SUPERCONDUCTIVITY

Discussion of phenomena occurring at low temperatures, held at the Royal Society of London on May 30, 1935.

Introductory Report

Prof. Max Lennan

When we speak of phenomena occurring at low temperatures, we are concerned chiefly with those properties of matter which are observed at temperatures obtained by means of liquid helium. Until 1923 liquid helium was produced only in Leiden. At the present time it is obtained not only in Holland, but also in the USA, Canada, England, Germany, and the Soviet Union.

New Methods for Liquefying Helium

The design of apparatus for the production of liquid helium after 1932 was improved in two directions. On the one hand, Simon and Mendelssohn developed a new type of installation, implemented in the Clarendon Laboratory at Oxford. In this installation liquid helium is obtained by means of a continuous process in a very inexpensive way, but in very small quantities. In this process cooling is achieved by adiabatic expansion of compressed gaseous helium. In addition, Simon and his collaborators obtain liquid helium by desorption of gaseous helium from charcoal.

According to another method, developed by Kapitza, the gas is first cooled by means of liquid nitrogen and then expands, doing external work in an expansion machine which is included in the cycle and operates at low temperatures without lubrication. In this way it is possible to reach a temperature of 10° K, after which liquefaction can already be produced with the aid of the Joule–Thomson effect.

Properties of Liquid Helium

At every pressure liquid helium has its own characteristic temperature at which it possesses the greatest density. Thus, at a pressure of 1 atm and at a temperature of 4.2° K, the density of liquid helium is 0.1252, which is approximately one eighth the density of water. The maximum density at a pressure of 1 atm, equal to 0.1473, is reached at 2.178° K. Many properties of liquid helium at the temperature of maximum density change discontinuously. Thus, the compressibility, the specific heat,

dielectric constant, and viscosity. Most of the other characteristic features it reveals in the region of change of temperature dependence.

The difference in the properties of liquid helium above and below the temperature \(2.178^\circ K\) is so considerable that special designations are usually introduced for these states: He I and He II. At the same time, despite the fact that the transition from one state to the other is not accompanied by the formation or release of latent heat, this transition can in some respects be regarded as a phase change. The relation between pressure and temperature and the other thermal relations characteristic of the transition of He I into He II, and also of liquid helium into solid helium, have been studied in great detail in Leiden. However, its state still remains insufficiently clear, both with respect to the nature of the transition and with respect to the possible structure of liquid He II. At present there are indications that He II does not correspond to a stable phase at \(0^\circ K\) and at low pressures, but the transition from He II to solid helium takes place with increasing pressure without energetic changes.

The lowest temperature attained by boiling under reduced pressure and by means of adiabatic demagnetization

The lowest temperature that has been attained with liquid helium alone is \(0.71^\circ K\), but recently a method has been developed for obtaining much lower temperatures. This method is based on the effect of cooling produced under certain conditions by means of adiabatic demagnetization. In 1926 Debye, and also Giauque, showed that if an experiment is begun from a sufficiently low temperature, then, by means of paramagnetic salts, appreciable cooling can be obtained. This method was tested by de Haas, Wiersma and Kramers, on the one hand, and by Simon and collaborators, on the other, and showed its considerable effectiveness. According to this method a salt is cooled with the aid of liquid helium, under reduced pressure, in a magnetic field of approximately 30 thousand gauss to a temperature of \(1.26^\circ K\). It is then thermally insulated, and the magnetic field is instantaneously reduced to a few hundred gauss or to even smaller values. Adiabatic demagnetization takes place, as a result of which the temperature is lowered. The temperature attained can be judged from the magnetic susceptibility of the same salt. By this method de Haas, working with KCr alums, attained in February 1935 a temperature of \(0.0044^\circ K\).

