNBr0.4)x, are superconducting below 0.36 K. Other more complicated organic materials have Tc values near 10 K (?442°F).

Although nearly all the classes of crystal structure are represented among superconductors, certain structures appear to be especially conducive to high-temperature superconductivity. The so-called A15 structure, shared by a series of intermetallic compounds based on niobium, produced several superconductors with Tc values above 15 K (?433°F) as well as the record holder, NbGe, at 23 K (?418°F). Indeed, the robust applications of superconductivity that depend on the ability to carry high current in the presence of high magnetic fields still exclusively use two members of this class: NbTi with Tc = 8 K (?445°F), and Nb3Sn with Tc = 18.1 K (?427°F).

After 1986 the focus of superconductivity research abruptly shifted to the copper-oxide-based planar structures, due to their significantly higher transition temperatures. Basically there are three classes of these superconductors, all of which share the common feature that they contain one or more conducting planes of copper and oxygen atoms. The first class is designated by the chemical formula La2 ?x Ax Cu O4, where the A atom can be barium, strontium, or calcium. Superconductivity was originally discovered in the barium-doped system, and systematic study of the substitutions of strontium, calcium, and so forth have produced transition temperatures as high as 40 K (?388°F).

The second class of copper-oxide superconductor is designated by the chemical formula Y1 Ba2 Cu3 O7??, with ? < 1.0. Here, single sheets of copper and oxygen atoms straddle the rare-earth yttrium ion and chains of copper and oxygen atoms thread among the barium ions. The transition temperature, 92 K (?294°F), is quite insensitive to replacement of yttrium by many other rare-earth ions.

The third class is the most complicated. These compounds contain either single thallium-oxygen layers, represented by the chemical formula Tl1 Can? 1Ba2 Cu nO2 n+3, where n refers to the number of copper-oxygen planes, or double thallium-oxygen layers, represented by the chemical formula Tl2Can?1Ba2 Cu nO2 n+4. The number of copper-oxygen planes may be varied, and as many as three planes have been included in the structure. Thallium may be replaced by bismuth, thus generating a second family of superconductors. In all of these compounds, the transition temperature appears to increase with the number of planes, but Tc decreases for larger values of n.

The spherical molecule comprising 60 carbon atoms (C60), known as a buckyball, can be alloyed with various alkaline atoms which contribute electrons for conduction. By varying the number of conductors in C60, it is possible to boost Tc to a maximum value of 52 K (?366°F).

Superconductivity was discovered in magnesium diboride (MgB2) in January 2001 in Japan. This material may be a good alternative for some of the applications envisioned for high-Tc superconductivity, since this compound has Tc of 39 K (?389°F), is relatively easy to make, and consists of only two elements.

__________________
||||||||||||||||||||50% Complete

Magnetic properties

The existence of the Meissner-Ochsenfeld effect, the exclusion of a magnetic field from the interior of a superconductor, is direct evidence that the superconducting state is not simply one of infinite electrical conductivity. Instead, it is a true thermodynamic equilibrium state, a new phase which has lower free energy than the normal state at temperatures below the transition temperature and which somehow requires the absence of magnetic flux.

The exclusion of magnetic flux by a superconductor costs some magnetic energy. So long as this cost is less than the condensation energy gained by going from the normal to the superconducting phase, the superconductor will remain completely superconducting in an applied magnetic field. If the applied field becomes too large, the cost in magnetic energy will outweigh the gain in condensation energy, and the superconductor will become partially or totally normal. The manner in which this occurs depends on the geometry and the material of the superconductor. The geometry which produces the simplest behavior is that of a very long cylinder with field applied parallel to its axis. Two distinct types of behavior may then occur, depending on the type of superconductor—type I or type II.

Below a critical field Hc which increases as the temperature decreases below Tc, the magnetic flux is excluded from a type I superconductor, which is said to be perfectly diamagnetic. For a type II superconductor, there are two critical fields, the lower critical field Hc1 and the upper critical field Hc2. In applied fields less than Hc1, the superconductor completely excludes the field, just as a type I superconductor does below Hc. At fields just above Hc1, however, flux begins to penetrate the superconductor, not in a uniform way, but as individual, isolated microscopic filaments called fluxoids or vortices. Each fluxoid consists of a normal core in which the magnetic field is large, surrounded by a superconducting region in which flows a vortex of persistent supercurrent which maintains the field in the core.

__________________
||||||||||||||||||||50% Complete

Thermal properties


The appearance of the superconducting state is accompanied by rather drastic changes in both the thermodynamic equilibrium and thermal transport properties of a superconductor.

The heat capacity of a superconducting material is quite different in the normal and superconducting states. In the normal state (produced at temperatures below the transition temperature by applying a magnetic field greater than the critical field), the heat capacity is determined primarily by the normal electrons (with a small contribution from the thermal vibrations of the crystal lattice) and is nearly proportional to the temperature. In zero applied magnetic field, there appears a discontinuity in the heat capacity at the transition temperature. At temperatures just below the transition temperature, the heat capacity is larger than in the normal state. It decreases more rapidly with decreasing temperature, however, and at temperatures well below the transition temperature varies exponentially as e??/kT, where ? is a constant and k is Boltzmann's constant. Such an exponential temperature dependence is a hallmark of a system with a gap ? in the spectrum of allowed energy states. Heat capacity measurements provided the first indications of such a gap in superconductors, and one of the key features of the macroscopic BCS theory is its prediction of just such a gap.

