SUPERCONDUCTIVITY

W. Meissner, Berlin-Charlottenburg

1. Fundamental facts. 2. Superelectrical conductivity in metals, alloys, and compounds. 3. Empirical regularities at the transition point of superelectrical conductivity and the form of the transition curve. 4. Experiments on the influence of a magnetic field and of deformation. 5. Experiments aimed at elucidating the nature of superelectrical conductivity. 6. Conclusions concerning the nature of superconductivity and the question of its theory.

1. Fundamental Facts

The phenomenon of superelectrical conductivity—or, briefly, superconductivity—was discovered in 1911 by Kamerlingh Onnes1. He established that, at approximately \(4.2^\circ\) abs., the resistance of mercury falls sharply, unexpectedly acquiring values that cannot be measured. This fall in resistance takes place within some hundredth part of a degree.

It is true that, according to our present ideas, in general all perfectly pure single crystals of metals, free from any stresses, should apparently have, at absolute zero of temperature, a resistance equal to zero, provided that they do not already become superconductors before then. However, in this general case of all metallic single crystals they do not lose their resistance all at once, as is characteristic of typical superconductors, but, on the contrary, slowly and gradually. For example, Fig. 1 gives the course of the resistance of various specimens of gold as a function of temperature. As we see, at very low temperatures the resistance \(R\) of a single crystal of gold still has a value of the order of \(3 \cdot 10^{-4} R_0\) (\(R_0\) is the resistance at \(0^\circ\)C; \(R\) is the resistance at the temperature of measurement). A specimen of lead investigated by me8 not long before this showed a similar “residual resistance” (a resistance independent of temperature at very low temperatures) even smaller: only \(1.5 \cdot 10^{-4} R_0\).

Of course, it cannot be considered that even the best of the investi—

given samples were ideal in all respects, but in any case a definite impression is created that, with further precautions, the order of the residual resistance can still be considerably lowered and, consequently, that in the limiting case of an ideal single crystal the resistance will indeed acquire a value equal to zero. It does not yet seem necessary to me to draw the conclusion, made by de Haas7, that crystals of perfectly pure metals, not subjected to any stresses, should allegedly, for certain reasons, still possess some residual resistance at absolute zero. One such argument is based on the fact that ideal crystals nevertheless have a mosaic structure, judging from the most recent experiments of A. Goetz.

Fig. 1. Resistance of various kinds of gold.

Fig. 2. Curves of the jump in the electrical conductivity of mercury.

However, this gradual decrease of the resistance of metals as the temperature approaches absolute zero is something quite different from superconductivity. First, superconductivity is observed even in the case of crystals that are by no means ideal, and secondly, it necessarily manifests itself in the sudden disappearance of resistance within some more or less short temperature interval lying substantially above absolute zero. Thus the ordinary character of the curve of resistance as a function of temperature changes completely. Thus, in Fig. 2 are shown Kamerlingh Onnes’s observations on mercury. It is remarkable that the form of the transition curve to superconductivity depends on the imposed current strength. Measurements of the resistance, taken as the ratio of the applied voltage to the observed current, lead

in this transitional region, to the establishment of the fact that at one and the same temperature one and the same mercury offers different resistance to currents of different strength. In short, in the region where superelectrical conductivity sets in, Ohm’s law ceases to be valid. Later still more careful experiments showed that, after the appearance in a metal of the state of superconductivity, there can no longer be any question either of any residual resistance or of any resistance depending on temperature and which for some reason could be ascribed to the properties of an ideal metal. Even a very large residual resistance, observed in mixed crystals of solid solutions (for example, \(0.7 R_0\)), completely disappears when superelectrical conductivity sets in. In the superconducting state the resistance is immeasurably small. According to the experiments of Kamerlingh Onnes \(^{98}\), the resistance of lead at \(4^\circ\) abs. is less than \(10^{-12} R\).

2. Superconductors of electricity (pure metals, alloys, and compounds)

In Leiden, superconductivity was discovered not only in mercury \(^{93,121}\), but it was also found (by Kamerlingh Onnes himself) in tin and lead \(^{96,104,121}\); Kamerlingh Onnes and Tuyn succeeded in establishing it in thallium \(^{31,34}\) and indium \(^{119,121}\), and de Haas and Voogd—in gallium \(^{31,34}\). In Charlottenburg, superconductivity was discovered by Meissner—in tantalum \(^{74,78}\), titanium \(^{77,80,84}\), and thorium \(^{78}\), and by Meissner and Franz—in niobium \(^{79,82}\). Among all chemical elements that are metals and have exhibited superelectrically conducting properties, the highest temperature of the jump in electrical conductivity so far has been encountered in niobium (8.4° abs.), the lowest—in gallium (1.1° abs.). Other metals, taken as pure as this was at all possible, were subjected to investigation for superconductivity in Charlottenburg by Meissner and Voigt \(^{91}\) down to 1.2° abs., and also, to a considerable extent, earlier in Leiden by Kamerlingh Onnes and his collaborators. In some metals, at the lowest temperatures, the beginning of a somewhat rather rapid fall of resistance is indicated (for example, in rubidium). There are grounds (on which we shall dwell further on) to think that molybdenum, at somewhat lower temperatures, will become superconducting. Apparently, in general it is not excluded that many more pure metals will turn out to be superconductors, if only it proves possible to lower the temperature sufficiently. In Table 1 the periodic system of the elements is printed, and in it all presently known superconductors are indicated in boldface, with, for each of them, the temperature of the jump in electrical conductivity. Those of the elements for which data are absent or unreliable are marked with a question mark. The crystal system plays an exclu-

V. MEISSNER

Periodic system of the elements. Superconducting elements (bold) and crystallographic data and distribution of outer electrons in shells

