The Absence Of Electrical Resistivity Biology Essay

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Surerconductivity is a phenomenon which occurs in certain materials and is characterized by the absence of electrical resistivity. Until recently, this phenomenon had been restricted to metals and alloys with transition temperatures of less than 23K. In 1986, superconductivity was discovered in a ceramic material. The ceramic-based materials are commonly known as high temperature (HTc) superconductors while the metallic and alloy materials are called low temperature (LTc) superconductors. Currently, only low temperature superconductors are of interest to the magnet designer and manufacturer.

Superconductors are divided into two types depending on their characteristic behavior in the presence of a magnetic field. Type I superconductors are comprised of pure metals, whereas Type II superconductors are comprised primarily of alloys or intermetallic compounds. Both, however, have one common feature: below a critical temperature Tc, their resistance vanishes. Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature, critical field, and critical current density at which superconductivity is destroyed. Properties of superconducting materials are altered locally by the presence of defects in the materials. A fluxoid encompassing or adjacent to such a defect in the material has its energy altered and its free motion through the superconductor is inhibited. This phenomenon, known as flux pinning, causes a field gradient in the superconductor and gives rise to a net current in the material. In the absence of defects in a Type II superconductor, no bulk current can be conducted without a transition into the normally conducting resistive state. Since the pinning force is small, fluxoids can be broken loose from their pinning centers, resulting in a net creep of the flux through a conductor as a function of time. This results in an effective voltage in a Type II superconductor. If the current density is low and the magnetic field is not intense, flux creep is insignificant and the induced voltage and effective resistance of the conductor will be essentially zero. At very high fields and high current densities, fluxoids will migrate rapidly, giving rise to a phenomenon called flux flow.

In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature(Tc). The electrical resistivity of a metallic conductor decreases gradually as the temperature is lowered. However, in ordinary conductors such as copper and silver, this decrease is limited by impurities and other defects. Even near absolute zero, a real sample of copper shows some resistance. In a superconductor however, despite these imperfections, the resistance drops abruptly to zero when the material is cooled below its critical temperature. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from around 20 K to less than 1 K. Solid mercury, for example, has a critical temperature of 4.2 K. The critical temperature at which the resistance vanishes in a superconductor is reduced when a magnetic field is applied. The maximum field that can be applied to a superconductor at a particular temperature and still maintain superconductivity is call the critical field, or Hc. The maximum critical field (Hc) in any Type I superconductor is about 2000 Gauss (0.2 Tesla), but in Type II materials superconductivity can persist to several hundred thousand Gauss (Hc2).

Superconductivity is use to produce superconducting magnets. The most outstanding feature of a superconducting magnet is its ability to support a very high current density with a vanishingly small resistance. This characteristic permits magnets to be constructed that generate intense magnetic fields with little or no electrical power input. This feature also permits steep magnetic field gradients to be generated at fields so intense that the use of ferromagnetic materials for field shaping is limited in effectiveness. Since the current densities are high, superconducting magnet systems are quite compact and occupy only a small amount of laboratory space. Another feature of superconducting magnets is the stability of the magnetic field in the persistent mode of operation. In the persistent mode of operation, the L/R time constant is extremely long and the magnet can be operated for days or even months at a nearly constant field, a feature of great significance where signal averaging must be performed over an extended period of time.

In future I discuss about flux pinning and flux flow, its magnetic field intensity, its phenomenon which includes flux jumping and fine filament concepts in superconductor, band gap between superconductors, energy band gap in superconductors as a function of temperature, Meissner effect, its application and uses, etc.

Superconductivity occurs in a large amount of materials, including simple elements like tin and aluminium, various metallic alloys, some heavily-doped semiconductors, and certain ceramic compounds containing copper and oxygen atoms lanes. Superconductivity does not occur in noble metals like gold and silver, nor in ferromagnetic metals.