Ordinarily a large electrical conductivity is accompanied by a large thermal conductivity, as in the case of copper, used in electrical wiring and cooking pans. However, the thermal conductivity of a pure superconductor is less in the superconducting state than in the normal state, and at very low temperatures approaches zero. Crudely speaking, the explanation for the association of infinite electrical conductivity with vanishing thermal conductivity is that the transport of heat requires the transport of disorder (entropy). The superconducting state is one of perfect order (zero entropy), and so there is no disorder to transport and therefore no thermal conductivity.

__________________
||||||||||||||||||||50% Complete

Two-fluid model

C. J. Gorter and H. B. G. Casimir introduced in 1934 a phenomenological theory of superconductivity based on the assumption that in the superconducting state there are two components of the conduction electron “fluid” (hence the name given this theory, the two-fluid model). One, called the superfluid component, is an ordered condensed state with zero entropy; hence it is incapable of transporting heat. It does not interact with the background crystal lattice, its imperfections, or the other conduction electron component and exhibits no resistance to flow. The other component, the normal component, is composed of electrons which behave exactly as they do in the normal state. It is further assumed that the superconducting transition is a reversible thermodynamic phase transition between two thermodynamically stable phases, the normal state and the superconducting state, similar to the transition between the liquid and vapor phases of any substance. The validity of this assumption is strongly supported by the existence of the Meissner-Ochsenfeld effect and by other experimental evidence. This assumption permits the application of all the powerful and general machinery of the theory of equilibrium thermodynamics. The results tie together the observed thermodynamic properties of superconductors in a very satisfying way.

__________________
||||||||||||||||||||50% Complete

Microscopic (BCS) theory

The key to the basic interaction between electrons which gives rise to superconductivity was provided by the isotope effect. It is an interaction mediated by the background crystal lattice and can crudely be pictured as follows: An electron tends to create a slight distortion of the elastic lattice as it moves, because of the Coulomb attraction between the negatively charged electron and the positively charged lattice. If the distortion persists for a brief time (the lattice may ring like a struck bell), a second passing electron will see the distortion and be affected by it. Under certain circumstances, this can give rise to a weak indirect attractive interaction between the two electrons which may more than compensate their Coulomb repulsion.

The first forward step was taken by Cooper in 1956, when he showed that two electrons with an attractive interaction can bind together to form a “bound pair” (often called a Cooper pair) if they are in the presence of a high-density fluid of other electrons, no matter how weak the interaction is. The two partners of a Cooper pair have opposite momenta and spin angular momenta. Then, in 1957, Bardeen, Cooper, and Schrieffer showed how to construct a wave function in which all of the electrons (at least, all of the important ones) are paired. Once this wave function is adjusted to minimize the free energy, it can be used as the basis for a complete microscopic theory of superconductivity.

The successes of the BCS theory and its subsequent elaborations are manifold. One of its key features is the prediction of an energy gap. Excitations called quasiparticles (which are something like normal electrons) can be created out of the superconducting ground state by breaking up pairs, but only at the expense of a minimum energy of ? per excitation; ? is called the gap parameter. The original BCS theory predicted that ? is related to Tc by ? = 1.76kTc at T = 0 for all superconductors. This turns out to be nearly true, and where deviations occur they are understood in terms of modifications of the BCS theory. The manifestations of the energy gap in the low-temperature heat capacity and in electromagnetic absorption provide strong confirmation of the theory.

__________________
||||||||||||||||||||50% Complete

An excellent research writing by honorable qurrat..Its very informative....Here i share with u all some latest advancement in superconductivity era!
Writing in the July 6, 2006, issue of Nature, scientists working at the Commerce Department's National Institute of Standards and Technology (NIST) Center for Neutron Research (NCNR) in collaboration with physicists from the University of Tennessee (UT) report strong evidence that magnetic fluctuations are key to a universal mechanism for pairing electrons and enabling resistance-free passage of electric current in high-temperature superconductors.

An important missing piece in the puzzle of high-temperature superconductivity, the finding should boost efforts to develop a variety of useful technologies now considered impractical for conventional superconductors, which work at markedly lower temperatures. Examples include loss-free systems for storing and distributing electric energy, superconducting digital routers for high-speed communications, and more efficient generators and motors.

The team was led by Pengcheng Dai, a UT-ORNL joint professor.

"Our results unify understanding of the role of magnetism in high-temperature superconductivity and move the research community one step closer to understanding the underlying pairing mechanism itself," says NIST physicist Jeffrey Lynn, a member of the collaboration. Better understanding of the mechanism of high-temperature superconductivity may lead to the discovery of new materials in which electrical resistance vanishes at even warmer temperatures.

Objects of intense scientific and technological interest since their discovery in 1986, high-temperature superconductors work their magic in ways different than materials that become superconducting at significantly colder temperatures, as first observed in 1911. In these conventional superconductors, vibrations in the materials' atomic latticework mediate the pairing process that results in the unimpeded flow of electrons.

Scientists have ruled out vibrations, or phonons, as the likely electron matchmaker in high-temperature superconducting compounds. And while they have assembled important clues over the last two decades, researchers have yet to pin down the electron-pairing mechanism in the high-temperature superconductors.

Reference:Science Journal.

__________________
No One is Perfect!
So IM No One

@Najabat

Thnx for the compliment, and a good addition from your side.



Regards,

__________________
||||||||||||||||||||50% Complete