Experiments on Superconductivity Conducted in Oxford

K. Mendelssohn

The experiments carried out in Oxford were concerned chiefly with the study of magnetic induction, as well as of the energy of various substances in the superconducting state. According to the observations of Meissner and Ochsenfeld^28 in a tin cylinder cooled in a mag-

field, the induction disappears upon transition through the value critical for superconductivity. Gorter\(^{29}\) has thermodynamically investigated the proposition that the reduction of the induction to zero distinguishes the superconducting state from the normal one. It is necessary, however, to emphasize that comparing the equality to zero of the resistivity \(R\) and of the magnetic induction \(B\) must be regarded as a purely empirical fact which cannot, generally speaking, be derived from electrodynamic considerations.

It therefore seems desirable first of all to determine whether, for all substances in the superconducting state, it is indeed characteristic that \(B=0\), and whether the thermal effect that should be expected according to Gorter’s investigations actually exists.

Change of Induction

Fig. 3 shows a typical critical curve for a superconductor which, in the case \(B=0\), indicates the difference between the values of the free energy in the normal and superconducting states.

Fig. 3.

At first the change in induction was investigated in solid and hollow bodies of spherical shape, and two different methods were used\(^{30}\). According to one of them, the critical curve was crossed in a constant field, but the temperature was varied \((p_4 \to p_3 \to p_4)\); according to the other, the temperature remained unchanged, but the field was varied \((p_2 \to p_5 \to p_2)\). In all cases it proved that, when the critical curve is crossed in the direction from the normal state to the superconducting one, at any point of it except \(T_0\), the induction decreases, but does not become zero. Thus, for example, when we cool a sphere in the absence of a field \((p_1 \to p_2)\), and then apply a field at constant temperature \((p_2 \to p_5)\), the induction in the body under investigation is equal to zero until we pass the critical value. This can be predicted purely electrodynamically for this special case from the condition \(R=0\). With a further increase of the field \((p_2 \to p_5)\), the sphere passes into the normal state, and the induction in it becomes normal.

However, if the field is then again decreased, the induction does not return to zero, but a certain part of the magnetic flux is “frozen” inside. This part is considerably larger for a hollow sphere than for a solid one. Since from these experiments it follows that the reversibility of changes in induction is determined by the geometric form of the specimen, in all subsequent experiments the investigations were carried out only on bodies of elongated shape placed in a longitudinal magnetic field.

The behavior of the induction was investigated in superconducting mercury, tin, lead, tantalum, and various alloys (SnBi, SnCd, PbBi, PbTl\(_2\))\(^{31}\). The only substance in which the changes occur completely reversibly is mercury. In a single crystal of tin, in polycrystalline tin, and in lead, from 6 to 15% of the total flux is “frozen,” passing through the body under investigation at the critical point \((p_2 \to p_5 \to p_2)\); the fraction of the flux frozen in tantalum is considerably larger and differs in different specimens. In all alloys the entire flux penetrating them is completely frozen. However, in some alloys a penetration of lines of force is observed even when they are below the critical curve\(^{32}\). Since these experiments indicate

Experiments on Superconductivity

depended on the amount of “frozen-in” flux, mainly on the purity of the specimen, a study was undertaken of lead containing an admixture of bismuth in amounts of 1, 4, and 10%. Indeed, the experiments showed that “freezing-in” is enhanced as the admixture of the second component increases.

This fact—that the relative magnitude of the residual flux depends on contamination of the substance—apparently has deep significance. Let us recall that alloys usually have much higher critical values than pure superconductors. But this means that those regions of the specimen in which contaminations or deliberately added inclusions of the second component form alloys will pass into the superconducting state more rapidly than the remaining parts of it. These regions with high critical values may form “rings,” which are responsible for the “freezing-in.” In alloys containing the second component in a considerable quantity, these “rings” form an all-encompassing network of “sponges”—regions with high critical value. Thanks to it, all lines of force penetrating the specimen will be caught by persistent currents. Since in many metals contaminations are located mainly on the boundary surfaces of crystallites, it is quite possible that the number of frozen-in lines of force is determined both by the sizes of the crystals and by the extent to which, in preparing the specimen under investigation, conditions of “self-purification” were ensured, as occurs, for example, in slow crystal growth.

It is known, moreover, that the critical value of the field for a given substance also changes when the crystal lattice is deformed, as caused, for example, by external pressure[^33]. Therefore not only contamination, but also any other disturbances of the regularity of the lattice present in considerable quantity may lead to the formation of a “sponge” consisting of regions with high critical values.

The next series of experiments concerned the determination of the width of the transition region between the superconducting state and the normal state.