Periods	Ia	IIa	IIIa	IVa	Va	VIa	VIIa	VIIIa
1	1 H
2 Shells Free atom	3 Li cub. 8 K | L 2 | 1	4 Be hex. 12 K | L 2 | 2	5 B ? K | L 2 | 2,1	6 C hex. 3(4) cub. 4 K | L 2 | 2,2
3 Shells Free atom Metal	11 Na cub. 8 L | M 8 | 1 8 | (1)	12 Mg hex. 12 L | M 8 | 2 8 | (2)?	13 Al cub. 12 L | M 8 | 2,1 8 | (2,1)?	14 Si cub. 4 L | M 8 | 2,2
4 Shells Free atom Metal	19 K cub. 8 M | N 8 | 1 8 | (1)	20 Ca cub. 12 M | N 8 | 2 8 | (2)	21 Sc ? M | N 8,1 | 2 8 | (3)	22 Ti 1.7° hex. 12 M | N 8,2 | 2 8 | (4)	23 V cub. 8 M | N 8,3 | 2 8 | (5)	24 Cr cub. 8 M | N 8,5 | 1 8,1 | (5)	25 Mn cub./te-? tp. 12 M | N 8,5 | 2 8,2 | (5)?	26 Fe cub. cub. M | 8,6 | 8,4 |
5 Shells Free atom Metal	37 Rb cub. 8 N | O 8 | 1 8 | (1)	38 Sr cub. 12 N | O 8 | 2 8 | (2)	39 Y ? N | O 8,1 | 2 8 | (3)	40 Zr cub. 8 hex. 12 N | O 8,2 | 2 8 | (4)	41 Nb 8.4° cub. 8 N | O 8,4 | 1 8 | (5)	42 Mo 1° cub. 8 N | O 8,5 | 1 8,1 | (5)	43 Ma N | O 8,6 | 1	44 I hex. N | 8,7 | —
6 Shells Free atom Metal	55 Cs cub. 8 N | O | P 18 | 8 | 1 —	56 Ba cub. 8 N | O | P 18 | 8 | 2 —	57—71 rare earths N | O | P 18—32 | 8,1 | 2 —	72 Hf hex. 12 O | P 8,2 | 2 —	73 Ta 4.38° cub. 8 O | P 8,3 | 2 —	74 W cub. 8 O | P 8,4 | 2 —	75 Re hex. 12 O | P 8,5 | 2 —	76 hex O (8,6) —
7 Shells Free atom Metal	87— —	88 Ra P | Q 8 | 2 —	89 Ac P | Q 8,1 | — —	90 Th 1.43° cub. 12 P | Q 8,3 | 1 —	91 Pa P | Q 8,4 | 1 —	92 U P | Q 8,5 | 1 —

SUPERCONDUCTIVITY

TABLE 1

[[unclear: beginning of caption]] bold type, their points of discontinuity of electrical conductivity in ° abs., crystal-
1) by the orbits of the free atom and 2) of an atom situated in a metal

VIIIa	Ib	IIb	IIIb	IVb	Vb	VIb	VIIb	VIIIb
								2 He
					7 N $K$     $L$ 2     2.3	8 O $K$     $L$ 2     2.4	9 F $K$     $L$ 2     2.5	10 Ne $K$     $L$ 2     2.6
					15 P $L$     $M$ 8     2.3	16 S $L$     $M$ 8     2.4	17 Cl $L$     $M$ 8     2.5	18 Ar $L$     $M$ 8     2.6
27 Co hex. 12 cub. 12 $M$     $N$ 8.7     2 8.5     (4)?	28 Ni cub. 12 $M$     $N$ 8.8     2 8.6     (4)?	29 Cu cub. 12 $M$     $N$ 18     1 18     (1)	30 Zn hex. 6 (12) $M$     $N$ 18     2 18     1 (1)	31 Ga 1.1° tetr. 1 (6) $M$     $N$ 18     2.1 18     2 (1)	32 Ge cub. 4 $M$     $N$ 18     2.2	33 As rhomb. 3 (6) $M$     $N$ 18     2.3	34 Se hex. 2 (6) $M$     $N$ 18     2.4	35 Br $M$     $N$ 18     2.5
45 Rh cub. 12 $N$     $O$ 8.8     1 —	46 Pd cub. 12 $N$     $O$ 8.10     —	47 Ag cub. 12 $N$     $O$ 18     1 18     (1)	48 Cd hex. 6 (12) $N$     $O$ 18     2 18     1 (1)	49 In 3.37° tetr. 4 (12) $N$     $O$ 18     2.1 18     2 (1)	50 Sn 3.69° tetr. 6 $N$     $O$ 18     2.2 18     2 (2)	51 Sb rhomb. 3 (6) $N$     $O$ 18     2.3	52 Te hex. 2 (6) $N$     $O$ 18     2.4	53 J rhomb. 1 $N$     $O$ 18     2.5
77 Ir cub. 12 $O$     $P$ 8.7     2 —	78 Pt cub. 12 $O$     $P$ 8.8     2 —	79 Au cub. 12 $O$     $P$ 18     1	80 Hg 4.12° hex. 6 $O$     $P$ 18     2 18     1 (1)	81 Tl 2.38° hex. 6 cub. 12 $O$     $P$ 18     2.1 18     2 (1)	82 Pb 7.26° cub. 12 $O$     $P$ 18     2.2 18     2 (2)	83 Bi rhomb. 3 (6) $O$     $P$ 18     2.3	84 Po $O$     $P$ 18     2.4	85—

a significant role. Whereas ordinary tin (tetragonal lattice) becomes superconducting already at \(3.7^\circ\) abs., gray tin (diamond-type lattice), according to the measurements of de Haas, Sizoo, and Voogd\({}^{28}\), is not superconducting even at lower temperatures (\(0.5^\circ\) abs.).

