Superconductivity – Wikipedia, wikipedia, The Free Free

It is called superconductivity to the intrinsic capacity that certain materials for conducting electric current or loss of energy in certain conditions have. It was discovered by Dutch physicist Heike Kamerlingh Onnes on April 8, 1911 in Leiden.

The electrical resistivity of a metallic conductor gradually decreases as the temperature is reduced. However, in ordinary conductors, such as copper and silver, impurities and other defects produce a limit value. Even close to absolute zero a copper sample has a non -zero resistance. The resistance of a superconductor, on the other hand, descends sharply to zero when the material cools under its critical temperature . An electric current that flows in a spiral of superconductor cable can persist indefinitely without power supply. Like ferromagnetism and atomic spectral lines, superconductivity is a phenomenon of quantum mechanics.

Superconductivity occurs in a wide variety of materials, including simple elements such as tin and aluminum, various metal alloys and some strongly doping semiconductors. Superconductivity, usually does not occur in noble metals such as copper and silver, or in most ferromagnetic metals. But in certain cases, gold is classified as superconductor; for its functions and the mechanisms applied.

Magnetic behavior [ To edit ]

Although the most outstanding property of superconductors is the absence of resistance, the truth is that we cannot say that it is an infinite conductive material, since this type of material alone makes no thermodynamic sense alone. Actually, a type I superconductor material is perfectly diamagnetic. This does not allow the field to penetrate, what is known as Meissner effect.

The magnetic field distinguishes two types of superconductors: those of type I, which do not allow an external magnetic field at all (which entails a high energy effort, and implies the abrupt break of the superconductor state if the critical temperature is exceeded), and those of type II, which are superconductors Imperfect , in the sense that the field really penetrates through small channels called Abrikosov vortices, or fluxons. These two types of superconductors are in fact two different phases that were predicted by Lev Davidovich Landau and Aleksey Alekséyevich Abriksov.

When we apply a weak magnetic field to a weak external magnetic field repelled it perfectly. If we increase it, the system becomes unstable and prefers to introduce vortices to reduce its energy. These are increasing in number by placing in vortex networks that can be observed by appropriate techniques. When the field is high enough, the number of defects is so high that the material ceases to be superconductor. This is the critical field which makes a material cease to be superconductor and that depends on the temperature.

Electrical behavior [ To edit ]

The appearance of superdiamagnetismo is due to the capacity of the material to create supercorrientes . These are electron currents that do not dissipate energy, so that they can be maintained forever without obeying the joule effect of energy loss by heat generation. The currents create the intense magnetic field necessary to support the Meissner effect. These same currents allow to transmit energy without energy expenditure, which represents the most spectacular effect of this type of materials. Because the amount of superconductor electrons is finite, the amount of current that the material can withstand is limited. Therefore, there is a critical current from which the material ceases to be superconductor and begins to dissipate energy.

In type II superconductors, the appearance of fluxons causes, even for currents lower than criticism, a certain energy dissipation is detected due to the clash of vortices with the atoms of the network.

Specific heat [ To edit ]

In metals the specific heat is a temperature function. When the temperature is very low, but the metal is in the normal state (that is, when it is not yet in superconductor state) the specific heat has the shape

${displaystyle C_{v}=aT+bT^{3},!}$

Where A and B are constant that can be measured through experiments. The first term (the linear term) reflects the electrical conduction, while the second term (the one that varies with the temperature cube) is due to the phonones (that is, to the vibrations of the network).

However, if we continue to cool and the metal passes to the superconductor state, this behavior changes radically: the specific heat has a discontinuity in the critical temperature, increasing significantly, and then vary in the form

${displaystyle C_{v}={begin{cases}{text{constante}}cdot T^{3},&{mbox{si }}Tsim T_{rm {c}}\{text{constante}}cdot e^{-alpha T_{rm {c}}/T},&{mbox{si }}Tsim 0end{cases}}}$

The following graph shows the dependence on the specific heat newly explained (blue), and, additionally, shows how resistivity (green) varies:

Note as the specific heat increases abruptly to a value equal to 2.5 times the value in normal state. This value is independent of the superconductor material, and is explained within the framework of the BCS theory.

History of Superconductivity [ To edit ]

Discovery [ To edit ]

Already in the century XIX Various experiments were carried out to measure electrical resistance to low temperatures, being James Dewar the pioneer in this field.

However, superconductivity as such would not be discovered until 1911, the year in which the Dutch physicist Heike Kamerlingh onnes observed that the electricity resistance of the mercury disappeared sharply by cooling to 4 K (-269 ° C), when what was expected was that gradually decrease to absolute zero. Thanks to its discoveries, mainly by its method to achieve the production of liquid helium, the Nobel Prize in Physics would receive two years later. During the first years the phenomenon was known as Supraconductivity .