The results obtained so far (unpublished measurements carried out jointly with Dr. E. Mittemom) apparently show that both the width of the transition region and the parallelism of the decrease of induction and resistance in pure metals depend strongly on the size, shape, and position of the crystal, and also on the purity of the substance investigated. Only more precise experiments, however, can indicate whether the change of induction in a perfectly pure single crystal is absolutely instantaneous.

We have already seen that the irreversibility of magnetic changes increases with an increase in the amount of admixtures in the metal, while in alloys these changes are completely irreversible. The width of the transition region also changes completely. Whereas in contaminated substances it is only a widened critical curve, in alloys it begins to play a primary role.

As was indicated above, in our experiments we had occasion to observe that at all temperatures lying below the normal transition point \((t_0)\), the lines of force enter into the interior of a specimen of alloy previously cooled in the absence of a field, although the tangential field strength has a value much smaller than the corresponding critical value. This agrees with our assumption concerning the formation inside the superconductor of sponge-like regions of high critical values. The pores of such a “sponge” are unable to withstand the magnetic field when the substance enclosed in them passes into the normal state, because the current induced in the individual pores or rings soon begins to exceed the critical value.

This assumption was quite recently tested and confirmed by experiments with an alloy of lead and bismuth[^34], when it turned out that,

Increasing the field, one can destroy the pores and “fill” them with magnetic flux, which is frozen in them when the field is changed back by the same amount.

Thus, when experiments with alloys are carried out, one should bear in mind that, as soon as a “sponge” has formed, we can no longer learn anything about changes of induction in its pores until the current density exceeds the critical value. This means that significant changes may take place in individual parts of the alloy, manifesting themselves, however, only in the creation of an inhomogeneity of the field inside the pores and not producing such changes of the induction of the whole specimen under investigation as could be determined experimentally. Further data concerning all these phenomena can be obtained by means of calorimetric experiments.

Hysteresis

Experiments on the reversibility of magnetic changes occurring when the superconducting state is transformed into the normal state have shown that, when freezing-in of lines of force takes place, i.e. when, as a result of the transformation, nonsuperconducting inclusions remain inside the specimen under investigation, there is considerable magnetic hysteresis. Naturally, the question arises as to the connection of this magnetic hysteresis with the hysteresis which we observe in experiments on conductivity, and, if such a connection exists, whether magnetic hysteresis is the sole cause observed in experiments on electrical conductivity. Of course, the dimensions of the superconducting transverse section of the wire and the distribution of current over it depend only on the presence of nonsuperconducting regions in the wire. Certain observations apparently show^35 that hysteresis of conductivity appears only when individual sections of the conductor have a form which disturbs the field and, possibly, causes freezing-in of lines of force.

On the other hand, it is evident that hysteresis of conductivity is encountered mainly in very pure substances, in which, apparently, only a small part of the flux which they contain in the normal state is frozen in. Some details of our experiments on the change of induction make it possible to expect, in transformations between the normal and superconducting states, still another new kind of hysteresis. We have seen that the width of the transition region changes from an almost instantaneous jump for pure substances to a very broad band on the \(H, T\)-diagram for alloys. When the temperature or field is decreased, superconductivity will occur first in alloys and impure metals in regions with a higher critical value. These regions form cells from which superconducting inclusions will subsequently grow throughout the whole specimen. In completely pure metals (single crystals), owing to the homogeneity of the substance, there can be no such cells, and we are inclined to suppose that phenomena analogous to supercooling of a very pure liquid below its melting point are possible here. Such a delayed transition from the normal state to the superconducting one should give rise to the phenomenon of conductivity hysteresis. We hope that magnetic experiments will clarify the question of the existence of such supercooling.*

Calorimetric experiments

Keesom^36, Rutgers^37, and Gorter^29 showed that thermal and magnetic phenomena in superconductors are closely connected with one another and that

* Experiments carried out after the discussion gave clear proof of the existence of such delayed processes.

the difference in the heat capacities for the superconducting and normal states, as well as the value of the heat of transformation, can be quantitatively predicted if only it is assumed that in the superconducting state \(B=0\).

At first we investigated the heat of transformation for the transition between the normal and superconducting states, carrying out adiabatic experiments on tin \(^{38}\). An extremely careful determination of the heat of transformation for thallium was performed by the isothermal method by Keesom and Kok \(^{39}\). These experiments, confirming the data of magnetic investigations, showed that in a pure metal there is only a very weak irreversibility.

If alloys behave in the same way as pure metals—Sn, Tl, etc.—and if for them equality to zero of the induction is accompanied by equality to zero of the resistance, then at their normal point of transformation there should likewise exist an anomaly of the heat capacity. In this case the jump in the heat capacity should be greater than in pure metals, since the critical curve has a much steeper slope, as was observed in some alloys. Therefore we undertook the determination of the specific heat of the alloy \(\mathrm{PbTl}_2\), whose critical values are, as is known, very large. Nevertheless, the measurements revealed no indications of a jump of this order of magnitude.