As Debye pointed out, the energy \(\mu H\) of a paramagnetic atom in a field of about 10 thousand gauss is of the order of magnitude and coincides with the thermal energy \(kT\) at \(1^\circ K\). Therefore paramagnetic saturation can be achieved in fields of this order at the temperature of liquid helium. But the nuclear magnetic moment is approximately one thousandth of the magnetic moment of the atom. This means that saturation of the nuclear moment may be expected in work with easily attainable fields in the region from \(0.001\) to \(0.01^\circ K\). Thus in some cases it is apparently quite possible to observe the influence of the nucleus on magnetic susceptibility.

Superconducting metals

Up to the present time superconductivity has been found in a number of elements listed in Table 1. To these should be added a large number of alloys, including some intermetallic-

chemical compounds, except for Au₂Bi, whose components, down to the temperatures to which they have been investigated, do not exhibit superconductivity. In addition, one must add certain nonmetallic compounds which, at ordinary temperatures, are only semiconductors.

TABLE 1

Superconducting elements

The question has long been discussed whether superconductivity is a general property, i.e., whether it can be observed in all metals under appropriate cooling. The new method of attaining very low temperatures by means of adiabatic demagnetization promises to bring us considerably closer to resolving this question. In particular, it would be extremely interesting to determine whether superconductivity can be observed in all monovalent metals and in ferromagnetics.

The Magnetic Field Outside Superconductors

A series of experiments on the investigation of the magnetic field outside a superconductor, undertaken by Meissner and his coworkers, recently opened new paths for the study of this question. The investigations are being carried out by four different methods. Meissner and his coworkers (Berlin) are studying the distribution of the field around cylinders, as well as inside a hollow cylinder, with the aid of a small test coil. Tarr (Toronto) measured the change of flux through fixed coils surrounding the bodies under investigation. De Haas and coworkers in Leiden measured the penetration of the field into a cylinder by threading through it a thin bismuth wire and observing changes in its resistance. Finally, Mendelssohn and Babbitt (Oxford) measured the magnetic moment induced in solid and hollow spheres when the magnetic field is varied, thereby returning to certain of the very first Leiden experiments.

When a pure metal at a temperature below its transition point is placed in a weak field, smaller than the critical field that destroys superconductivity, we obtain a quite definite result. In this case, in accordance with arguments based on ordinary electrodynamics, superconductors behave (in any case, after excluding a very thin surface layer) as if their magnetic permeability were equal to zero. But when the transition to the superconducting state takes place in the presence of a magnetic field, and it is immaterial how this transition is effected—by cooling in an unchanged magnetic field

or else by decreasing the intensity of the magnetic field, which had previously exceeded the critical value—in this case the experiments agree with one another only in the sense that they never give exactly the expected result. Nevertheless, certain experimental facts are singled out more or less definitely, at least for most of the metals investigated. First, there is no doubt that at the moment of transformation the external field is spontaneously redistributed, approaching almost the distribution that would occur if the induction inside the body were everywhere equal to zero. Secondly, the field inside a cavity, if it exists there, is in any case extremely insignificant, thereby itself constituting an extraordinarily strange fact: the existence of an apparently isolated part of the magnetic field in a stable state. Thirdly, in a solid body some variable part of the initial magnetic flux, as a result of the transformation, appears to be locked inside the body. Also, both outside and inside the cavity, this locked field cannot be disturbed by any external actions as long as the body remains in the superconducting state.

Gorter and Casimir proposed, in order to explain this third effect, to assume that the body passes into the superconducting state in layers. Indeed, experiments carried out in Toronto showed that the amount of locked flux for a given metal depends chiefly on the shape of the body under investigation. On the other hand, both in Berlin and in Toronto it was shown that it is quite immaterial whether we cool, for example, a cylinder from the outside or, having insulated it from the outside, pass liquid helium through an opening made in it.

The question of the magnetic flux in a superconductor is connected with the phenomenon of hysteresis, observed when the magnetic field is isothermally brought to values lying above the critical one and then lowered again. Another, although usually less emphasized, case of hysteresis is observed in the transformation that takes place as a result of a change in temperature in an unchanged magnetic field.

Superconductivity of thin films

A series of experiments on the investigation of the transformation points of thin films of tin and lead was carried out by Grayson-Smith, Meissner, and Wilhelm in Toronto. For thicknesses of the order of 1–10 μ, a certain lowering of the transformation point is observed, which may be a consequence of stresses caused by the nonuniform contraction of the film and of the substrate on which it is fixed. But for films with a thickness less than 1.0 μ for tin and 0.8 μ for lead, the transformation point begins to fall very rapidly, to the point that a film thinner than 0.3 μ cannot be made superconducting even at a temperature of 2°K (the lowest attained up to now in Toronto temperature). At the same time the region of transformation becomes extremely broadened.

The transformation points of these films proved to be very sensitive to an increase in the measuring current. In the case of the thinnest films that could still be made superconducting, the resistance reappeared already after bringing the current up to one sixth of the value necessary to create the critical magnetic field at the surface of the film. The action of an external magnetic field on the films was studied during the past year. It turned out that when the resistance reappears, then, in order to produce superconductivity, fields considerably exceeding the usual critical ones are required. This effect is noticeable even in comparatively thick films (up to 30 μ and more), prepared from substances whose normal transformation point does not differ greatly from the transformation point of tin. In this case the transverse field necessary for restoring superconductivity

the field is always considerably greater than the longitudinal one. The actions of the external field and of the internal current apparently add together, i.e., their effects are not independent. This shows that, perhaps, there exists some critical limit for the current density of superconductivity, but up to now it has not been possible to detect it because of the action of the magnetic field created by this current.

Another curious result of these experiments is the discovery of the influence, on the surface of a tin film, of a layer of nonsuperconducting metal deposited on it. It turned out that even for rather thick films (9 μ thick) a significant disturbance of superconductivity occurs. Thus, although the presence of a free surface is not a necessary condition for the onset of superconductivity, it nevertheless has a definite connection with this phenomenon.

Hall Effect in Superconductors

For the study of the Hall effect in superconductors, Burton, Grayson-Smith, and Tarr recently constructed a completely superconducting galvanometer, which aroused considerable interest. They are working with apparatus entirely immersed in liquid helium.

In addition to the study of the Hall effect, this galvanometer has also found application in the study of the thermoelectric effect between superconductors and of the distribution of undamped currents in a superconductor.

Thermal Conductivity at Low Temperatures

De Haas and Bremmer carried out a whole series of measurements of thermal resistance at the temperature of liquid helium, both in superconductors and in nonsuperconducting metals. For pure superconducting metals, when below the transition point, it was found that the thermal conductivity increases when the electrical superconductivity is destroyed by a magnetic field. Qualitatively this is not difficult to explain, since it is natural that in this case the thermal conductivity should disappear in that part which was due to the electrons responsible for superconductivity. However, quantitative agreement of this behavior of thermal conductivity with other experiments encounters considerable difficulties.

It follows from theory that the thermal resistance of an ideal lattice at a temperature of 0° K should become equal to zero. It actually reaches a minimum at a certain temperature lying in the region of existence of liquid helium, and this minimum decreases with increasing purity of the metal. This excess of thermal resistance in the region of very low temperatures is ascribed to impurities and irregularities in the structure of the lattice and is thus explained analogously to the residual electrical resistance.

In their experiments with nonsuperconducting metals, De Haas and Bremmer try to separate the action of irregularities from the action of the perfect lattice. This apparently must be achieved if we wish to learn anything more about the connection of thermal conductivity with other properties of superconductors.

Anomalous Behavior of Some Alloys

Recently it was found that in some superconducting alloys, especially in PbTl₂, the parallelism between changes in the magnetic and thermal properties is more perfect than in pure metals. In these alloys the destruction of superconductivity occurs only in extremely strong magnetic fields. But, in addition, Keesom recently found that

in contrast to Silsbee’s hypothesis, the maximum current that can flow in them without resistance is not at all equal to the current that, on the surface of the conductor, produces the critical magnetic field. Tarr (Toronto) found that the flux which existed in the alloy above the transition point is completely “locked in” in all the alloys studied when the body passes into the superconducting state, whereas in all pure metals, except tantalum, almost the entire original magnetic flux is expelled outward upon the transition to the superconducting state. Keesom found that the critical magnetic field penetrating to the center of the cylinder at any temperature is considerably smaller than the critical field which must be applied in order to restore resistance. In one of the alloys investigated, the destruction of superconductivity causes, instead, an increase in thermal conductivity, not its usual decrease. Tantalum behaves, as Tarr’s experiments have shown, more like an alloy than like a pure metal.

Furthermore, Silsbee and his coworkers have recently found that, like the alloys studied by Keesom, tantalum is abnormally sensitive to the current flowing in it.

Application of Calorimetry under Low-Temperature Conditions to Measurements of Radioactivity

Recently Simon pointed out the possibility of applying calorimetric methods at low temperatures to measure the action of γ-rays. The possibility of measuring by such a method the absorption of X-rays and γ-rays of various wavelengths in gaseous helium would be of considerable interest to radiologists. The realization of this possibility would make it possible to determine, for various frequencies, the irradiation dose in absolute units.

Application of Thermodynamics. Specific Heats

From a number of studies carried out in Leiden (Keesom and others) it has become clear that the heat capacity of superconductors at the transition point changes discontinuously. This transformation, apparently, is not accompanied by the formation of a noticeable amount of latent heat. However, an energy change, similar in nature to the effect of latent heat, occurs in the case when the normal state is restored by means of a magnetic field at a temperature lying below the transition point. Moreover, when a magnetic field is applied adiabatically, a change in temperature is observed.

The only significant success in the theoretical study of superconductivity was the consideration undertaken by Gorter and Casimir of the relation between the described behavior of the specific heat and the critical magnetic field. Assuming that the energy of a superconductor in a magnetic field changes in the same way as in a diamagnetic body with permeability equal, for fields smaller than the critical value, to \(-\frac{1}{4\pi}\), these authors considered a thermodynamic cycle in which the body is first cooled in the absence of a field; then the field is applied isothermally and increased to some value exceeding the critical one; after that the body is heated to a state lying above the transition point.

If the reversibility of the cycle is assumed, this gives a relation between the specific heat and the critical value of the field at various temperatures. The experimental data for tin and thallium are in excellent agreement with the thermodynamic calculations.

Electromagnetic Theory of Superconductivity

The ordinary electromagnetic equations are not applicable to superconductors, since they become indeterminate. Becker and his collaborators suggested that the natural form of the ordinary equations will be obtained if the acceleration of the electrons can be taken into account. In this way they obtained a relation between the rate of change of the current and the electric field, from which it follows that, during a change of current, the field can exist instantaneously. A distribution of currents in a surface layer of thickness \(10^{-5}\)—\(10^{-4}\) cm was obtained. The consequences of such a treatment are in a certain contradiction with Meissner’s experiments, in which a spontaneous redistribution of the magnetic field during a purely thermal transformation was observed. Considering this to be evidence of the incorrectness of the conception of accelerating electrons, London has recently arrived at the conclusion that it is necessary to create a new form of electromagnetic equations specifically for superconductors. On the other hand, Grayson Smith (Toronto) interpreted these experiments as evidence of the spontaneous appearance of local vortex currents, i.e., he adopted the point of view first expressed by Frenkel. According to this point of view, in order to explain Meissner’s experiments and to obtain agreement with Gorter’s thermodynamic calculation, a very large diamagnetic susceptibility must be ascribed to the body. The smallest effective dimensions of the vortices then agree, in order of magnitude, with the critical thickness of thin films at which a noticeable disturbance of superconductivity begins.