In 1913 it is discovered that a sufficiently large magnetic field also destroys the superconductor state, discovering three years later the existence of a critical electric current.

Since it is an essentially quantum phenomenon, no progress was made in the understanding of superconductivity, since the understanding and mathematical tools available to the physicists of the time were not enough to face the problem until the fifties. Therefore, the investigation was until then phenomenological, such as the discovery of the Meissner effect in 1933 and its first explanation through the development of the London equation two years later by the brothers Fritz and Heinz London.

Main theories [ To edit ]

The greatest advances in the understanding of superconductivity took place in the fifties: in 1950 the Ginzburg-Landau theory is published, and in 1957 the BCS theory would see the light.

The BCS theory It was developed by Bardeen, Cooper and Schrieffer (from its initials the name arises BCS ), thanks to which the three would receive the Nobel Prize in Physics in 1972. This theory could be developed thanks to two fundamental clues offered by experimental physicists in the early fifties:

The Ginzburg-Landau theory It is a generalization of London theory developed by Vitaly Ginzburg and Lev Landau in 1950. ^{[ first ]} Although this theory precedes seven years to the BCS theory, the physicists of Western Europe and the United States paid little attention for its most phenomenological character than theoretical, together with the incommunication of those years between both sides of the steel curtain. This situation changed in 1959, the year in which Lev Gor’kov showed that it could be derived rigorously from the microscopic theory ^{[ 2 ]} In an article that also published in English. ^{[ 3 ]} ​

In 1962 Brian David Josephson predicted that there could be electric current between two superconductors even if there was a small separation between them, due to the tunnel effect. A year later Anderson and Rowell confirmed it experimentally. The effect would be known as Josephson effect, and is among the most important phenomena of superconductors, having a variety of applications, from the magnetoenphalyography to the prediction of earthquakes.

High temperature superconductors [ To edit ]

After some years of relative stagnation, in 1987 Bednorz and Müller discovered that a family of ceramic materials, copper oxides with perovsquita structure, were superconductors with critical temperatures greater than 90 Kelvin. These materials, known as high temperature superconductors, stimulated a renewed interest in superconductivity research. As a theme of pure research, these materials constitute a new phenomenon that is only explained by the fact that electrons or “Cooper” pairs pass. And, because the superconductor state persists up to more manageable temperatures, higher than the boiling point of liquid nitrogen, many commercial applications would be viable, especially if materials with even higher critical temperatures were discovered.

How to obtain superconductor materials [ To edit ]

Due to the low temperatures that are needed to achieve superconductivity, the most common materials are usually cooled with liquid helium (liquid nitrogen is only useful when high temperature superconductors are handled). The necessary assembly is complex and expensive, using applications such as the construction of very powerful electromagnets for nuclear magnetic resonance.

However, in the 80s high temperature superconductors were discovered, which show the phase transition to temperatures higher than the liquid-vapor transition from liquid nitrogen. This has greatly reduced the costs in the study of these materials and open the door to the existence of superconductor materials at room temperature, which would mean a revolution in the industry of the century XXI . The greatest disadvantage of these materials is their ceramic composition, which makes it not appropriate to manufacture cables by plastic deformation, the most obvious use of this type of materials. However, new techniques have been developed for the manufacture of tapes such as IBAD (assisted deposition by ion beam). Through this technique, cables of lengths greater than 1 kilometer have been achieved.

Although the phenomenon of superconductivity is an open theme in physics, there are currently two fundamental approaches: the microscopic or quantum mechanical (based on the BCS theory) and the macroscopic or phenomenological (in which the Ginzburg-Landau theory is focused ).

A superconductor is not simply a driver normal perfect [ To edit ]

Contrary to what one might think in principle, a superconductor behaves in a very different way to normal drivers: it is not a driver whose resistance is nearby to zero, but resistance is exactly equal to zero. This cannot be explained through the models used for the usual conductors, such as the Drude model.

To demonstrate this we will assume the opposite hypothesis: Imagine for a moment that a superconductor behaves like a normal driver. In this case, we would have that electrons are scattered in some way and their movement equation would be:

${DisplayStyle m {frac {d} {dt}} langle {thing {v}} Rangle = -e {thing {e}}}$

where

${DisplayStyle Langle {thing {v} Rangle}$

It is the average speed of electrons, m them, It is its load and

${displaystyle {vec {E}}}$

The electric field in which they move. Assuming that this field varies gently, when solving it we would reach Ohm’s law:

${DisplayStyle {thing {j}} = sigma {thing {e}} = {frac {no {2} tau} {m} {thing {e}}}$

where

${DisplayStyle {thing {j}}}$

It is current density,

${displaystyle sigma }$

electrical conductivity,

${displaystyle tau }$

half of the average time between two collisions, and n The density of electrons.

