Physics:Matthias rules

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Short description: Physical laws about superconductivity
Not to be confused with Matthiessen's rule.

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.

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.
Further information: Physics:History of superconductivity

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]

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) (in en). 100 Years of Superconductivity. Taylor & Francis. ISBN 978-1-4398-4948-4. https://books.google.com/books?id=fnbRBQAAQBAJ&dq=matthias+rules+john+hulm&pg=PA216. 
  5. ↑ 5.0 5.1 5.2 5.3 5.4 5.5 Geballe, T. H.; Hulm, J. K. (1996). Bernd Theodor Matthias 1918–1990. National Academy of Science. http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/matthias-bernd.pdf. 
  6. ↑ Matthias, B. T.; Geballe, T. H.; Geller, S.; Corenzwit, E. (1954-09-15). "Superconductivity of Nb 3 Sn" (in en). Physical Review 95 (6): 1435. doi:10.1103/PhysRev.95.1435. ISSN 0031-899X. Bibcode: 1954PhRv...95.1435M. https://link.aps.org/doi/10.1103/PhysRev.95.1435. 
  7. ↑ Matthias, B. T. (1955-01-01). "Empirical Relation between Superconductivity and the Number of Valence Electrons per Atom" (in en). Physical Review 97 (1): 74–76. doi:10.1103/PhysRev.97.74. ISSN 0031-899X. Bibcode: 1955PhRv...97...74M. https://link.aps.org/doi/10.1103/PhysRev.97.74. 
  8. ↑ 8.0 8.1 Grimaldi, C. (2001). "Possible mechanisms of high TC superconductivity". in Cifarelli, Luisa (in en). 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. https://books.google.com/books?id=vjCtzYfcfBQC&dq=grimaldi+superconductivity+matthias+rules&pg=PA30. 
  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 20.5K" (in en). Proceedings of the National Academy of Sciences 61 (2): 621–628. doi:10.1073/pnas.61.2.621. ISSN 0027-8424. PMID 16591705. 
  10. ↑ Matthias, B. T. (1957-01-01), Gorter, C. J., ed. (in en), Chapter V Superconductivity in the Periodic System, Progress in Low Temperature Physics, 2, Elsevier, pp. 138–150, doi:10.1016/s0079-6417(08)60104-3, ISBN 9780444533081, https://www.sciencedirect.com/science/article/pii/S0079641708601043, retrieved 2023-08-09 
  11. ↑ Bardeen, J.; Cooper, L. N.; Schrieffer, J. R. (December 1957). "Theory of Superconductivity". Physical Review 108 (5): 1175–1204. doi:10.1103/PhysRev.108.1175. Bibcode: 1957PhRv..108.1175B. 
  12. ↑ "Prize Recipient" (in en). http://www.aps.org/programs/honors/prizes/prizerecipient.cfm. 
  13. ↑ Matthias, Bernd T. (1976), Douglass, D. H., ed., "Some Surprises in Superconductivity" (in en), 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, http://link.springer.com/10.1007/978-1-4615-8795-8_39, 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. doi:10.1103/PhysRevLett.43.1892. Bibcode: 1979PhRvL..43.1892S. https://link.aps.org/doi/10.1103/PhysRevLett.43.1892. 
  15. ↑ 15.0 15.1 15.2 15.3 Seidel, Paul (2015-01-22) (in en). Applied Superconductivity: Handbook on Devices and Applications. John Wiley & Sons. ISBN 978-3-527-67066-6. https://books.google.com/books?id=PuhpBgAAQBAJ. 
  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. doi:10.1007/BF01303701. Bibcode: 1986ZPhyB..64..189B. 
  18. ↑ 18.0 18.1 18.2 18.3 Uchida, Shin-ichi (2014-11-20) (in en). High Temperature Superconductivity: The Road to Higher Critical Temperature. Springer. ISBN 978-4-431-55300-7. https://books.google.com/books?id=j8WPBQAAQBAJ. 
  19. ↑ 19.0 19.1 19.2 Mazin, Igor I. (2010). "Superconductivity gets an iron boost" (in en). Nature 464 (7286): 183–186. doi:10.1038/nature08914. ISSN 0028-0836. PMID 20220835. Bibcode: 2010Natur.464..183M. https://www.nature.com/articles/nature08914. 
  20. ↑ Conder, K (2016-08-01). "A second life of the Matthias's rules". Superconductor Science and Technology 29 (8): 080502. doi:10.1088/0953-2048/29/8/080502. ISSN 0953-2048. Bibcode: 2016SuScT..29h0502C. 



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