The form of the curve of the jump in the electrical conductivity of metals depends not only on the strength of the current (Fig. 2), but also on the degree of purity and on the crystalline state itself. According to the measurements of de Haas and Voogd\({}^{39}\), the curve of the jump in electrical conductivity for single crystals of tin is close to a discontinuity in the mathematical sense of the word. De Haas and Voogd suppose that in an ideal and perfectly pure crystal of a metallic superconductor the process of disappearance of resistance actually occurs literally by a jump (discontinuously), i.e., within an immeasurably small temperature interval, provided only that the current is sufficiently small. In the case of a not entirely pure substance or crystals one obtains a substantially larger (measurable) temperature interval for the region of transition to the superconducting state; the same will be true in the case of insufficiently small currents. To what extent the transition region and its width depend on the form of regular crystallization of one substance or another, and what difference there is in the length of the interval of the jump in electrical conductivity for a single crystal and a polycrystal—this question still requires special investigation. According to the aforementioned measurements of de Haas and Voogd, even the height of the jump in electrical conductivity in tin that crystallizes in a chaotically irregular manner does not depend on the direction of the current relative to the crystallographic axes. Next, it should be especially noted that exactly the same jump curve is obtained whether we take the metal from the state of ordinary electrical conductivity into the state of superconductivity, or in the reverse direction. This is shown, for example, by the precise measurements in the region of the jump in electrical conductivity of tin, carried out by Meissner\({}^{70}\).

The first investigations of superconductivity in alloys were carried out by Kamerlingh Onnes\({}^{96}\). He found that an amalgam of tin becomes superconducting at a temperature somewhat higher than mercury itself, and that alloys of mercury with gold and cadmium are also superconductors. In the course of time, a whole series of alloys was then investigated for superconductivity in Leiden and Toronto. The superconductors discovered among them are listed in Table 2. The numbers in parentheses denote, as before, references to the bibliography. The letter L marks measurements made in Leiden, the letter T—in Toronto. The letter E indicates that the alloy was taken as eutectic. Where an intermetallic compound is involved, its formula is given. It is especially interesting that among the alloys there are also some in which not one of the components separately has so far been observed as a superconductor.

Such, for example, is the gold–bismuth alloy. In this case, judging from the latest investigations of de Haas and Jurriaans[^26], we are dealing with the compound Au$_2$Bi. It remains an open question whether gold or bismuth separately may be regarded as superconductors; but at some temperature so low that it has not yet been possible to establish it for them, a jump in electrical conductivity should be expected. Table 2 also attests to the following fact: all the temperatures of the jump in electrical conductivity for alloys of bismuth with known superconductors lie considerably higher than the jump temperatures for the alloyed superconductors themselves taken separately. Bismuth, consequently, has the property of raising the jump temperature. As far as can be judged from individual observations, the nonmetallic compound sulfur behaves like bismuth. Such an increase in the temperature of the jump in the electrical conductivity of alloys is observed in two cases for arsenic, in one case for phosphorus, and in one for silver. Conversely, alloys containing cadmium, zinc, calcium, or lithium as the second component give a lowering of the jump temperature compared with the superconductors entering into their composition as the first component. In alloys with copper, superconductivity has not at all been observed up to now down to low temperatures of 2.25° abs. for some and 1.31° abs. for other alloys.

In addition to the alloys of two components cited in Table 2, several more alloys with a larger number of components were investigated in Toronto by McLennan, Allen, and Wilhelm: Rose’s alloy Bi$_2$SnPb (jump at 8.5° abs.)[^55], Wood’s alloy (jump at 8.2° abs.)[^55], one alloy of lead, bismuth, and antimony (jump at 8.9° abs.)[^56], one alloy of lead, arsenic, and bismuth (jump at 9.0° abs.)[^56], and one alloy of lead, bismuth, antimony, and arsenic (jump at 9.0° abs.)[^56].

In order to trace more precisely the dependence of the temperature of the jump in electrical conductivity in binary alloys on concentration, systematic investigations of a whole series of alloys were carried out in Charlottenburg (Meissner, Franz, and Westerhoff). First of all, a number of alloys of two superconductors[^86], [^87] were investigated, namely: a series of indium–lead alloys (giving an uninterrupted series of solid solutions), a series of lead–mercury alloys (in which, on the mercury side, there is a eutectic region), a series of tin–thallium alloys (with a sharply expressed eutectic point and a region lying nearer to tin), a series of indium–thallium alloys (possessing, in the range of intermediate concentrations, a eutectic region, on both sides of which solid-solution regions are situated), and a series of lead–thallium alloys (in which a eutectic region is likewise located in the middle). Then a series of lead–bismuth alloys was subjected to investigation (with the exception of bismuth itself). In addition to testing for superconductivity, in all cases the specific resistances were also noted—the values $R/R_0$—at 77° abs., 20° abs., and sometimes also at 4.2° abs., in order to have some idea of the boundaries of the eutectic region. The results of all measurements of the temperature of the jump in electrical conductivity of the listed alloys are presented in Figs. 3–10.

In some cases the values of the temperature for the beginning, middle, and end of the jump interval are given. By the middle of the interval is meant here the temperature at which the resistance falls by one half. The following most important conclusions can be drawn from all these investigations, and in particular from those recorded in Figs. 3–10.

The points representing the series of values of the temperature for the jump in electrical conductivity in alloys with unlimited mutual solubility of both components (forming a solid solution at all concentrations, Fig. 3) are situated on a smooth curve between two points representing the temperatures of the jump in electrical conductivity of the alloyed superconductors. On the diagram thus obtained, a small admixture of the other component near each of the pure components has almost no influence on the jump temperature. In fact, it is observed that impure metals generally have approximately the very same jump temperature as completely pure ones.

