A brief overview of the theories of superconductivity and the problems of high-temperature superconductivity are analyzed. School Encyclopedia Explanation of Superconductivity
2. What temperature is called critical?
Critical temperature is the temperature at which conductors go into a superconducting state.3. What effect is called isotopic? Why is the isotope effect the key to explaining superconductivity?
The isotope effect is that the square of the temperature is inversely proportional to the mass of ions in the crystal lattice. This means that at a critical temperature, the structure of the crystal lattice of a superconductor has a great influence on the movement of electrons - the resulting attractive forces between electrons exceed the Coulomb repulsive forces.4. How does the nature of the movement of electrons in a superconductor differ from their movement in a conductor? How can one mechanically model the motion of Cooper pairs in a superconductor?
In a conductor, electrons move independently of each other, but in a superconductor (at a critical temperature) their movements are interconnected. If we compared the movement of electrons in a conductor with a flow of balls rolling down an inclined plane and bumping into pins, then the movement of electrons in a superconductor can be represented as the movement of an inclined plane, but the balls are connected in pairs by springs.5. Why does superconductivity disappear at temperatures above critical? What explains the promising development of high-temperature superconductors?
At temperatures above the critical value, electrons again begin to move chaotically, and Cooper pairs are destroyed. The prospects for the development of high-temperature superconductors will reduce energy losses during transmission over long distances and increase the speed of computers.Superconductivity, as a phenomenon, arises as a result of the formation of Cooper pairs of electrons that behave like a single particle.
Superconductivity is a strange thing and, to some extent, even counterintuitive. When an electric current flows through an ordinary wire, then, as a result of the presence of electrical resistance on the wire, the current does some work aimed at overcoming this resistance from the atoms, as a result of which heat is released. Moreover, each collision of an electron - a current carrier - with an atom slows down the electron, and the atom-brake itself heats up - that’s why the spiral of the electric stove becomes so red and hot. The thing is that the spiral has an electrical resistance, and, as a result, when an electric current flows through it, it releases thermal energy ( cm. Ohm's law).
In 1911, the Dutch experimental physicist Heike Kammerlingh Onnes (1853-1926) made an amazing discovery. By immersing the wire in liquid helium, the temperature of which was no more than 4 ° above absolute zero (which, recall, is -273 ° C on the Celsius scale or -460 ° F on the Fahrenheit scale), he found that at ultra-low temperatures the electrical resistance drops almost to zero. Why this was happening, he, in fact, could not even guess, but the fact turned out to be obvious. At ultra-low temperatures, electrons experienced virtually no resistance from the atoms of the metal crystal lattice and provided superconductivity.
But why is this happening? This remained a secret until 1957, when three more experimental physicists - John Bardeen (1908-1991), Leon Cooper (b. 1930) and John Robert Schrieffer (b. 1931) came up with explanation for this effect. The theory of superconductivity is now called the “BCS theory” in their honor - after the first letters of the names of these physicists.
And its essence lies in the fact that at ultra-low temperatures, heavy metal atoms practically do not vibrate due to their low thermal motion, and they can be considered virtually stationary. Since any metal has the electrically conductive properties inherent in metal only because it releases the electrons of the outer layer into “free floating” ( cm. Chemical bonds), we have what we have: ionized, positively charged nuclei of the crystal lattice and negatively charged electrons freely “floating” between them. And now the conductor comes under the influence of the electrical potential difference. Electrons - willy-nilly or not - move, being free, between positively charged nuclei. Each time, however, they weakly interact with the nuclei (and among themselves), but immediately “escape.” However, at the same time that electrons “slip” between two positively charged nuclei, they seem to “distract” them to themselves. As a result, after an electron “slips” between two nuclei, they come closer for a short time. Then the two nuclei, of course, smoothly move apart, but the job is done - a positive potential has arisen, and more and more negatively charged electrons are attracted to it. The most important thing here is to understand: due to the fact that one electron “slips” between atoms, it thereby creates favorable energy conditions for the advancement of another electron. As a result, electrons move inside the atomic-crystalline structure in pairs - they simply cannot do otherwise, since this is energetically unfavorable for them. To better understand this effect, we can use an analogy from the world of sports. Cyclists on the track often use “drafting” tactics (namely, “hanging on the tail” of an opponent) and, thereby, reduce air resistance. Electrons do the same, forming Cooper pairs.