Now, if we assume that resistance tends to zero, we would have to conduct the conduct to infinity and therefore the time between collisions,

${displaystyle tau }$

, would tend infinity. In other words, there would be no collisions at all. This is the idea of ​​how a driver would behave normal that had zero resistance. However, this would mean that, since current density cannot be infinite, the only possibility is that the electric field is void:

${displaystyle {vec {E}}=0}$

However, taking into account Faraday’s law, a null electric field implies that the magnetic field must be constant:

${Displaystyle charged the Times {thing {e}} =-{frac {partial {thing {b}}} {partial t}}} = 0rightarrow {thing {b}} (t) = {text {constante}}}}}$

But this comes into contradiction with the Meissner effect, so that superconductivity is a very different phenomenon than that would imply a “perfect conductivity”, and requires a different theory that explains them.

BCS theory [ To edit ]

The most accepted microscopic theory to explain the superconductors is the BCS theory , presented in 1957. Superconductivity can be explained as an application of the Bose-Einstein condensate. However, electrons are fermions, so they cannot be applied directly. The idea on which the BCS theory is based is that electrons mate forming a couple of fermions that behave like a boson. This couple is called the Cooper’s pair and their link is justified in the interactions of electrons together by the crystalline structure of the material.

Ginzburg-Landau theory [ To edit ]

Another different approach is through the Ginzburg-Landau theory , which focuses more on macroscopic properties than on microscopic theory, based on the rupture of symmetries in the phase transition.

This theory predicts much better the properties of inhomogeneous substances, since the BCS theory is applicable only if the substance is homogeneous, that is, if the energy of the forbidden band is constant in space. When the substance is inhomogeneous, the problem can be intractable from the microscopic point of view.

The theory is based on a variational calculation in which it is to minimize the free energy of Helmholtz with respect to the electron density found in the superconductor state. The conditions to apply the theory are:

• The managed temperatures have to be close to the critical temperature, since it is based on a Taylor series development around T _c .
• Wave pseudofunction Φ , as well as the potential vector
  ${displaystyle {vec {A}}}$

  , they have to vary gently.

This theory predicts two characteristic lengths:

• Penetration length: It is the distance that penetrates the magnetic field into the superconductor material
• Coherence length: It is the approximate size of the Cooper’s torque

Classification [ To edit ]

Superconductors can be classified according to:

• His physical behavior , they can be of type I (with an abrupt change from one phase to another, or in other words, if it suffers a change of first order phase) or type II (if they go through a mixed state in which both phases coexist, or In other words, if you suffer a second -order phase change).

• The theory that explains them , calling conventional (if explained by the BCS theory) or not conventional (otherwise).

• Its critical temperature , being high temperature (They are generally called that if you can reach their conductive state, cooling them with liquid nitrogen, that is, if T _c > 77k ), O of low temperature (If that is not the case).

Applications [ To edit ]

Superconductor magnets are some of the most powerful known electromagnes. They are used in MAGLEV trains, in machines for nuclear magnetic resonance in hospitals and in the direction of the particle accelerator beam. They can also be used for magnetic separation, where weak magnetic particles are extracted from a less magnetic particle background, as in pigment industries.

Superconductors have also been used to make digital circuits and radiofrequency and microwave filters for mobile phone base stations.

Superconductors are used to build Josephson unions, which are the construction blocks of Squids (quantum interference superconductors), the most sensitive known magnetometers. A series of Josephson devices have been used to define the volt in the international system (SI). Depending on the modality of operation, a Josephson Union can be used as a photon detector or as a mixer. The great change in the transition resistance of the normal state to the superconductor state is used to build thermometers in cryogenic photons detectors.

New markets are appearing where the relative efficiency, size and weight of devices based on high temperature superconductors are higher than the additional expenses they suppose.

Promising future applications include high -performance transformers, energy storage devices, electric power transmission, electric motors (for example, for vehicle propulsion, such as MAGLEV empties or trains) and magnetic levitation devices. However, superconductivity is sensitive to moving magnetic fields so that applications that use alternating current (for example, transformers) will be more difficult to elaborate than those that depend on direct current.

See also [ To edit ]

References [ To edit ]

external links [ To edit ]