V. MEISSNER

TABLE 2

Temperature of the jump in electrical conductivity in binary alloys, in ° abs., according to measurements in Leipzig (L) and Toronto (T)

Second component	Pb	Sn	Tl	Au
	7,26 L	3,71	2,37	--
P	$E$ 7,8 T (56)
As	$E$ 8,4 T (56)	$E$ 4,1 T (56)
Sb	$E$ 6,6 T (55)	Sb$_2$ Sn$_3$ 3,8 L (1)	Sb$_2$ Tl$_7$ 5,2 T (56)
Bi	$E$ 8,8 T (55)	$E$ 3,8 L (21)	Bi$_5$ Tl$_3$ 6,4 T (55)	Au$_2$ Bi 1,8 L (18, 20 and 26)
Zn		$E$ 3,65 L (21)
Cd		$E$ 3,61 L (21)	$E$ 2,54 (21)
Hg			Hg$_5$ Tl$_2$ 3,82 L (24)
Tl	Pb Tl$_2$ 4,05 L (24)
Ag	$E$ 7,2 T (56)		$E$ 2,67 L (24)
Au	$E$ 7,0 T (56)		$E$ 1,92 L (21)
Ca	7,0 T (56)
Li	7,2 T (56)

Note: The numbers in parentheses are the numbers of the literature references in the list.

If an alloy gives a solid solution only with a predominance of one component (Figs. 4 and 5), then the magnitude of the jump in the region of mixed crystals changes gradually with the change in concentration—up to the limiting concentration lying at the boundary of the solid solutions and the eutectic. Further, in the adjoining eutectic region, the value of the jump in temperature at first remains approximately the same—as for the limiting concentration of mixed crystals, since at the beginning of the eutectic region it is precisely they that form the continuous path for the electric current, as the main

conducting phase. At concentrations at which this is no longer the case, there occurs a rapid transition to the value of the jump temperature that exists at the other end of the eutectic region. In the given case, when the alloy no longer has a second region of solid solutions, this means that the temperature of the jump in electrical conductivity at the end of the eutectic region acquires the value characteristic of the second pure component.

Fig. 3. Temperatures of the jump in electrical conductivity for indium–lead alloys.

In those cases where the eutectic region is located in the middle of the concentration scale (Fig. 6), for the two neighboring regions of solid solutions the same pattern of the course of the jump points holds as for the preceding alloys, in which the eutectic region adjoined one component, and the region of mixed crystals to the other.

Fig. 4. Temperatures of the jump in electrical conductivity for lead–mercury alloys.

But whereas in the case of alloys with unlimited mutual solubility the jump points were located in the interval between the limiting values of the jump temperatures characteristic of each of the components, in the presence of a eutectic this is by no means obligatory. For example, such series of alloys as tin–thallium, indium–thallium, and lead–bismuth give, for mixed crystals of limiting concentration, values of the jump temperature considerably exceeding both values for the pure components. The magnitude of the jump temperature for these mixed crystals of limiting concentration is decisively influenced by the degree of supercooling of the eutectic; this, of course, does not at all explain the fact itself, as a whole, of the increase in the jump temperature of electrical conductivity for mixed crystals of limiting concentration. With a sufficiently rapid fall of temperature, the eutectic region noticeably expands precisely in the sense in which this is represented in Fig. 7 for indium–thallium alloys. At low temperatures those boundaries of the solid solution and eutectic are no longer established which correspond to stable equilibrium; this occurs owing to the comparatively weak mobility of these atoms. Depending on the rate of cooling, a greater or lesser degree of supercooling can be obtained. Thus, by artificially inducing supercooling of the alloy, one observes an increase in the residual resistance and in the jump temperature (Fig. 8).

Fig. 5. Temperatures of the jump in electrical conductivity for tin–thallium alloys. × denotes the beginning, ⊗ the middle, and ○ the end of the jump.

The lead–thallium series of alloys is of interest because several different crystal lattices are encountered in it (Fig. 9). Although here too there exist—

there exists a eutectic region, but at no concentration is the jump temperature higher than that for lead. In general, the presence of an increase in the jump temperature is connected with the position of the eutectic region. If it

Fig. 6. Temperatures of indium–thallium alloys. × denotes the beginning, ⊗ the middle, and ○ the end of the jump.

Fig. 7. Boundaries of the eutectic region as a function of temperature.

is located closer to the metal with the lower jump temperature, then an increase in the jump temperature above that for the second metal is impossible. On the other hand, according to Fig. 9, there exists a region of mixed crystals in which

Fig. 8. Effect of supercooling on the critical jump temperature of a mixed crystal. Limiting concentration in an indium–thallium alloy (66.6 atomic percent thallium).

Fig. 9. Jump temperature of lead–thallium alloys.

there are still higher jump points, or not. It is impossible to extrapolate the curve toward pure carbon, since alloys with a higher carbon content—greater than 63 atomic percent—have not yet been obtained.

This method of determining the jump temperature for pure metals by means of ...

this is indicated by the dotted line in Fig. 9, we shall evidently arrive at a transition temperature which cubic thallium would have if it were stable not only above 231° C, but also at lower temperatures. This transition temperature would then be considerably lower than for hexagonal thallium, and, perhaps, would prove to be unattainably low. On what considerations such a line of reasoning as that just presented is based, we cannot discuss this question in greater detail here.

In the lead–bismuth series of alloys there are two eutectic regions (Fig. 10). One, extending from 20 to 25 at. percent bismuth, contains, besides mixed crystals of cubic bismuth with cubic lead, also mixed crystals of hexagonal bismuth with hexagonal lead. The second eutectic region, extending from 35 and almost to 100 at. percent bismuth, contains mixed crystals of limiting concentration—

Fig. 10. Transition temperature of lead–bismuth alloys.

Fig. 11. Transition temperature of the molybdenum–carbon system. × denotes the beginning, ⊗ the middle, and ○ the end of the transition.

—of hexagonal bismuth and lead, along with rhombohedral bismuth or with mixed crystals of a solid solution of limiting concentration—a very small amount of lead in rhombohedral bismuth.