It is important to understand here that at ultra-low temperatures All electrons form Cooper pairs. Now imagine that each such pair is a noodle-like bundle, at each end of which there is a charge-electron. Now imagine that in front of you is a whole bowl of such “noodles”: it all consists of Cooper pairs intertwined. In other words, electrons in a superconducting metal interact with each other in pairs, and all their energy is spent on this. Accordingly, electrons simply do not have energy left to interact with the nuclei of atoms in the crystal lattice. Eventually it gets to the point where the electrons slow down so much that they have nothing left to lose (energetically), and the nuclei surrounding them “cool down” so much that they are no longer able to “slow down” free electrons. As a result, electrons begin to move between metal atoms, losing virtually no energy as a result of collisions with atoms, and the electrical resistance of the superconductor goes to zero. For their discovery and explanation of the effect of superconductivity, Bardeen, Cooper and Schrieffer received the Nobel Prize in 1972.
Many years have passed since then, and superconductivity has gone from being a unique and laboratory-curious phenomenon to a generally accepted fact and a source of multibillion-dollar income for enterprises in the electronics industry. The point is that any electric current excites a magnetic field around itself ( cm. Faraday's law of electromagnetic induction). Because superconductors conduct current for long periods of time with virtually no loss when maintained at ultra-low temperatures, they are an ideal material for making electromagnets. And, if you have ever undergone a medical diagnostic procedure called electron tomography, which is performed on a scanner using the principle of nuclear magnetic resonance (NMR), then you, perhaps without knowing it, were just centimeters from superconducting electromagnets . It is they who create the field that allows doctors to obtain high-precision cross-sectional images of human body tissue without the need to resort to a scalpel.
Modern superconductors retain their unique properties when heated up to temperatures of about 20K (twenty degrees above absolute zero). For a long time this was considered the temperature limit of superconductivity. However, in 1986, employees of the Swiss laboratory of the computer company IBM, Georg Bednorz (b. 1950) and Alexander Müller (b. 1927) discovered an alloy whose superconducting properties are maintained at 30K. Today, science knows of materials that remain superconductors even at 160K (that is, just below -100°C). At the same time, the generally accepted theory that would explain this class high temperature superconductivity, has not yet been created, but it is absolutely clear that it is impossible to explain it within the framework of the BCS theory. High-temperature superconductors have not found practical application today due to their extreme high cost and fragility, but developments in this direction continue.
John Bardeen, 1908-91
American physicist, one of the few two-time Nobel Prize winners. Born in Madison, Wisconsin in the family of a pathologist professor. Educated at Madison and Princeton universities. In the break between his studies in the first and second years, he worked for several years at the oil company Gulf Oil as a seismologist-explorer of oil deposits. During World War II he served in the US Navy Navigation Laboratory in Washington, and after the war he worked in the radio laboratory of the Bell Telephone Company, where he co-invented the transistor, for which he was awarded his first Nobel Prize in Physics in 1956. After this, Bardeen became a professor at the University of Illinois, where he began developing the BCS theory, for which, together with his co-authors, he received the Nobel Prize for the second time in 1972.
(77 K), a much cheaper cryogenic liquid.
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Subtitles
History of discovery
The basis for the discovery of the phenomenon of superconductivity was the development of technologies for cooling materials to ultra-low temperatures. In 1877, French engineer Louis Cayette and Swiss physicist Raoul Pictet independently cooled oxygen to a liquid state. In 1883, Zygmunt Wróblewski and Karol Olszewski performed nitrogen liquefaction. In 1898, James Dewar managed to obtain liquid hydrogen.