This result agrees with the observed fact that in most superconducting regions the \(H,T\)-diagram of induction is not equal to zero. In addition, it confirms our supposition of the presence of a “sponge,” formed by regions with large critical values, and shows that the skeleton of this sponge, if it can be distinguished at induction equal to zero, can occupy only a relatively small volume.

Fig. 4.

The curve shows preliminary results of calorimetric measurements carried out by Miss D. R. Moore, which apparently give direct confirmation of our “sponge model.” In these experiments the heat capacity of an alloy of tin with bismuth, present in an amount of 4%, was measured in the presence of a frozen field and in its absence. Curve 1 shows the heat capacity of a specimen cooled in the absence of a magnetic field. Curve 2 was obtained by switching on a strong field and switching it off at a lower temperature. It is evident that the frozen field destroys superconductivity in the pores of the sponge.

We have already pointed out earlier that the description of the superconducting “state” by equating the induction to zero loses its meaning if the superconducting regions under consideration reach atomic dimensions or magnitudes comparable with the depth of penetration of the magnetic field into the superconductor at the boundary surface*. This depth of penetration was calculated by Becker, Heller, and Sauter \(^{42}\), and also by F. London and H. London \(^{43}\), and it turned out that it depends on the number of superconducting electrons. If it is assumed that this number is of the same order as the number of atoms, then a value of approximately \(10^{-6}\ \mathrm{cm}\) is obtained. Thus, with a sufficiently thin framework of the sponge, the relative volume occupied by it may be large.

* For a more complete theoretical treatment of the behavior of small superconducting regions, see Gorter \(^{41}\).

Let us note, however, that for the thermal properties of superconducting alloys the two models predict identical effects.

Summarizing all the experiments described above, we are inclined to think that, within the accuracy of the methods used, Gorter’s ideal model of a superconductor with induction equal to zero is realized in the case of pure, properly monocrystalline tin. Further experiments should show whether the change in induction on placing it in an external magnetic field is in fact discontinuous, or whether it is spread over some temperature interval and, consequently, whether the heat liberated in the transformation is a “latent heat” manifested at a certain definite temperature, or whether we are dealing with a simple anomaly of the specific heat, which never becomes infinite. The resolution of these questions will not lead to a significant change in Gorter’s thermodynamic relations; however, it will be very important for the conception of the superconducting and normal “phases.” If the transformation does not proceed discontinuously, i.e. if there exists some intermediate state covering a broad region in the \(H, T\)-diagram, as should be the case owing to the presence of statistical deviations, then, for example, “phase” boundaries should not exist. The existence of such “phase” boundaries in the case of an “ideal” superconductor has not yet been investigated.

The interpretation of experimental facts by means of the assumption of the existence of two “phases” in the case of alloys may apparently play a considerably smaller role than in the case of pure metals. This assumption would be justified if regions with a high critical value, i.e. the “skeleton,” form a superconductor similar to a pure superconducing metal, in which the critical curve indicates the difference of the free energies in the superconducting and normal “phases.” Then the formation of macroscopic superconducting regions with a high critical value would be possible, with a heat capacity obeying Rutgers’ formula and with magnetic properties similar to those of pure tin. The exclusion of such a possibility at present would, it is true, be somewhat premature; nevertheless, it must be noted that no experiments so far have revealed such behavior.

If superconductivity in strong fields is limited to regions of the order of the depth of penetration of the magnetic field, or even of the order of atomic dimensions, then the formation of macroscopic regions with a “high critical value” becomes fundamentally impossible, and a description by means of two “phases” loses all meaning. On the other hand, this means that the skeleton of the sponge becomes very thin, but the magnetic induction in it need not necessarily be equal to zero, although it may occupy a considerable part of the whole volume of the alloy. It is possible, finally, that the number of superconducting electrons in alloys with a high critical value is small, and that in accordance with this the magnetic field penetrates to a depth greater than \(10^{-6}\) cm. In that case the superconducting regions in which the critical value is large, and \(B \ne 0\), can, with the same chemical properties of the alloy, occupy more space. In all these cases the common characteristics of two different phases are lost—the “phase” boundary and the difference of free energies determined from the critical curve.

We believe that all the experimental data obtained so far concerning contaminated metals and alloys can be explained by means of such an idea of inhomogeneities and of the “sponge” formed by them, characterized by a high critical value. Such a model can replace the ad hoc assumption made by Gorter in his recent theoretical work about a thin distribution of superconducting and normal regions, and thereby altogether relieves us of the need for new assumptions for which no reasonable ...

and sufficiently simple grounds. The explanation proposed by us appears plausible also because with its help we can trace the gradual emergence of the phenomenon with the growth of inhomogeneities and impurities, and in some cases we also obtain direct indications of the existence of such “depths.”

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