Abstract
At ambient temperatures bismuth has a layered structure and shows an extremely strong fluctuation of the resistance in a magnetic field, as well as substantial diamagnetism, meaning it is repelled by a magnetic field, as an applied magnetic field creates an induced magnetic field in the opposite direction.
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Notes
- 1.
This property of bismuth was actually often used to measure magnetic fields, but its behaviour was still far from understood.
- 2.
Kapitsa had also tried to use the Obreimov-Shubnikov and the Bridgman methods to obtain crystal rods of about 3–5 mm in length with the crystallographic axis parallel and perpendicular to the axis of the rod, i.e. with perfect cleavage planes perpendicular or parallel to the length of the rods, but had not succeeded and developed an alternative method.
- 3.
This must have been the steatite brought over from Leningrad as mentioned before.
- 4.
The firm was founded in 1879 in Germany by Eugen Hartmann, who was joined in 1882 by Wunibald Braun forming the firm E. Hartmann & Co and continuing as Hartmann and Braun from 1901. By the turn of the century it had become a leading supplier of instrumentation devices. After several takeovers in the post-war years, it was finally taken over in 1999 by Asea Brown Boveri (ABB) AG and fully integrated into the ABB Group.
- 5.
Hilger was founded in 1874 by two German precision optical instrument technicians Adam and Otto Hilger. They had fled Germany a few years previously to escape religious persecution and set up manufacturing of precision optical and mechanical instruments in London. The company prospered and also started to make high quality synthetic crystals since crystals that had previously been used did not keep pace with the increasing demands on optical components for infrared spectroscopy. Hilger started to grow and process synthetic crystals in house, which implied the birth of crystal growth at Hilger. In 1948 Hilger amalgamated with the metrology instrument manufacturer E.R. Watts and the company became known as Hilger and Watts. In July 2010 Hilger was acquired by the US corporation Dynasil. (Information from the website www.hilger-crystals.co.uk.)
- 6.
A German firm in Berlin. The Firma Kahlbaum Laborpräparate was founded in 1890, merged in 1927 with Firma Schering to form Schering-Kahlbaum AG, which was acquired in 2006 by Bayer AG.
- 7.
Casimir cannot have known the Shubnikovs very well, else he would certainly have remembered that her first name was Olga; so it is also doubtful that he knew her as being charming.
- 8.
And six publications in Proc. Roy. Acad. Amsterdam 33 (1930) 130–133; 327–331; 351–362; 363–378; 418–432; 433–439, which were also published as Leiden Communications (207a (1930) 3; 207b (1930) 9; 207c (1930) 17; 207d (1930) 35; 210a (1930) 3; 210b (1930) 21).
- 9.
At nitrogen temperatures (about −200 °C) the quantum effects already disappear.
- 10.
It was apparently first called as such in 1950 by B.I. Verkin, B.G. Lazarev, N.S. Rudenko, Periodicheskaja zavisimost’ vospriikchivosti metallov ot polja pri nizkikh temperaturakh (Periodic dependence of the susceptibility of metals on the field at low temperatures), Zhurn. eksperim. i teoret. fiziki 20 (1950) 93–97. This shows that Shubnikov’s name was not completely shunned by physicists even before Stalin’s death.
- 11.
Pieter Martinus van Alphen (1906–1967). Obtained his PhD with De Haas in 1933 and later went to work for the Philips company in Eindhoven (Netherlands).
- 12.
David Shoenberg (1911–2004) carried out many experiments on magnetic oscillations, at Cambridge and at Kapitsa’s institute in Moscow. “In his pioneering experiments of the 1960’s, Shoenberg revealed the richness and deep essence of the quantum oscillation effect and showed how the beauty of the effect is disclosed under nonlinear conditions imposed by interactions in the system under study.” (V.M. Pudalov, David Shoenberg and the beauty of quantum oscillations, Low Temp. Phys. 37 (2011) 8–18, p. 8.)
- 13.
The Fermi surface is an abstract boundary (i.e. not in real space) useful for predicting the thermal, electrical, magnetic, and optical properties of metals, semimetals and doped semiconductors. The shape of the Fermi surface is derived from the periodicity and symmetry of the crystalline lattice and from the occupation of electronic energy bands. Electrons in crystals are arranged in energy bands separated by regions in energy which cannot be occupied by electrons (energy gaps). The existence of a Fermi surface is a direct consequence of the Pauli exclusion principle (Wikipedia).
- 14.
J.W. Blom (1908–1975): studied in Leiden, gained his PhD with De Haas in 1950 on the Magneto-resistance for crystals of gallium, but always wanted to become a teacher. From 1944 he taught at the Rembrandt Lyceum in Leiden, later became director of a secondary school in Den Helder and in 1961 of his former school, the Rembrandt Lyceum in Leiden.
- 15.
Diamagnetism is the phenomenon that, when an external magnetic field is applied to a material, an induced magnetic field is created in a direction opposite to the external field. It is a (rather weak) quantum mechanical effect occurring in all materials. When it is the only contribution to the material’s magnetism, the material is called a diamagnet. It was first discovered in bismuth and antimony by the Dutch botanist and physician Sebald Justinus Brugmans (1763–1819). In 1845 Michael Faraday (1791–1861) demonstrated that every material reacted (in either a diamagnetic or (para)magnetic way) to an external magnetic field and coined the name diamagnetism, contrary to substances that are called magnetic as they are attracted by a magnet. The magnetic group was later subdivided into ferromagnetic and paramagnetic substances.
- 16.
In the classical theory it would be zero.
- 17.
The actual predictions of his theory indeed qualitatively resemble the experimental data, but the magnetisation came out much too small. This was later rectified. It goes beyond the scope of this book to treat this here in any detail.
- 18.
The Fermi-level or Fermi-energy is the topmost energy filled by an electron at absolute zero, where it is equal to the chemical potential. In a band structure picture, the Fermi level can be considered to be a hypothetical energy level of an electron, such that at thermodynamic equilibrium this energy level would have a 50% probability of being occupied at any given time.
- 19.
- 20.
There can also be no doubt that as a woman she was in a disadvantageous position, both in Leningrad and in Leiden, but especially in Leiden.
- 21.
This shows that as a woman she was not taken as seriously as her husband and even belittled; it would have been unthinkable for Shubnikov to have been given such a name.
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Reinders, L.J. (2018). Shubnikov’s Scientific Work in Leiden: Shubnikov—De Haas Effect. In: The Life, Science and Times of Lev Vasilevich Shubnikov. Springer Biographies. Springer, Cham. https://doi.org/10.1007/978-3-319-72098-2_5
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