In 1893, the Dutch physicist Heike Kamerlingh Onnes began to study the problem of ultra-low temperatures. He managed to create the best cryogenic laboratory in the world, in which he obtained liquid helium on July 10, 1908. Later he managed to bring its temperature to 1 Kelvin. Kamerlingh Onnes used liquid helium to study the properties of metals, in particular to measure the dependence of their electrical resistance on temperature. According to the classical theories that existed at that time, the resistance should fall smoothly with decreasing temperature, but there was also an opinion that at too low temperatures the electrons would practically stop and the metal would completely stop conducting current. Experiments conducted by Kamerlingh Onnes with his assistants Cornelis Dorsman and Gilles Holst initially confirmed the conclusion about a smooth decrease in resistance. However, on April 8, 1911, he unexpectedly discovered that at 3 Kelvin (about −270 °C) electrical resistance was practically zero. The next experiment, carried out on May 11, showed that a sharp drop in resistance to zero occurs at a temperature of about 4.2 K (later, more accurate measurements showed that this temperature is 4.15 K). This effect was completely unexpected and could not be explained by the then existing theories.
Zero resistance is not the only distinguishing feature of superconductors. One of the main differences between superconductors and ideal conductors is the Meissner effect, discovered by Walter Meissner and Robert Oxenfeld in 1933.
It was later discovered that superconductors are divided into two large families: type I superconductors (which, in particular, include mercury) and type II (which are usually alloys of different metals). The work of L.V. Shubnikov in the 1930s and A.A. Abrikosov in the 1950s played a significant role in the discovery of type II superconductivity.
Of great importance for practical applications in high-power electromagnets was the discovery in the 1950s of superconductors capable of withstanding strong magnetic fields and transmitting high current densities. Thus, in 1960, under the leadership of J. Künzler, the Nb 3 Sn material was discovered, a wire from which is capable of passing a current with a density of up to 100 kA/cm² at a temperature of 4.2 K, being in a magnetic field of 8.8 T.
In 2015, a new record was set for the temperature at which superconductivity is achieved. For H 2 S (hydrogen sulfide) at a pressure of 100 GPa, a superconducting transition was recorded at a temperature of 203 K (-70 ° C).
Classification
There are several criteria for classifying superconductors. Here are the main ones:
Properties of superconductors
Zero electrical resistance
For direct electric current, the electrical resistance of a superconductor is zero. This was demonstrated in an experiment where an electric current was induced in a closed superconductor, which flowed in it without attenuation for 2.5 years (the experiment was interrupted by a strike of workers delivering cryogenic liquids).
Superconductors in a high-frequency field
Strictly speaking, the statement that the resistance of superconductors is zero is true only for direct electric current. In an alternating electric field, the resistance of a superconductor is nonzero and increases with increasing field frequency. This effect, in the language of the two-fluid model of a superconductor, is explained by the presence, along with the superconducting fraction of electrons, of ordinary electrons, the number of which, however, is small. When a superconductor is placed in a constant field, this field inside the superconductor becomes zero, since otherwise the superconducting electrons would accelerate to infinity, which is impossible. However, in the case of an alternating field, the field inside the superconductor is non-zero and also accelerates normal electrons, with which both finite electrical resistance and Joule thermal losses are associated. This effect is especially pronounced for such frequencies of light for which the quantum energy h ν (\displaystyle h\nu ) sufficient to transfer a superconducting electron to the group of normal electrons. This frequency usually lies in the infrared region (about 10 11 Hz), therefore, in the visible range, superconductors are practically no different from ordinary metals.
Phase transition to the superconducting state
The temperature range of transition to the superconducting state for pure samples does not exceed thousandths of a Kelvin and therefore a certain value makes sense T s- temperature of transition to the superconducting state. This quantity is called critical transition temperature. The width of the transition interval depends on the heterogeneity of the metal, primarily on the presence of impurities and internal stresses. Current known temperatures T s vary from 0.0005 K for magnesium (Mg) to 23.2 K for the intermetallic compound of niobium and germanium (Nb 3 Ge, in film) and 39 K for magnesium diboride ( 2) for low-temperature superconductors ( T s below 77 K, the boiling point of liquid nitrogen), to about 135 K for mercury-containing high-temperature superconductors.
Currently, the HgBa 2 Ca 2 Cu 3 O 8+d (Hg−1223) phase has the highest known value of the critical temperature - 135 K, and at an external pressure of 350 thousand atmospheres the transition temperature increases to 164 K, which is only 19 K lower than the minimum temperature recorded under natural conditions on the Earth's surface. Thus, superconductors in their development have gone from metallic mercury (4.15 K) to mercury-containing high-temperature superconductors (164 K). In 2000, it was shown that slight fluorination of the above-mentioned mercury ceramics allows one to raise the critical temperature at normal pressure to 138 K.
The transition of a substance to the superconducting state is accompanied by a change in its thermal properties. However, this change depends on the type of superconductors in question. Thus, for type I superconductors in the absence of a magnetic field at the transition temperature T c the heat of transition (absorption or release) goes to zero, and therefore suffers a jump in heat capacity, which is characteristic of a phase transition of the ΙΙ kind. This temperature dependence of the heat capacity of the electronic subsystem of a superconductor indicates the presence of an energy gap in the distribution of electrons between the ground state of the superconductor and the level of elementary excitations. When the transition from the superconducting state to the normal state is carried out by changing the applied magnetic field, then heat must be absorbed (for example, if the sample is thermally insulated, then its temperature decreases). And this corresponds to a phase transition of the 1st order. For type II superconductors, the transition from the superconducting to the normal state under any conditions will be a phase transition of type II.
Meissner effect
An even more important property of a superconductor than zero electrical resistance is the so-called Meissner effect, which consists of the displacement of a constant magnetic field from a superconductor. From this experimental observation, it is concluded that there are continuous currents inside the superconductor, which create an internal magnetic field that is opposite to the external applied magnetic field and compensates for it.
Isotopic effect
Isotopic effect for superconductors is that temperatures T s are inversely proportional to the square roots of the atomic masses of isotopes of the same superconducting element. As a result, monoisotopic preparations differ somewhat in critical temperatures from the natural mixture and from each other.
London moment
The rotating superconductor generates a magnetic field precisely aligned with the axis of rotation, the resulting magnetic moment is called the “London moment”. It was used, in particular, in the Gravity Probe B scientific satellite, where the magnetic fields of four superconducting gyroscopes were measured to determine their rotation axes. Since the rotors of gyroscopes were almost perfectly smooth spheres, the use of the London moment was one of the few ways to determine their axis of rotation.
London's gravitomagnetic moment
A rotating and at the same time accelerating, that is, increasing the frequency of revolutions, ring of superconductor generates a gravitational field. Experiments related to the London gravitomagnetic moment were carried out by Martin Tajmar of the Austrian company ARC Seibersdorf Research and Clovis de Matos of the European Space Agency (ESA) in 2006. Experimenters for the first time measured a gravitomagnetic field artificially created in this way. Tajmar and de Matos believe that this effect explains the mystery of the difference between the mass of Cooper pairs previously measured with high accuracy (these are electrons that provide conductivity in a superconductor) and the same mass obtained on paper - according to calculations of quantum theory.
The researchers called the experimentally discovered gravitational effect “Gravitomagnetic London moment”, by analogy with a similar magnetic effect: the emergence of a magnetic field during the rotation of a superconductor, called the “London moment”.
The field caused in this way was 100 million times weaker than the gravitational field of the Earth. And although this effect was predicted by the General Theory of Relativity, this field strength turned out to be 20 orders of magnitude stronger than the calculated value.
Theoretical explanation of the superconductivity effect
A completely satisfactory microscopic theory of superconductivity is currently missing.
Already at a relatively early stage of the study of superconductivity, at least after the creation of the Ginzburg-Landau theory, it became obvious that superconductivity is a consequence of the unification of a macroscopic number of conduction electrons into a single quantum mechanical state. The peculiarity of electrons bound in such an ensemble is that they cannot exchange energy with the lattice in small portions, less than their binding energy in the ensemble. This means that when electrons move in a crystal lattice, the energy of the electrons does not change, and the substance behaves like a superconductor with zero resistance. Quantum mechanical analysis shows that in this case there is no scattering of electron waves by thermal vibrations of the lattice or impurities. And this means the absence of electrical resistance. Such a combination of particles is impossible in an ensemble of fermions. It is characteristic of an ensemble of identical bosons. The fact that electrons in superconductors are combined into bosonic pairs follows from experiments measuring the magnitude of the magnetic flux quantum that is “frozen” in hollow superconducting cylinders. Therefore, already in the middle of the 20th century, the main task of creating the theory of superconductivity was the development of a mechanism for electron pairing. The first theory claiming to provide a microscopic explanation of the causes of superconductivity was the theory of Bardeen - Cooper - Schrieffer, created by them in the 50s of the 20th century. This theory received universal recognition under the name BCS and was awarded the Nobel Prize in 1972. When creating their theory, the authors relied on the isotopic effect, that is, the influence of the mass of the isotope on the critical temperature of the superconductor. It was believed that its existence directly indicates the formation of a superconducting state due to the operation of the phonon mechanism.
The BCS theory left some questions unanswered. On its basis, it turned out to be impossible to solve the main problem - to explain why specific superconductors have one or another critical temperature. In addition, further experiments with isotopic substitutions showed that, due to the anharmonicity of zero-point vibrations of ions in metals, there is a direct effect of the ion mass on the interionic distances in the lattice, and therefore directly on the Fermi energy of the metal. Therefore, it became clear that the existence of the isotopic effect is not evidence of the phonon mechanism, as the only possible one responsible for the pairing of electrons and the occurrence of superconductivity. Dissatisfaction with the BCS theory in later years led to attempts to create other models, such as the spin fluctuation model and the bipolaron model. However, although they considered various mechanisms for combining electrons into pairs, these developments also did not lead to progress in understanding the phenomenon of superconductivity.
The main problem for the BCS theory is the existence of , which cannot be described by this theory.
Applications of Superconductivity
Significant progress has been made in obtaining high-temperature superconductivity. Based on metal ceramics, for example, the composition YBa 2 Cu 3 O x , substances have been obtained for which the temperature T c transition to the superconducting state exceeds 77 K (nitrogen liquefaction temperature). Unfortunately, almost all high-temperature superconductors are not technologically advanced (brittle, do not have stable properties, etc.), as a result of which superconductors based on niobium alloys are still mainly used in technology.
The phenomenon of superconductivity is used to produce strong magnetic fields (for example, in cyclotrons), since there are no thermal losses when strong currents passing through the superconductor, creating strong magnetic fields. However, due to the fact that the magnetic field destroys the state of superconductivity, so-called so-called magnetic fields are used to obtain strong magnetic fields. Type II superconductors, in which the coexistence of superconductivity and a magnetic field is possible. In such superconductors, a magnetic field causes the appearance of thin filaments of normal metal penetrating the sample, each of which carries a magnetic flux quantum (Abrikosov vortices). The substance between the threads remains superconducting. Since there is no full Meissner effect in a type II superconductor, superconductivity exists up to much higher magnetic field values H c 2. The following superconductors are mainly used in technology:
Miniature superconducting ring devices - SQUIDS, whose action is based on the connection between changes in magnetic flux and voltage, are found in important applications. They are part of ultra-sensitive magnetometers that measure the Earth’s magnetic field, and are also used in medicine to obtain magnetograms of various organs.
Superconductors are also used in maglevs.