In conventional superconductors, superconductivity is caused by a force of attraction between certain conduction electrons arising from the exchange of phonons, which causes the conduction electrons to exhibit a superfluid phase composed of correlated pairs of electrons. There also exists a class of materials, known as unconventional superconductors, that exhibit superconductivity but whose physical properties contradict the theory of conventional superconductors..

Elementary properties of superconductors

Most of the physical properties of superconductors vary from material to material, such as the heat capacity and the critical temperature at which superconductivity is destroyed. On the other hand, there is a class of properties that are independent of the underlying material. For instance, all superconductors have exactly zero resistivity to low applied currents when there is no magnetic field present. The existence of these "universal" properties implies that superconductivity is a thermodynamic phase, and thus possess certain distinguishing properties which are largely independent of microscopic details.

Zero electrical resistance

Suppose we were to attempt to measure the electrical resistance of a piece of superconductor. The simplest method is to place the sample in an electrical circuit, in series with a voltage (potential difference) source V (such as a battery), and measure the resulting current. If we carefully account for the resistance R of the remaining circuit elements (such as the leads connecting the sample to the rest of the circuit, and the source's internal resistance), we would find that the current is simply V/R. According to Ohm's law, this means that the resistance of the superconducting sample is zero. Superconductors are also quite willing to maintain a current with no applied voltage whatsoever, a property exploited in the coils of MRI machines, among others.

In a normal conductor, an electrical current may be visualized as a fluid of electrons moving across a heavy ionic lattice. The electrons are constantly colliding with the ions in the lattice, and during each collision some of the energy carried by the current is absorbed by the lattice and converted into heat (which is essentially the vibrational kinetic energy of the lattice ions.) As a result, the energy carried by the current is constantly being dissipated. This is the phenomenon of

electrical resistance. The situation is different in a superconductor. In a conventional superconductor, the electronic fluid cannot be resolved into individual electrons, instead consisting of bound pairs of electrons known as Cooper pairs. This pairing is caused by an attractive force between electrons from the exchange of phonons. Due to quantum mechanics, the energy spectrum of this Cooper pair fluid possesses an energy gap, meaning there is a minimum amount of energy ΔE that must be supplied in order to excite the fluid. Therefore, if ΔE is larger than the thermal energy of the lattice (given by kT, where k is Boltzmann's constant and T is the temperature), the fluid will not be scattered by the lattice. The Cooper pair fluid is thus a superfluid, meaning it can flow without energy dissipation. Experiments have in fact demonstrated that currents in superconducting rings persist for years without any measurable degradation. (Note: actually, in a class of superconductors known as type II superconductors, a small amount of resistivity appears when a strong magnetic field and electrical current are applied. This is due to the motion of vortices in the electronic superfluid, which dissipates some of the energy carried by the current. If the current is sufficiently small, the vortices are stationary, and the resistivity vanishes.)

Superconducting phase transition

In superconducting materials, the characteristics of superconductivity appear when the temperature T is lowered below a critical temperature Tc. The value of this critical temperature varies from material to material. Conventional superconductors usually have critical temperatures ranging from less than 1K to around 20K. Solid mercury, for example, has a critical temperature of 4.2K. As of 2001, the highest critical temperature found for a conventional superconductor is 39K for magnesium diboride (MgB2), although this material displays enough exotic properties that there is doubt about classifying it as a "conventional" superconductor. Cuprate superconductors can have much higher critical temperatures: YBa2Cu3O7, one of the first cuprate superconductors to be discovered, has a critical temperature of

92K, and mercury-based cuprates have been found with critical temperatures in excess of 130K. The explanation for

these high critical temperatures remains unknown.(Electron pairing due to phonon exchanges explains superconductivity

in conventional superconductors, while it does not explain superconductivity in the newer superconductors that have a

very high Tc)

The onset of superconductivity is accompanied by abrupt changes in various physical properties, which is the hallmark

of a phase transition. For example, the electronic heat capacity is proportional to the temperature in the normal

(non-superconducting) regime. At the superconducting transition, it suffers a discontinuous jump and thereafter ceases to

be linear. At low temperatures, it varies instead as e-α/T for some constant α. (This exponential behavior is one of the

pieces of evidence for the existence of the energy gap.)

