Kamerlingh Onnes Research Articles

Museums theme – Quest for Absolute Zero: A Human Story about Rivalry and Cold

In 2008 Rijksmuseum Boerhaave organised an exhibition on the occasion of the centennial of the liquefaction of helium by Kamerlingh Onnes in Leiden. Quest for Absolute Zero was the first major temporary exhibition aimed at new target groups. Therefore the focus was on the human scale and the colourful story behind the ‘man of Absolute Zero’. The fierce competition with James Dewar from the Royal Institution was also highlighted. The outcome of Quest for Absolute Zero was extremely positive for Rijksmuseum Boerhaave in terms of visitor numbers, media coverage, collaborations and side events. The project also proved to be a very useful lever for the renewal of the permanent exhibition, scheduled to open in December 2017.

A New Interpretation of Contributions Presented at the Solvay Conference 1911. Can We Falsify the “Geocentric” Foundations of Quantum Mechanics in the Solar System?

We have studied the contributions and presentations published in the Proceedings of the Solvay Conference 1911. Based on the lecture of Ernest Solvay on the “gravito-matérialitique” we can distinguish two features of the Earth´s gravitational field – 1. “gravité réelle” described by the Newton´s gravitational law and 2. “gravité potentielle” acting as an agent of the self-organization on quantum particles and creating structures described by the Planck constant hEARTH. From the discussions followed after the presentations of Walther Nernst and Albert Einstein we interpreted the Nernst- Lindemann Formula for the specific heat of solids using the comment of Heike Kamerlingh Onnes (the discoverer of the superconductivity) as two transverse and one longitudinal oscillations of phonon in the surroundings at temperature T. In order to falsify this “geocentric” model of foundations of quantum mechanics in the spirit of Karl Popper we propose to initiate the CURE Project (China – USA – Russia – European Union) (cure = to solve a problem) in order to build quantum laboratories on different orbits around the Earth, on the surface of the Moon and Mars, and in the Lagrange points of the system the Earth – Moon and the Earth – Sun to get new experimental data for the specific heat of solids, the critical temperatures of superconductors, chemical and physical self-organized reactions (Liesegang rings, Belousov- Zhabotinsky waves, chemical clocks, Bose-Einstein condensates, de Broglie waves, etc.). There is space enough for all participants on this CURE Project to collect new valuable data describing this “hidden variable” presented by Ernest Solvay in his forgotten lecture in 1911.

The Bose-Einstein statistics: Remarks on Debye, Natanson, and Ehrenfest contributions and the emergence of indistinguishability principle for quantum particles

The principal mathematical idea behind the statistical properties of black-body radiation (photons) was introduced already by L. Boltzmann (1877/2015) and used by M. Planck (1900; 1906) to derive the frequency distribution of radiation (Planck’s law) when its discrete (quantum) structure was additionally added to the reasoning. The fundamental physical idea – the principle of indistinguishability of the quanta (photons) – had been somewhat hidden behind the formalism and evolved slowly. Here the role of P. Debye (1910), H. Kamerlingh Onnes and P. Ehrenfest (1914) is briefly elaborated and the crucial role of W. Natanson (1911a; 1911b; 1913) is emphasized. The reintroduction of this Natanson’s statistics by S. N. Bose (1924/2009) for light quanta (called photons since the late 1920s), and its subsequent generalization to material particles by A. Einstein (1924; 1925) is regarded as the most direct and transparent, but involves the concept of grand canonical ensemble of J. W. Gibbs (1902/1981), which in a way obscures the indistinguishability of the particles involved. It was ingeniously reintroduced by P. A. M. Dirac (1926) via postulating (imposing) the transposition symmetry onto the many-particle wave function. The above statements are discussed in this paper, including the recent idea of the author (Spałek 2020) of transformation (transmutation) – under specific conditions – of the indistinguishable particles into the corresponding to them distinguishable quantum particles. The last remark may serve as a form of the author’s post scriptum to the indistinguishability principle.