Finally, one should also dwell on the measurements of Meissner, Franz, and Westerhoff^86 for the molybdenum–carbon system. According to the investigations of Schenck and others^22, molybdenum in a certain temperature range forms a compound with carbon, in particular Mo₂C. However, Meissner, together with his collaborators, investigated molybdenum–carbon alloys, and over the whole temperature range considered they mostly turned out to be mixed crystals. The transition temperatures found for the various alloys must in any case be attributed chiefly to the mixed crystals of molybdenum–carbon; the transition curve for this case is shown in Fig. 11. Here we again have a case similar to the above-mentioned gold–bismuth alloy: as there, superconductivity is observed only in an alloy, while in the components separately it has not yet been established. However, since here we are dealing not only with a compound but also with a solid solution, it is permissible to continue the transition-temperature curve to the left, up to pure molybdenum itself. Thus, at 1° abs., pure molybdenum, in all probability, becomes superconducting. Then, as the curve approaches 50 at. percent molybdenum, it rises very steeply upward. The region between 50 and 60 at. percent has not yet been investigated, and therefore it still remains unknown whether in this interval

whether there are still higher transition points or not. It is impossible to extrapolate the curve toward pure carbon, since alloys with a high carbon content—with more than 63 atomic percent—have not yet been obtained.

This method of determining the transition temperature for pure metals by extrapolating curves for mixed crystals can naturally also be applied to the study of other metals. Meissner, Franz, and Westerhoff in this way studied superconductivity in a whole series of solid solutions, especially also mixed crystals in which one component is a superconductor and the other a metal which until now had not been observed as a superconductor. The following solid solutions are in question: 9.8 atomic percent tin in antimony, 1 and 2.7 atomic percent lead in cadmium, 5.7 and 4 atomic percent thallium in silver, 2 atomic percent lead in magnesium, 6 atomic percent thallium in magnesium, 5.6 atomic percent tin in copper, 8 atomic percent mercury in copper, 5 atomic percent tin in iron, 6.8 atomic percent tin in nickel, 8.2 atomic percent tin in silver, and 19.4 atomic percent mercury in cadmium. Unfortunately, over the entire range of temperatures attained, down to 1.26° absolute, none of these solid solutions proved to be a superconductor, so that no conclusions could be drawn concerning the superconductivity of the metals antimony, cadmium, silver, magnesium, copper, iron, and nickel. Owing to the slight solubility of the superconductor in each of these metals, the increase in the transition temperature is evidently so insignificant that it remains in the region of unattainable temperatures.

We have already spoken in part about intermetallic compounds that exhibited superconductivity. A systematic investigation of such compounds with good conductors is still continuing. There are extensive investigations by Meissner, Franz, and Westerhoff on the study of the superconductivity of compounds of metals with sulfur, carbon, nitrogen, oxygen, boron, silicon, arsenic, selenium, and tellurium.

The most interesting and important result of these investigations is perhaps that many compounds of one or another metal with a good dielectric, such as, for example, with sulfur, nitrogen, oxygen, or boron, proved to be superconductors, even in cases where superconductivity was not observed in the pure metal itself, even at the lowest temperatures attained. The first such example is CuS, a superconductor at 1.6° absolute.^76 Among other investigated compounds of metals with sulfur, superconductivity was found in none. According to measurements in Charlottenburg, as yet unpublished, PbSn Bi₂ S₃ is not superconducting down to 1.3° absolute; according to measurements in Toronto^57, the same can be said also of Ag₂S, Bi₂S₃, and FeS down to 1.9° absolute. MacLennan, Allen, and Wilhelm, to be sure, found superconductivity in one sample of galena; however, measurements in Charlottenburg showed that lead sulfide is a superconductor only in the presence of a certain excess of lead, while actually pure PbS is not a superconductor. The sulfide metals investigated, in particular also copper sulfide and galena, in the sense of the drop in resistance with decreasing temperature behaved exactly as if they were pure metals. The jump of the curve in the transition to superconductivity in copper sulfide occurred over less than one hundredth of a degree, as in a pure metal.

The nitrides studied in Charlottenburg[^83][^85], listed in Table 3, are, beyond any doubt, compounds and not mixed crystals, as was shown by the X-ray photographs of them taken by Becker and Ebert[^123]. All nitrides were obtained from Friedrich (see Osram). The degree of purity of some of them was not very high, as shown by Friedrich’s analyses and Noddack’s X-ray photographs. The corresponding specimens also showed a relatively larger residual resistance before the conductivity jump and a more extended interval of the jump.

TABLE 3

Superconductivity in nitrides

Substance	Jump interval, ° abs.	Metal jump temperature, ° abs.	Crystal lattice: compound	Crystal lattice: metal	Lattice constants in \(10^{-8}\) cm: compound	Lattice constants in \(10^{-8}\) cm: metal	\(R_t/R_0\) before the jump, relative residual resistance	No. of literature reference in the list
ScN	—	—	NaCl	—	4.44	—	0.82	83
TiN	4.2—2.6	—	NaCl	hexagonal	—	\(a\ \ c\ \ c:a\)	0.9	83
TiN	1.6—1.2	1.77	NaCl	hexagonal	4.40	2.97 4.72 1.59	0.4	83
TiN	5.7—5.4	—	NaCl	—	—	—	0.10
Single-crystal wire	1.2	1.77	NaCl	hexagonal	4.40	2.97 4.72 1.59	0.004	85
VN	3.2—1.3	—	NaCl	centered cubic	4.40	—	—
VN	—	—	NaCl	centered cubic	4.28	3.04	0.7	83
ZrN	7.8—3.2	—	NaCl	hexagonal	4.63	3.23 5.14 1.59	0.85	83
ZrN	9.45	—	NaCl	hexagonal	4.63	3.23 5.14 1.59	0.035	85
Single-crystal wire	9.45	—	NaCl	hexagonal	4.63	3.23 5.14 1.59	0.035	85
ZrN—TiN	5.3—3.0	—	NaCl	—	—	—	0.74	83

Among the oxides studied in Charlottenburg[^83] (some of these works have not yet been published), two superconductors were found, namely: SnO and NbO. However, in both cases there is no complete certainty that the superconductivity is not due to the presence of some impurity of pure tin or of the corresponding pure niobium. The oxides which, in the investigation, did not show superconducting properties down to \(1.3^\circ\) abs. were the following: WO\(_2\), Mo\(_2\)O\(_5\), CdO, Tl\(_2\)O\(_3\), Pb\(_2\)O, PbO\(_2\), Sn\(_2\)O\(_3\). According to measurements in Toronto, CuO is also not a superconductor.

Among the carbides studied in Charlottenburg[^83][^85] (Table 4), among the silicides[^85] (Table 5), and among the borides[^85] (Table 6).

TABLE 4

Superconductivity in carbides

Substance	Transition interval, ° abs.	Transition temperature of the metal, ° abs.	Crystal lattice — compounds	Crystal lattice — metal	Lattice constants in \(10^{-8}\) cm — compounds	Lattice constants in \(10^{-8}\) cm — metal	\(R'/R_0\) before transition, or corresponding residual resistance	No. in literature of reference in first review
RuC	—	—	—	hexagonal	—	\(a\ \ c\ \ c/a\) 2.69 4.28 1.59	0.370	59
Fe\(_3\)C	—	—	rhombic	body-centered cub.	\(a\ 4.52\) \(b\ 5.08\) \(c\ 6.73\)	2.861	0.350	85
VC	—	?	NaCl type	body-centered cub.	4.30	3.04	0.69	83
TiC	1.1?	1.77	”	hexagonal	4.60	\(a\ \ b\ \ c/a\) 2.97 4.72 1.59	0.59	83
TiC single-crystal wire	?	1.77	”	”	4.60	2.97 4.72 1.59	0.044	85
WC	4.2—2.5	—	hexagonal	body-centered cub.	\(a\ 2.90\) \(c\ 2.830\) \(c:a\ 0.975\)	3.157	0.38	83
W\(_2\)C	3.5—2.05	—	—	”	—	3.157	0.085	59
MoC	7.8—7.6	—	hexagonal?	”	—	3.138	0.76	83
Mo\(_2\)C	?2—2.4	—	hexagonal?	”	—	3.138	0.37	83
TaC	9.5—9.3	4.4	NaCl type	”	4.49	3.27	0.35	83
TaC single-crystal wire	9.5—7.6	4.4	”	”	4.49	3.27	0.96	85
NbC	10.5—10.1	8.4	”	”	4.40	3.31	0.61	83
HfC single-crystal wire	—	—	—	hexagonal	—	\(a\ \ c\ \ c/a\) 3.32 5.46 1.64	0.22	85
ZrC single-crystal wire	4.06—3.35	—	NaCl type	”	4.76	\(a\ \ c\ \ c/a\) 3.23 5.14 1.59	0.10 0.001	85

in any case there were quite a few not compounds at all, but mixed crystals, just as we have already encountered this circumstance for molybdenum carbide (Fig. 11). However, in individual cases the roentgenograms made by Becker and Ebert^124, Westgren and Fragmén^125 gave a pure, impurity-free, regular structure; and precisely for these, depending on the method of their preparation, very small values of the residual resistance and narrow intervals of the jump were observed.

MacLennan, Allen, and Wilhelm^59 found that \(W_2C\) at \(2.05^\circ\) abs. is a superconductor, whereas \(RuC\), on the contrary, is not a superconductor even at \(1.9^\circ\) abs.

TABLE 5

Superconductivity in silicides

Substance	Jump interval, ° abs.	Jump temperature for metals, ° abs.	\(R/R_0\) before the jump, or corresponding residual resistance at \(1.30^\circ\) abs.	No. of literature reference according to the list
Ta Si	4.38—4.25	4.40	0.079	85
Cu\(_3\) Si	—	—	0.65	unpublished
Mo Si\(_2\)	—	—	0.304	unpublished
Ni—Si	—	—	0.135	85
17 atomic percent Si	—	—	0.135	85
Fe—Si	—	—	0.421	85
28 atomic percent Si	—	—	0.421	85

The roentgenographic determination of interatomic distances in nitrides, carbides, etc., gave one more important result: it turned out that not only is the lattice constant of the compound in general greater than the constant for the pure metal, but also greater is even the shortest distance that separates, in the compound, an atom of the metal from its nearest neighbor, also a metal. This is important for understanding the origin of the superconducting state.

TABLE 6

Superconductivity in borides

Substance	Jump interval, ° abs.	Jump temperature for metals, ° abs.	\(R/R_0\) before the jump, or corresponding residual resistance at \(1.26^\circ\) abs.	No. of literature reference according to the list
Zr B	3.8—2.82	—	0.0354	85
Hf B	—	—	0.081	85
Ti B	—	1.77	0.272	85

In individual cases, compounds exhibited resistance curves containing not a single jump to superconductivity, but two whole step-like drops of resistance—the entire jump occurring, as it were, in two stages at two different temperatures. Such, for example, is titanium nitride (Fig. 12). Apparently this double jump is caused by the fact that, in the titanium nitride specimen investigated, near the jump the titanium nitride did not constitute a continuous phase, but was surrounded by titanium itself, which throughout the entire region, from \(1.77^\circ\) abs. to \(1.3^\circ\) abs., is superconducting; this corresponds to the second interval of the jump in the titanium nitride specimen. In other cases the residual resistance of the second phase surrounding the first (which becomes superconducting earlier) was so small (for example, in zirconium carbide) that after the first jump there remained, at a lower temperature, a vanishingly small jump to be made.

Fig. 12. Jump curve for titanium nitride. \(000\)—points observed when lowering the temperature, \(xxx\)—when raising it.

In Charlottenburg, selenides \(PbSe\), \(CuSe\), and \(Bi_2Se_3\) were also investigated, as well as tellurides \(CuTe\) and \(Bi_2Te_3\), arsenides \(Cu_3As\), \(MoAs_2\), \(NiAs\), \(Fe_2As\), and alloys with arsenic \(Ag—As\), \(Sb—As\), down to a temperature of \(1.3^\circ\) abs. However, in none of these cases was superconductivity found.

3. Empirical regularities at the point of the jump in electrical conductivity and the form of the curve near the jump

The experimental material presented in the preceding paragraph permits the following conclusion to be drawn concerning both the point of the jump itself and the form of the curve near the jump.

Superconductivity is by no means a purely atomic property. Thus, there are absolutely no parallels

between the ordinal number and superconductivity; one cannot observe any clear dependence of superconductivity on the atomic volume either. There is absolutely no connection between the transition temperature and the characteristic temperature, which under ordinary conditions precisely determines the magnitude of the electrical resistance (Table 7). Nevertheless, of course, the characteristic temperature must play some role in superconductivity as well. For alloys and chemical compounds the values of the characteristic temperature have not yet been studied, and the possible dependence

TABLE 7

Temperature of the jump in electrical conductivity and the characteristic temperature of pure metals

Superconductor	Nb	Pb	Ta	Hg	Sn	In	Tl	Ti	Th	Ga
Temperature of the jump in abs.	8.4	7.26	4.38	4.12	3.69	3.37	2.38	1.77	1.43	1.1
Characteristic temperature	—	92	228	37	210	198	140	342	168	—

between them and the transition temperature is still unknown. Superconductivity is greatly influenced by the crystal lattice of the superconductor. Depending on the crystal lattice, different modifications of one and the same metal may either possess superconductivity or not, and in any case the temperatures of the jump in electrical conductivity for all modifications differ greatly from one another. But nevertheless, whether the substance under investigation is in the form of a single crystal or a polycrystal is not of decisive importance.

The question of whether superconductors are confined to a definite series of metals and, if so, to which one exactly, must obviously remain open until metals that have not yet revealed superconductivity are subjected to investigation at substantially lower temperatures, below \(1^\circ\) abs. Considering the position of pure-metal superconductors in the periodic system of the elements, one is led to ask whether superconductors prefer certain places in the system. We shall dwell on this in more detail in § 6. In any case, it is impossible to discern any regularity in the distribution of the values of the transition temperature in this region of the periodic system.

Every solid solution of two superconductors is likewise a superconductor. In this case, dissolution in the given superconductor of another one with a higher transition temperature raises, and of one with a lower transition temperature lowers, the transition temperature of the original pure component. The only noted exception to this rule is alloys of lead with bismuth; however, this exception may be explained by the fact that bismuth

enters the alloy in a cubic lattice, and it is possible that, if it could be obtained as cubic and in pure form, it would have a transition temperature higher than that of lead. The transition temperatures of a series of mixed crystals with unlimited solubility of both components always lie in the interval bounded by the temperatures of the pure components. In alloys having a eutectic region, the transition temperature of mixed crystals with the limiting content of one of the components (a saturated solid solution) lies considerably higher than the transition temperatures of the purest components themselves. In the eutectic region the transition temperature is determined chiefly by the transition temperature of that one of the limiting solid solutions which constitutes the phase providing a continuous path for the electric current.

The chemical compounds considered, of two metals or of a metal with a nonconductor, are especially remarkable in that their residual resistance at low temperatures is of just the same order of smallness as in pure metals and, in other respects, if they become superconductors at all, they behave in exactly the same way as pure superconducting metals. On looking at the periodic system (Table 1), it is striking that carbon, boron, and silicon are in the very same group as those transition metals with which they form compounds, superconducting in some cases at a fairly high temperature. For mixed crystals formed by a compound together with a metal, everything that has been said concerning mixed crystals of two pure metals holds true.

The width of the transition interval, i.e. the magnitude of the temperature range within which the transition to the state of superelectrical conductivity occurs—assuming the strength of the applied current to be very small—depends strongly on the degree of purity of the metal or compound. In a very pure metal or chemical compound (for example, CuS) the transition to superconductivity is almost mathematically discontinuous, especially if the substance under investigation is taken in the form of a single crystal. But in mixed crystals the width of the transition interval depends on the concentration of the second component.

As the concentration is increased, the transition interval also increases up to a certain maximum, then decreases again with further approach to the second pure component or to saturation of the solid solution. Table 8 demonstrates this in several examples. How this phenomenon occurs may be imagined as follows. In mixed crystals, as in any statistical distribution, there are the most diverse concentrations lying within a certain quite definite region around the mean value of the concentration. If the concentration is so small that the mixed…

if the crystal is a pure solvent, then this region (range) of concentrations present, in essence, cannot be very large. The situation is analogous at the other boundary of solid solutions, where the dissolved substance or a saturated solid solution is present in pure or almost pure form,

TABLE 8

Interval of the jump in electrical conductivity
in mixed crystals

Mixed crystals of solid solutions	Dissolved metal in atomic percent	Jump interval in mm Hg	Jump interval in ° abs.
Sn in Tl	0	7	0.06
Sn in Tl	10	18	0.10
Sn in Tl	16	51	0.23
Sn in Tl	20.5	182	0.078
Sn in Tl	23.3	74	6.13
Tl in In	0	6	0.02
Tl in In	12.3	25	0.07
Tl in In	27	55	0.17
Tl in In	36	59	0.18
Tl in In	42	17	0.10
In in Tl	0	7	0.06
In in Tl	16.5	68	0.20
In in Tl	24	65	0.13
In in Tl	28	74	0.13
Pb in In	0	6	0.02
Pb in In	8	176	0.25

the concentration of which can likewise be disturbed to a negligible extent by the nonuniformity of its distribution. Conversely, in the middle of the concentration scale this region of different, actually existing concentrations, in accordance with its statistical nature, expands strongly in both directions and may manifest itself in full measure. It is quite possible that in such solid solutions complete superconductivity can occur only when, upon a fall in temperature, the superconducting state is ensured for both boundaries of this concentration region. Theoretically, these boundaries should in general be very far from the mean value of the concentration. But in practice it is quite possible that concentrations differing significantly from the mean value for the given mixed crystal can no longer affect the conductivity at all, because the overwhelming part of all concentration regions lying closest to the mean value has already become superconducting and, most importantly,

create a continuous superconducting path for the electric current.*

Fig. 13 explains these considerations for the case of alloys that give solid solutions at all concentrations. The solid curve depicts the mean jump temperatures; the two dashed curves, the beginning and the end of the jump interval. Thus, for example, for a mixed crystal with the concentration corresponding to point \(A\), the jump interval is determined by the length of the segment \(A'A''\). Drawing from point \(A'\) an isotherm to its intersection with the dashed curve of the lower boundary (end) of the jump at point \(B\), we obtain the concentration of that alloy which becomes superconducting at the temperature of the isotherm \(A'B\). Conversely, drawing from \(A''\) an isotherm to its intersection with the dashed curve of the upper boundary (beginning) of the jump at point \(C\), we in this way find the concentration of that alloy which becomes superconducting at the temperature of the isotherm \(CA''\). Consequently, point \(A\), corresponding to the mean value of the concentration, is associated with an entire range of concentrations, in the interval between \(C\) and \(B\).

Fig. 13. Diagram of the values of the jump interval in a sequence of mixed crystals of different concentration.

4. Experiments on the influence of a magnetic field and deformation

As we have already emphasized in § 1, the jump temperature, and especially the shape of the jump curve (see Fig. 2), depend on the applied current strength. This phenomenon occurs by no means because the superconductor, possessing some residual resistance, is thereby supposedly heated somewhat. Such an explanation was initially proposed already by Kamerlingh Onnes^94. Careful investigations^115,120 showed that, as was first suggested by Silsbee^107,108, the influence of the current strength on the character of the transition to the superconducting state is due exclusively to the magnetic field produced by the current itself. An external magnetic field, provided that at the surface of the superconductor it has the same intensity as the magnetic field produced by the current in the superconductor, produces exactly the same effect as the current itself. Thus, if superconductivity disappears at a certain sufficiently strong current, the same result will be produced by a corresponding increase of the external magnetic field. On the other hand, even at stronger currents or external magnetic fields one can again obtain the superconducting state by lowering the temperature. The equivalence

* After this, the presence, for example, of relatively few islands of other concentrations, even if they make one of the extreme regions of concentration superconducting, of course can no longer in any way be reflected in the superconducting properties of the specimen as a whole. —Trans. note.

SUPERCONDUCTIVITY

the influence of the current and of the magnetic field was demonstrated in Leiden by Tuyn and Kamerlingh Onnes[^120] also in the following way. Inside a solid cylinder made of a superconductor (tin), a copper wire was stretched coaxially. If the superconductivity in the tin is first destroyed by increasing the current, it can again be restored by passing through the copper wire a sufficiently strong current in such a direction as to reduce the magnetic field produced by the current in the superconductor itself.

The entire body of investigations on the influence of a magnetic field on superconductivity, carried out in Leiden by Kamerlingh Onnes, de Haas, Tuyn, Sizoo, and Voogd,* led in particular to the following conclusion: the “magnetic threshold” for superconductivity, or the “critical value of the magnetic field” (the field at which superconductivity disappears), increases strongly with decreasing temperature. The order of magnitude of the field that destroys superconductivity does not depend on whether we direct the magnetic field parallel or perpendicular to the current. But at the same time the very character of the influence of the magnetic field on superconductivity depends essentially on the direction of the field. As an example, Fig. 14 gives the picture of the influence of a longitudinal (directed parallel to the current) field \(H\) on the superconductivity of a single crystal of tin (from the work of de Haas and Voogd[^36]). Increasing the magnetic field at constant temperature causes a loss of superconductivity at a quite definite field strength (103 gauss at \(2.92^\circ\) abs.). However, the full value of the residual resistance is acquired at a somewhat greater field strength (104 gauss). If one then again decreases the field strength while keeping the temperature constant, it is no longer possible to carry out the reverse transition to superconductivity along the very same curve along which the disappearance of superconductivity occurred. Moreover, the sudden jump of electrical conductivity occurs at a value of the field strength that is necessarily smaller than that which characterized the moment of disappearance of superconductivity when the magnetic field was increased. In addition, in contrast to the value of the field strength causing the disappearance

Fig. 14. Influence of a longitudinal magnetic field on the superconductivity of a single crystal of tin at \(2.92^\circ\) abs.

* See the literature Nos. 29, 30, 33, 35–38, 40, 98, 99, 100, 110, 111, 115, 116, 120.

of superconductivity, a new step of superconductivity upon reduction of the field occurs quite unexpectedly, at an indefinite value of the field, and appears to depend only on chance. A substantially different picture is found in the phenomena caused by a change in the magnitude of a transverse (directed perpendicular to the current) magnetic field (Fig. 15). When the field strength is increased, superconductivity disappears in this case very gradually (over the interval from 68 to 102 gauss). When the field strength is decreased, on the contrary, what is observed is precisely the sudden removal of almost all the resistance, and always almost exactly at one and the same field strength (95 gauss). After this there remains only a very small resistance, which disappears only very gradually; zero resistance is then reached at the very same field strength at which the state of superconductivity had previously ceased as a result of the increase of the magnetic field. Whether these phenomena also depend on the direction of the crystallographic axes with respect to the current and the magnetic field requires more precise experiments to determine. Judging from the observations made so far, there seems to be no such dependence. However, neither the appearance nor the disappearance of resistance in a polycrystalline substance in general occurs as abruptly as in single crystals. The transition curves to the superconducting state are situated within a definite region of values of the magnetic field.

Fig. 15. Effect of a transverse field on the superconductivity of a single crystal of tin at 2.89° abs.

In all cases investigated so far—for example, single crystals of lead, thallium, indium, and mercury—the curve of transition from the superconducting state to the normal one when the magnetic field is strengthened is quite different from the curve of the reverse transition when the field is weakened. Here one always obtains “hysteresis loops,” the name given to these double transition curves by the Leiden physicists by analogy with loops of magnetic hysteresis. In a polycrystalline substance, however, the hysteresis loop is in general considerably narrower*, than in single crystals, so that the very existence of this loop was at first overlooked in experiments with polycrystals.

Sometimes, in particular for mercury (Fig. 16), step-like

* Despite the great width of the interval of curves in the transition region. