Matthias rules

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In physics, the Matthias rules refers to a historical set of empirical guidelines on how to find superconductors. These rules were authored Bernd T. Matthias who discovered hundreds of superconductors using these principles in the 1950s and 1960s. Deviations from these rules have been found since the end of the 1970s with the discovery of unconventional superconductors.

Contents

History

Bernd T. Matthias (left) points to the element niobium on the periodic table while John Eugene Kunzler looks on. After reporting to the American Physical Society that a ductile alloy of niobium and zirconium will remain superconducting at liquid helium temperature. Matthias and Kunzler periodic table.jpg
Bernd T. Matthias (left) points to the element niobium on the periodic table while John Eugene Kunzler looks on. After reporting to the American Physical Society that a ductile alloy of niobium and zirconium will remain superconducting at liquid helium temperature.

Superconductivity was first discovered in solid mercury in 1911 by Heike Kamerlingh Onnes and Gilles Holst, who had developed new techniques to reach near-absolute zero temperatures. [1] [2] [3]

In subsequent decades, superconductivity was found in several other materials; In 1913, lead at 7 K, in 1930's niobium at 10 K, and in 1941 niobium nitride at 16 K.

In 1933, Walther Meissner and Robert Ochsenfeld discovered that superconductors expelled applied magnetic fields, a phenomenon that has come to be known as the Meissner effect.

Bernd T. Matthias and John Kenneth Hulm were encouraged by Enrico Fermi to start a systematic experimental investigation in the 1950s, looking for superconductors in different elements and compounds. For this reason, they developed a technique based on the Meissner effect. [4] [5]

In collaboration with Theodore H. Geballe, Matthias broke the record in 1954, with the discovery of superconductivity in niobium–tin (Nb3Sn) which had the highest known transition temperature of about 18 K. [6] [5] Later Matthias would try to come up with general empirical properties to find superconducting alloys. In the same year he published a first version of his famous guidelines which came to be known, as the "Mathias rules". [5] [7] Matthias was able to show in 1962 that some deviations from his rules where due to impurities or defects in the materials. [5] Using his rules, Matthias and collaborators found in 1965 that niobium–germanium (Nb3Sn) with a record critical temperature above 20 K. [8] [9]

Matthias published a first outline his rules in 1957. [5] [10] A successful microscopic theory of superconductivity would no come up until the same year, with the development of the BCS theory by John Bardeen, Leon Cooper, and John Robert Schrieffer. [11]

Geballe and Matthias won the Oliver E. Buckley Condensed Matter Prize in 1970 for "For their joint experimental investigations of superconductivity which have challenged theoretical understanding and opened up the technology of high field superconductors." [12]

One of the first deviations of Matthias' rules was found with the discovery of superconductivity in molybdenum sulfide and selenides. Matthias postulated an additional criterion in 1976 at the Rochester Conference on superconductivity to include these materials. [13]

Another violation of Matthias rules appeared in 1979, with the discovery of heavy fermion superconductors by Frank Steglich [14] where magnetism was expected to play a role, contrary to the Matthias rules. [15]

Matthias held the record of highest critical temperature superconductor found until the discovery of high-temperature superconductors were discovered in 1986 by Georg Bednorz and K. Alex Müller. [5] [16] [17] [18]

Description

The Matthias rules are a set of guidelines to find low temperature superconductors but were never provided in list form by Matthias.

A popular summarized version of these rules reads: [19] [20] [15] [8]

  1. High symmetry is good, cubic symmetry is the best.
  2. High density of electronic states is good.
  3. Stay away from oxygen.
  4. Stay away from magnetism
  5. Stay away from insulators.
  6. Stay away from theorists!

Rule 2, rules out materials near metal-insulator transition like oxides. Rule 4, rules out material that are in close vicinity to ferromagnetism or antiferromagnetism. [18] Rule 6 is not an official rule and is often added to indicate skepticism of the theories of the time. [15]

Other equivalent principles as stated by Matthias, indicate to work mainly with d-electron metals; with the average number of valence electrons, preferably odd numbers 3, 5, and 7 and high electron density or high electron density of state at the Fermi level. [18]

In 1976, Mattias added the criterion to include "elements which will not react at all with molybdenum alone form superconducting compounds with Mo3S4 and Mo3Se4, S or Se" due to deviations in molydenum compounds. [15]

Failure and extensions

It has been argued that all of Matthias' rules have been shown to not be completely valid. [19] Specially the rules are not valid for high-temperature superconductors, alternative rules for these materials have been suggested. [18] [19]

Related Research Articles

<span class="mw-page-title-main">BCS theory</span> Microscopic theory of superconductivity

In physics, theBardeen–Cooper–Schrieffer (BCS) theory is the first microscopic theory of superconductivity since Heike Kamerlingh Onnes's 1911 discovery. The theory describes superconductivity as a microscopic effect caused by a condensation of Cooper pairs. The theory is also used in nuclear physics to describe the pairing interaction between nucleons in an atomic nucleus.

<span class="mw-page-title-main">Superconductivity</span> Electrical conductivity with exactly zero resistance

Superconductivity is a set of physical properties observed in certain materials where electrical resistance vanishes and magnetic fields are expelled from the material. Any material exhibiting these properties is a superconductor. Unlike an ordinary metallic conductor, whose resistance decreases gradually as its temperature is lowered, even down to near absolute zero, a superconductor has a characteristic critical temperature below which the resistance drops abruptly to zero. An electric current through a loop of superconducting wire can persist indefinitely with no power source.

Unconventional superconductors are materials that display superconductivity which does not conform to conventional BCS theory or its extensions.

<span class="mw-page-title-main">Meissner effect</span> Expulsion of a magnetic field from a superconductor

The Meissner effect is the expulsion of a magnetic field from a superconductor during its transition to the superconducting state when it is cooled below the critical temperature. This expulsion will repel a nearby magnet.

<span class="mw-page-title-main">Heike Kamerlingh Onnes</span> Dutch physicist, Nobel prize winner (1853–1926)

Heike Kamerlingh Onnes was a Dutch physicist and Nobel laureate. He exploited the Hampson–Linde cycle to investigate how materials behave when cooled to nearly absolute zero and later to liquefy helium for the first time, in 1908. He also discovered superconductivity in 1911.

<span class="mw-page-title-main">High-temperature superconductivity</span> Superconductive behavior at temperatures much higher than absolute zero

High-temperature superconductors are defined as materials with critical temperature above 77 K, the boiling point of liquid nitrogen. They are only "high-temperature" relative to previously known superconductors, which function at even colder temperatures, close to absolute zero. The "high temperatures" are still far below ambient, and therefore require cooling. The first break through of high-temperature superconductor was discovered in 1986 by IBM researchers Georg Bednorz and K. Alex Müller. Although the critical temperature is around 35.1 K, this new type of superconductor was readily modified by Ching-Wu Chu to make the first high-temperature superconductor with critical temperature 93 K. Bednorz and Müller were awarded the Nobel Prize in Physics in 1987 "for their important break-through in the discovery of superconductivity in ceramic materials". Most high-Tc materials are type-II superconductors.

A room-temperature superconductor is a material capable of displaying superconductivity at temperatures above 0 °C, which are commonly encountered in everyday settings. As of 2023, the material with the highest accepted superconducting temperature was highly pressurized lanthanum decahydride, whose transition temperature is approximately 250 K (−23 °C) at 200 GPa.

<span class="mw-page-title-main">Superconducting magnet</span> Electromagnet made from coils of superconducting wire

A superconducting magnet is an electromagnet made from coils of superconducting wire. They must be cooled to cryogenic temperatures during operation. In its superconducting state the wire has no electrical resistance and therefore can conduct much larger electric currents than ordinary wire, creating intense magnetic fields. Superconducting magnets can produce stronger magnetic fields than all but the strongest non-superconducting electromagnets, and large superconducting magnets can be cheaper to operate because no energy is dissipated as heat in the windings. They are used in MRI instruments in hospitals, and in scientific equipment such as NMR spectrometers, mass spectrometers, fusion reactors and particle accelerators. They are also used for levitation, guidance and propulsion in a magnetic levitation (maglev) railway system being constructed in Japan.

<span class="mw-page-title-main">History of superconductivity</span>

Superconductivity is the phenomenon of certain materials exhibiting zero electrical resistance and the expulsion of magnetic fields below a characteristic temperature. The history of superconductivity began with Dutch physicist Heike Kamerlingh Onnes's discovery of superconductivity in mercury in 1911. Since then, many other superconducting materials have been discovered and the theory of superconductivity has been developed. These subjects remain active areas of study in the field of condensed matter physics.

<span class="mw-page-title-main">Niobium–tin</span> Superconducting intermetallic compound

Niobium–tin is an intermetallic compound of niobium (Nb) and tin (Sn), used industrially as a type-II superconductor. This intermetallic compound has a simple structure: A3B. It is more expensive than niobium–titanium (NbTi), but remains superconducting up to a magnetic flux density of 30 teslas [T] (300,000 G), compared to a limit of roughly 15 T for NbTi.

<span class="mw-page-title-main">Pseudogap</span> State at which a Fermi surface has a partial energy gap in condensed matter physics

In condensed matter physics, a pseudogap describes a state where the Fermi surface of a material possesses a partial energy gap, for example, a band structure state where the Fermi surface is gapped only at certain points.

Frank Steglich is a German physicist and the founding director of the Max Planck Institute for Chemical Physics of Solids in Dresden, Germany.

<span class="mw-page-title-main">Iron-based superconductor</span>

Iron-based superconductors (FeSC) are iron-containing chemical compounds whose superconducting properties were discovered in 2006. In 2008, led by recently discovered iron pnictide compounds, they were in the first stages of experimentation and implementation..

<span class="mw-page-title-main">122 iron arsenide</span>

The 122 iron arsenide unconventional superconductors are part of a new class of iron-based superconductors. They form in the tetragonal I4/mmm, ThCr2Si2 type, crystal structure. The shorthand name "122" comes from their stoichiometry; the 122s have the chemical formula AEFe2Pn2, where AE stands for alkaline earth metal (Ca, Ba, Sr or Eu) and Pn is pnictide (As, P, etc.). These materials become superconducting under pressure and also upon doping. The maximum superconducting transition temperature found to date is 38 K in the Ba0.6K0.4Fe2As2. The microscopic description of superconductivity in the 122s is yet unclear.

Heavy fermion superconductors are a type of unconventional superconductor.

Gilbert "Gil" George Lonzarich is a solid-state physicist who works at the Cavendish Laboratory at the University of Cambridge. He is particularly noted for his work on superconducting and magnetic materials.

Several hundred metals, compounds, alloys and ceramics possess the property of superconductivity at low temperatures. The SU(2) color quark matter adjoins the list of superconducting systems. Although it is a mathematical abstraction, its properties are believed to be closely related to the SU(3) color quark matter, which exists in nature when ordinary matter is compressed at supranuclear densities above ~ 0.5 1039 nucleon/cm3.

Lanthanum decahydride is a polyhydride or superhydride compound of lanthanum and hydrogen (LaH10) that has shown evidence of being a high-temperature superconductor. It has a superconducting transition temperature TC around 250 K (−23 °C; −10 °F) at a pressure of 150 gigapascals (GPa), and its synthesis required pressures above ~160 GPa.

John Kenneth Hulm was a British-American physicist and engineer, known for the development of superconducting materials with applications to high-field superconducting magnets. In 1953 with George F. Hardy he discovered the first A-15 superconducting alloy.

References

  1. ↑ Sengers, Johanna Levelt: How Fluids Unmix: Discoveries by the School of Van der Waals and Kamerlingh Onnes. (Edita—the Publishing House of the Royal, 2002, 318 pp)
  2. ↑ van Delft, Dirk (2007) Freezing physics, Heike Kamerlingh Onnes and the quest for cold, Edita, Amsterdam, ISBN   9069845199.
  3. ↑ Blundell, Stephen: Superconductivity: A Very Short Introduction. (Oxford University Press, 1st edition, 2009, p. 20)
  4. ↑ Rogalla, Horst; Kes, Peter H. (2011-11-11). 100 Years of Superconductivity. Taylor & Francis. ISBN   978-1-4398-4948-4.
  5. 1 2 3 4 5 6 Geballe, T. H.; Hulm, J. K. (1996). Bernd Theodor Matthias 1918–1990 (PDF). National Academy of Science.
  6. ↑ Matthias, B. T.; Geballe, T. H.; Geller, S.; Corenzwit, E. (1954-09-15). "Superconductivity of Nb 3 Sn". Physical Review. 95 (6): 1435. Bibcode:1954PhRv...95.1435M. doi:10.1103/PhysRev.95.1435. ISSN   0031-899X.
  7. ↑ Matthias, B. T. (1955-01-01). "Empirical Relation between Superconductivity and the Number of Valence Electrons per Atom". Physical Review. 97 (1): 74–76. Bibcode:1955PhRv...97...74M. doi:10.1103/PhysRev.97.74. ISSN   0031-899X.
  8. 1 2 Grimaldi, C. (2001). "Possible mechanisms of high TC superconductivity". In Cifarelli, Luisa (ed.). Superconducting Materials for High Energy Colliders: Proceedings of the 38th Workshop of the INFN Eloisatron Project, Erice, Italy, 19-25 October 1999. World Scientific. ISBN   978-981-02-4319-7.
  9. ↑ Arrhenius, G.; Corenzwit, E.; Fitzgerald, R.; Hull, G. W.; Luo, H. L.; Matthias, B. T.; Zachariasen, W. H. (1968). "SUPERCONDUCTIVITY OF NB 3 (AL, GE) ABOVE 20.5°K". Proceedings of the National Academy of Sciences. 61 (2): 621–628. doi: 10.1073/pnas.61.2.621 . ISSN   0027-8424. PMC   225205 . PMID   16591705.
  10. ↑ Matthias, B. T. (1957-01-01), Gorter, C. J. (ed.), Chapter V Superconductivity in the Periodic System, Progress in Low Temperature Physics, vol. 2, Elsevier, pp. 138–150, doi:10.1016/s0079-6417(08)60104-3, ISBN   9780444533081 , retrieved 2023-08-09
  11. ↑ Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. (December 1957). "Theory of Superconductivity". Physical Review. 108 (5): 1175–1204. Bibcode:1957PhRv..108.1175B. doi: 10.1103/PhysRev.108.1175 .
  12. ↑ "Prize Recipient". www.aps.org. Retrieved 2023-08-09.
  13. ↑ Matthias, Bernd T. (1976), Douglass, D. H. (ed.), "Some Surprises in Superconductivity", Superconductivity in d- and f-Band Metals, Boston, MA: Springer US, pp. 635–642, doi:10.1007/978-1-4615-8795-8_39, ISBN   978-1-4615-8797-2 , retrieved 2023-08-10
  14. ↑ Steglich, F.; Aarts, J.; Bredl, C. D.; Lieke, W.; Meschede, D.; Franz, W.; Schäfer, H. (1979-12-17). "Superconductivity in the Presence of Strong Pauli Paramagnetism: Ce${\mathrm{Cu}}_{2}$${\mathrm{Si}}_{2}$". Physical Review Letters. 43 (25): 1892–1896. Bibcode:1979PhRvL..43.1892S. doi:10.1103/PhysRevLett.43.1892. hdl: 1887/81461 . S2CID   123497750.
  15. 1 2 3 4 Seidel, Paul (2015-01-22). Applied Superconductivity: Handbook on Devices and Applications. John Wiley & Sons. ISBN   978-3-527-67066-6.
  16. ↑ Saunders, P. J.; Ford, G. A. (2005). The Rise of the Superconductors. Boca Raton, FL: CRC Press. ISBN   0-7484-0772-3.
  17. ↑ Bednorz, J. G.; Müller, K. A. (1986). "Possible high Tc superconductivity in the Ba-La-Cu-O system". Zeitschrift für Physik B . 64 (2): 189–193. Bibcode:1986ZPhyB..64..189B. doi:10.1007/BF01303701. S2CID   118314311.
  18. 1 2 3 4 Uchida, Shin-ichi (2014-11-20). High Temperature Superconductivity: The Road to Higher Critical Temperature. Springer. ISBN   978-4-431-55300-7.
  19. 1 2 3 Mazin, Igor I. (2010). "Superconductivity gets an iron boost". Nature. 464 (7286): 183–186. Bibcode:2010Natur.464..183M. doi:10.1038/nature08914. ISSN   0028-0836. PMID   20220835. S2CID   4391681.
  20. ↑ Conder, K (2016-08-01). "A second life of the Matthias's rules". Superconductor Science and Technology. 29 (8): 080502. Bibcode:2016SuScT..29h0502C. doi: 10.1088/0953-2048/29/8/080502 . ISSN   0953-2048. S2CID   123619400.
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