Functional form of the superconducting critical temperature from machine learning

Predicting the critical temperature $T_c$ of new superconductors is a notoriously difficult task, even for electron-phonon paired superconductors for which the theory is relatively well understood. Early attempts by McMillan and Allen and Dynes to improve on the weak-coupling BCS formula led to closed-form approximate relations between $T_c$ and various measures of the phonon spectrum and the electron-phonon interaction appearing in Eliashberg theory. Here we propose that these approaches can be improved with the use of machine learning algorithms. As an initial test, we train a model for identifying low-dimensional descriptors using the $T_c < 10$ K data tested by Allen and Dynes, and show that a simple analytical expression thus obtained improves upon the Allen-Dynes fit. Furthermore, the prediction for the recently discovered high $T_c$ material H$_3$S at high pressure is quite reasonable. Interestingly, $T_c$'s for more recently discovered superconducting systems with a more two-dimensional electron-phonon coupling, which do not follow Allen and Dynes' expression, also do not follow our analytic expression. Thus, this machine learning approach appears to be a powerful method for highlighting the need for a new descriptor beyond those used by Allen and Dynes to describe their set of isotropic electron-phonon coupled superconductors. We argue that this machine learning method, and its implied need for a descriptor characterizing Fermi surface properties, represents a promising new approach to superconductor materials discovery which may eventually replace the serendipitous discovery paradigm begun by Kamerlingh Onnes.

High-temperature superconductors: underlying physics and applications

Abstract Superconductivity was discovered in 1911 by Kamerlingh Onnes and Holst in mercury at the temperature of liquid helium (4.2 K). It took almost 50 years until in 1957 a microscopic theory of superconductivity, the so-called BCS theory, was developed. Since the discovery a number of superconducting materials were found with transition temperatures up to 23 K. A breakthrough in the field happened in 1986 when Bednorz and Müller discovered a new class of superconductors, the so-called cuprate high-temperature superconductors with transition temperatures as high as 135 K. This surprising discovery initiated new efforts with respect to fundamental physics, material science, and technological applications. In this brief review the basic physics of the conventional low-temperature superconductors as well as of the high-temperature superconductors are presented with a brief introduction to applications exemplified from high-power to low-power electronic devices. Finally, a short outlook and future challenges are presented, finished with possible imaginations for applications of room-temperature superconductivity.

The Path to Type-II Superconductivity

Following the discovery of superconductivity by Heike Kamerlingh Onnes in 1911, research concentrated on the electric conductivity of the materials investigated. Then, it was Max von Laue who in the early 1930s turned his attention to the magnetic properties of superconductors, such as their demagnetizing effects in a weak magnetic field. As a consultant at the Physikalisch-Technische Reichsanstalt in Berlin, von Laue was in close contact with Walther Meissner at the Reichsanstalt. In 1933, Meisner together with Robert Ochsenfeld discovered the perfect diamagnetism of superconductors (Meissner–Ochsenfeld effect). This was a turning point, indicating that superconductivity represents a thermodynamic equilibrium state and leading to the London theory and the Ginzburg–Landau theory. In the early 1950s in Moscow, Nikolay Zavaritzkii carried out experiments on superconducting thin films. In the theoretical analysis of his experiments, he collaborated with Alexei A. Abrikosov and for the first time they considered the possibility that the coherence length ξ can be smaller than the magnetic penetration depth λ m . They called these materials the “second group”. Subsequently, Abrikosov discovered the famous Abrikosov vortex lattice and the superconducting mixed state. The important new field of type-II superconductivity was born.

Investigations into the origin of Einstein’s Sink

Einstein's sink is a well-known object among physics and astronomy students at Leiden University. Stories about its origin have been passed down since it was moved to the large lecture room of the then newly built Oort Building in 1998. These stories claim that it was seen as an Einstein relic by the physics faculty, kept close to inspire young minds. After researching this story, I found that the sink is from the early 20th century and that it once stood in the large lecture room of the Kamerlingh Onnes Laboratory in Leiden. It is likely that at this time it was used by many scientists, including Einstein. However, my research also shows that the move from the KOL was done purely for financial reasons and had nothing to do with Einstein. It is possible that the story was made up to conceal this fact, creating a more appealing reason for these cutbacks. The sink is seen by many as a connection to Einstein's and the university's past and is liked for this fact and not the aforementioned legend.

Anisosphere analysis of the equivalence between a precessing Foucault pendulum and a torsional balance

The residual anisotropy of a real Foucault pendulum is responsible for an oscillatory behaviour of the precession angle according to the original description given by Kamerlingh Onnes in his dissertation. A simulation of the experimental procedure of enchained runs, consisting of starting a short experiment at the azimuth at which a precedent similar experiment has been stopped, has been performed using the anisosphere model. It leads to the conclusion that the precessing pendulum undergoes oscillations in precession associated with an extremely shallow potential well analogous to the potential well of a very slow torsional balance. Such systems are therefore rendered sensitive to extremely-low-energy perturbations. To the author’s knowledge, the hypersensitivity of the oscillatory precession of the anisotropic Foucault pendulum has been unravelled for the first time thanks to the analysis and visualization power of the anisosphere model. In particular, the periodic apparent motion of celestial bodies appears to modify the anisotropy characteristic of the precession potential well. This may provide likelihood for the similar responses of the paraconical pendulum of Allais during the 1950’s and of the torsion pendulum of Saxl and Allen in 1970 to certain Sun-Moon-Earth syzygies.