Behavior of heat capacity (C) and resistivity (ρ) at the superconducting phase transition

The order of the superconducting phase transition is still a matter of debate. It had long been thought that the transition is second-order, meaning there is no latent heat. However, recent calculations have suggested that it may actually be weakly first-order due to the effect of long-range fluctuations in the electromagnetic field.

Meissner effect

When a superconductor is placed in a weak external magnetic field H, the field penetrates for only a short distance λ, called the penetration depth, after which it decays rapidly to zero. This is called the Meissner effect. For most superconductors, the penetration depth is on the order of a hundred nm. The Meissner effect is sometimes confused with the "perfect diamagnetism" one would expect in a perfect electrical conductor: according to Lenz's law, when a changing magnetic field is applied to a conductor, it will induce an electrical current in the conductor that creates an opposing magnetic field. In a perfect conductor, an arbitrarily large current can be induced, and the resulting magnetic field exactly cancels the applied field.

The Meissner effect is distinct from perfect diamagnetism because a superconductor expels all magnetic fields, not just those that are changing. Suppose we have a material in its normal state, containing a constant internal magnetic field. When the material is cooled below the critical temperature, we would observe the abrupt expulsion of the internal magnetic field, which we would not expect based on Lenz's law. A conductor in a static field, such as the dome of a Van de Graff generator, will have a field within itself, even if there is no net charge in the interior.The Meissner effect was explained by London and London, who showed that the electromagnetic free energy in a superconductor is minimized provided

<math> \nabla^2\math bf{H} = \lambda^{-2} \math bf{H} <math>

where H is the magnetic field and λ is the penetration depth. This equation, which is known as the London equation,

predicts that the magnetic field in a superconductor decays exponentially from whatever value it possesses at the surface.

The Meissner effect breaks down when the applied magnetic field is too large. Superconductors can be divided into two classes according to how this breakdown occurs. In Type I superconductors, superconductivity is abruptly destroyed when the strength of the applied field rises above a critical value Hc. Depending on the geometry of the sample, one may obtain an intermediate state consisting of regions of normal material carrying a magnetic field mixed with regions of superconducting material containing no field. In Type II superconductors, raising the applied field past a critical value Hc1 leads to a mixed state in which an increasing amount of magnetic flux penetrates the material, but there remains no resistance to the flow of electrical current as long as the current is not too large. At a second critical field strength Hc2, superconductivity is destroyed. The mixed state is actually caused by vortices in the electronic superfluid, sometimes called "fluxons" because the flux carried by these vortices is quantized. Most pure elemental superconductors (except niobium) are Type I, while almost all impure and compound superconductors are Type II.

Variation of internal magnetic field (B) with applied external magnetic field (H) for Type I and Type II

superconductors

We consider a cylinder with perfect conductivity and raise a magnetic field from zero to a finite value H(it is a constant). A surface current is induced whose magnetic field, according to Lenz's rule, is opposed to the applied field and cancels it in the interior. Since the resistance is zero the current will continue to flow with constant strength as long as the external field is kept constant and consequently the bulk of the cylinder will stay field-free. This is exactly what happens if we expose a lead cylinder in the superconducting state (T < Tc) to an increasing field, see the path (a) to (c) in Fig. So below Tc lead acts as a perfect diamagnetic material. There is, however, another path leading to the point (c). We start with a lead cylinder in the normal state (T > Tc) and expose it to a field which is increased from zero to H. Eddy currents are induced in this case as well but they decay rapidly and after a few hundred microseconds the field lines will fully penetrate the material (state (b) in Fig. 4). Now the cylinder is cooled down. At the very instant the temperature drops below Tc, a surface current is spontaneously created and the magnetic field is expelled from the interior of the cylinder. This surprising observation is called the Meissner-Ochsenfeld effect after its discoverers; it cannot be explained by the law of induction because the magnetic field is kept constant.