The phenomenon of dependence of the temperature of transition to the superconducting state on the magnitude of the magnetic field is used in cryotrons - controlled resistances.
see also
Notes
- The discovery of superconductivity - a chapter from the book by J. Trigg “Physics of the 20th Century: Key Experiments”
- Dirk van Delft and Peter Kes.
The phenomenon of superconductivity in materials
The phenomenon of superconductivity was first discovered in 1911 by a Dutch scientist. . Since then, intensive searches have been conducted for new superconducting materials, which would allow the use of this phenomenon in specific devices with maximum energy and economic benefits. Dutch scientist G. Kamerlingh-Onkes discovered the phenomenon of superconductivity. Superconductivity opens up fantastic prospects for electrical engineering, energy, and transport. After all, if the resistance of the conductor is zero, then an arbitrarily large current can be passed through it, and there will be absolutely no heating losses. This is an electrical engineers dream! Due to the heating of conventional wires, up to 20% of all generated electricity is irretrievably lost, and in power lines made of superconductors, the losses will be negligible. American professor Richard McPhee calculated that an arm-thin superconducting cable could handle all the peak power generated by US power plants. The opportunity to receive super powerful magnetic fields, which are so necessary when creating thermonuclear reactors, unique designs of current generators, new physical devices, magnetic levitation trains and many other useful things.The phenomenon of superconductivity in composites
Creating composites, you can form the necessary physical properties and thereby solve a variety of physical problems. One of them is the creation superconducting devices. This is a very big problem, people of different professions are involved in working on it. The task for physicists and chemists is to obtain substances that have superconductivity. And the use of already known superconducting materials to create a specific product - a superconducting wire - is a typical task for materials scientists.Superconducting wire - composite
Many years of theoretical and experimental research have led physicists to this conclusion regarding the design of superconducting wires: to ensure reliable operation superconducting wire possible if it represents composite, consisting of a thermally conductive (for example, copper) matrix in which continuous superconducting fibers are evenly distributed, oriented along the axis of the wire.
Superconducting copper wire. It is desirable that the diameter of these fibers does not exceed several micrometers, and their number is measured in thousands or tens of thousands. In this case, the volume concentration of fibers in the matrix should be 5-7%, and the diameter of the entire wire should be about 1 mm. Superconducting fibers
The task of materials scientists is to learn how to produce such a wire; it is not an easy task. The fact is that traditional methods for solving it are not suitable:- There are no micrometer-diameter superconducting fibers that are also hundreds of meters or kilometers long.
- Even if they existed, it would hardly be possible to guarantee that they would not break somewhere during processing, which means that there would be no confidence in the quality of the composite and its reliability.
Bronze as a material for creating superconducting fiber. The disadvantage of the bronze matrix is reduced thermal and electrical conductivity compared to copper. This disadvantage can be reduced by using a mixed matrix, including pure copper along with bronze. But when heated, copper can react with tin, which will again worsen its electrical and thermophysical performance. To prevent this from happening, it is necessary to place barriers between copper and bronze, which will also reduce eddy currents. Tantalum is convenient for this purpose. What does a wire containing Nb 3 Sn fibers look like? Schematically, its structure consists of 19 polygons, the shape of which is close to hexagonal - these are wires made of bronze - Nb 3 Sn composite. All of them are located in a copper matrix. The cross-section of one such wire consists of 187 groups containing Nb 3 Sn fibers, with each group containing 19 such fibers, and between them is a bronze matrix. In total, the composite wire contains 67,507 fibers with a diameter of ~ 5 µm (or rather, each fiber consists of a niobium core coated with a layer of Nb 3 Sn ~ 1 µm thick). To complete the manufacturing process, the entire composite is shaped into a rectangular shape so that it can be wound tightly onto the core. Such a rectangular composite conductor, having a cross-section of 1.75x5.46 mm, is capable of passing a current of 5000 A in a 6 T field and 1250 A in a 12 T field. But the technical requirements are increasing every year, and to meet them, materials with even higher properties. This means we need to go further, put forward new ideas, develop new technologies, create new ones.
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