The anisosphere model: a novel differential phase space representation for Foucault pendulums and 2D oscillators

It is customary to describe the behaviour and stability of oscillators with the help of phase space representation. However, two-dimensional (2D) oscillators like the Foucault pendulum call for a 4D phase space that is not simple to visualize. Applying celestial body perturbation theory to the Foucault pendulum in his doctor dissertation, Nobel laureate Kamerlingh Onnes showed that the essential features of a Foucault pendulum are its inherent circular and linear anisotropies. A spherical differential 2D sub-space can be defined, where the group of the points of a spherical surface with respect to the operation rotation about a diametral axis is isomorphic with the group of sequential states of oscillation of a 2D pendulum with respect to the operation translation in time. Any Foucault pendulum is then characterized by two elliptical eigenstates which are represented by the poles of that rotation axis on the so-called anisosphere. Such poles play the role of attractor/repellor when “dichroic” damping is present. Moreover, they move drastically within a meridian plane when nonlinear restoring torque giving rise to Airy precession occurs. The concept of anisosphere constitutes a very powerful tool for analysing and optimizing actual Foucault pendulum implementations. That feature is illustrated by a numerical model.

Foucault and the rotation of the Earth

Abstract In February 1851, Leon Foucault published in the Comptes rendus his famous pendulum experiment performed at the “Observatoire de Paris”. This ended two centuries of quest for an experimental demonstration of Earth rotation. One month later, the experiment was reproduced at larger scale in the Pantheon and, as early as the summer of 1851, it was being repeated in many places across the world. The next year, Foucault invented the gyroscope to get a still more direct proof of Earth rotation. The theory relied on the masterpiece treatise of Laplace on celestial mechanics, published in 1805, which already contained the mathematical expression of the force that would be discovered by Gustave Coriolis 30 years later. The idea of a fictitious inertial force proposed by Coriolis prevailed by the end of 19th century, as it was conceptually simpler than Laplace's approach. The full theory of the Foucault pendulum, taking into account its unavoidable imperfections, was not obtained until three decades later by Kamerlingh Onnes, the future discoverer of liquid helium and superconductivity. Today, Foucault's exceptional creativity is still a source of inspiration for research and the promotion of science through experimental proofs widely available to the public.

The anisosphere as a new tool for interpreting Foucault pendulum experiments. Part I: harmonic oscillators

In an attempt to explain the tendency of Foucault pendula to develop elliptical orbits, Kamerlingh Onnes derived equations of motion that suggest the use of great circles on a spherical surface as a graphical illustration for an anisotropic bi-dimensional harmonic oscillator, although he did not himself exploit the idea any further. The concept of anisosphere is introduced in this work as a new means of interpreting pendulum motion. It can be generalized to the case of any two-dimensional (2-D) oscillating system, linear or nonlinear, including the case where coupling between the 2 degrees of freedom is present. Earlier pendulum experiments in the literature are revisited and reanalyzed as a test for the anisosphere approach. While that graphical method can be applied to strongly nonlinear cases with great simplicity, this part I is illustrated through a revisit of Kamerlingh Onnes’ dissertation, where a high performance pendulum skillfully emulates a 2-D harmonic oscillator. Anisotropy due to damping is also described. A novel experiment strategy based on the anisosphere approach is proposed. Finally, recent original results with a long pendulum using an electronic recording alidade are presented. A gain in precision over traditional methods by 2–3 orders of magnitude is achieved.

Story of superconductivity

Electricity is carried through metallic wires, called conductors. In the process, electrons move through metallic conductors that offer resistance (the value depends on the particular metal used), to the passage of electrons. This leads to the production of heat and loss of energy. This heating process is utilised in many electrical devices. However, for transmission of electrical energy from the power plants to the user and in many other applications, it would be a great boon if no energy was lost to resistance. The discovery of superconductivity by Heike Kamerlingh Onnes in 1911 at Leiden, offered a glimmer of hope to make this dream possible. It was a discovery totally unexpected at that time, and we owe this discovery to the painstaking and methodical investigations of Onnes–first to produce very low temperatures, and then measure properties of materials at these freezing temperatures.

Kamerlingh Onnes en Einstein: ‘Uw hulp zal dus veel goeds tot stand kunnen brengen’

Kamerlingh Onnes and Einstein In 1901 Albert Einstein unsuccessfully applied for the post of assistant in Heike Kamerlingh Onnes’ cryogenics laboratory. Ten years later the two scientists finally met each other. Einstein was interested in the experimental research taking place in Leiden into critical light scattering, a field to which he had made theoretical contributions himself. Kamerlingh Onnes on his part hoped Einstein might throw light on the unexplained phenomenon of superconductivity and on the influence of quantum effects on Leiden’s key research topic: equation of state.

Discoveries in Superconductivity, Persistent-Switch Magnets, and Magnetic Cooling

A historical review of developments in superconducting magnets begins with Kamerlingh Onnes’ construction of the first one in 1914 and extends to the invention of the superconducting persistent switch reported in 1963. A section on magnetic cooling includes refrigeration by paramagnetic salts and by nuclei in metals, as well as direct nuclear demagnetization in which only the nuclei are cooled.

Foucault Pendulum without Driving

Foucault pendulums are two-dimensional harmonic oscillators to which the Coriolis force is applied. The Foucault parameter ΩF is the ideal rate of rotation of the plane of oscillation due to the Coriolis force. Kamerlingh Onnes pointed out that the actual behavior of Foucault pendulums can be understood only by taking into account the unavoidable mechanical asymmetry, i.e., the difference between the frequency in the X-direction and that in the Y-direction, which is called the asymmetry parameter δ. Our equations of motion for Foucault pendulums are linear and their solutions are easily obtained. We are interested in slowly varying rotations of the plane of oscillation, where the angle of rotation is denoted by φ. The motion of the bob consists of rapid simple oscillations and the slow rotations mentioned above. Eliminating the rapid oscillations, we obtain an analytic expression for tan 2φ, which is a periodic function with period \(\pi /\sqrt{\Omega _{\text{F}}^{2} + \delta ^{2}} \). The graphs of the rotation φ versus time t have two distinct appearances. Under the condition ΩF ≥ δ|cos(2θ)| (θ is the initial value of φ), φ decreases monotonically, which is the behavior expected for Foucault pendulums. Otherwise φ repeatedly increases and decreases, which is the behavior of pendulums describing Lissajous figures. The vertical component of angular momentum is also calculated analytically.

100 years of Philips Research

On Thursday 23 October 1913, a Dutch newspaper published the following advertisement: Hiring: A capable young scientist with a doctorate in physics. Must be a good experimenter. Letters containing information on age, life history and references may be submitted to Philips in Eindhoven. Two days later, a candidate applied: Gilles Holst. At that time, Holst was working in Leiden as an assistant to Heike Kamerlingh Onnes, a recent Nobel Prize winner.

Paul Ehrenfest’s final years

New access to his correspondence sheds light on the tragic life and death of one of the pioneers of modern physics.

A Perspective on Medical Applications of High Temperature Superconductors

Superconductivity was first discovered in mercury in 1911 by Dutch physicist Kamerlingh Onnes of Leiden University. Superconductivity has also been discovered in a number of other metallic elements. Collectively these elements are called low temperate superconductors (LTS). In 1986, Bednorz and Muller discovered superconductivity in a brittle ceramic Ba-La-Cu-O compound at 30 K [1]. A number of other compounds like yttrium barium copper oxide (YBCO), bismuth strontium calcium copper oxide (BSCCO) and thallium barium calcium copper oxide (TBCCO) have been found to superconduct at even higher temperatures. The highest superconducting temperature of 138 K was observed in a thallium-doped, mercuric cuprate in 1994. A new family of arsenic based superconducting materials termed oxypnictides has been discovered recently. These compounds are collectively called high temperature superconductors (HTS).

Heike Kamerlingh Onnes and the Nobel Prize in Physics for 1913: The Highest Honor for the Lowest Temperatures

One century ago this year the Dutch experimental physicist Heike Kamerlingh Onnes (1853–1926) was awarded the Nobel Prize in Physics for his work in low-temperature physics, in particular for his production of liquid helium. I trace the route to his Nobel Prize within the context of his and his colleagues’ research in his laboratory at the University of Leiden, and in light of his nominators and the nominations he received in the five years 1909–1913.

1932, a watershed year in nuclear physics

The consequences, for good and ill, of that annus mirabilis of discovery and invention are still very much with us.