Superconductivity was discovered in 1911 by Onnes, who was studying the resistivity of solid mercury at cryogenic temperatures using the recently-discovered liquid helium as a refrigerant. At the temperature of 4.2K, he observed that the resistivity abruptly disappeared. For this discovery, he was awarded the Nobel Prize in Physics in 1913. In subsequent decades, superconductivity was found in several other materials. In 1913, lead was found to superconduct

at 7K, and in 1941 niobium nitride was found to superconduct at 16K.

The next important step in understanding superconductivity occurred in 1933, when Meissner and Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon which has come to be known as the Meissner effect.

In 1935, F. and H. London showed that the Meissner effect was a consequence of the minimization of the electromagnetic free energy carried by superconducting current.

In 1950, the phenomenological Ginzburg-Landau theory of superconductivity was devised by Landau and Ginzburg. This theory, which combined Landau's theory of second-order phase transitions with a Schrödinger-like wave equation, had great success in explaining the macroscopic properties of superconducters. In particular, Abrikosov showed that

Ginzburg-Landau theory predicts the division of superconductors into the two categories now referred to as Type I and Type II. Abrikosov and Ginzburg were awarded the 2003 Nobel Prize for their work (Landau having died in 1968.)

Also in 1950, Maxwell and Reynolds found that the critical temperature of a superconductor depends on the isotopic mass of the constituent element. This important discovery pointed to the electron-phonon interaction as the microscopic mechanism responsible for superconductivity.

The complete microscopic theory of superconductivity was finally proposed in 1957 by Bardeen, Cooper, and Schrieffer.

This BCS theory explained the superconducting current as a superfluid of Cooper pairs, pairs of electrons interacting through the exchange of phonons. For this work, the authors were awarded the Nobel Prize in 1972. The BCS theory was set on a firmer footing in 1958, when Bogoliubov showed that the BCS wave function, which had originally been derived from a variational argument, could be obtained using a canonical transformation of the electronic

Hamiltonian. In 1959, Gor'kov showed that the BCS theory reduced to the Ginzburg-Landau theory close to the critical

temperature.

In 1962, the first commercial superconducting wire, a niobium-titanium alloy, was developed by researchers at

Westinghouse. In the same year, Josephson made the important theoretical prediction that a supercurrent can flow

between two pieces of superconductor separated by a thin layer of insulator. This phenomenon, now called the

Josephson effect, is exploited by superconducting devices such as SQUIDs. It is used in the most accurate available

measurements of the magnetic flux quantum h/e, and thus (coupled with the quantum Hall resistivity) for Planck's

constant h. Josephson was awarded the Nobel Prize for this work in 1973.

In 1986, Bednorz and Mueller discovered superconductivity in a lanthanum-based cuprate perovskite material, which had

a transition temperature of 35K (Nobel Prize in Physics, 1987). It was shortly found that replacing the lanthanum with

yttrium, i.e. making YBCO, raised the critical temperature to 92K, which was important because liquid nitrogen could

then be used as a refrigerant (at atmospheric pressure, the boiling point of nitrogen is 77K.) This is important

commercially because liquid nitrogen can be produced cheaply on-site with no raw materials, and is not prone to some

of the problems (solid air plugs, etc) of helium in piping. Many other cuprate superconductors have since been

discovered, and the theory of superconductivity in these materials is one of the major outstanding challenges of

theoretical condensed matter physics.

Type I superconductors are superconductors that cannot be penetrated by magnetic flux lines (complete Meissner effect). As such, they have only a single critical temperature at which the material ceases to superconduct, becoming resistive. Elementary metals, such as aluminium, mercury and lead behave as typical Type I superconductors below their respective critical temperatures.

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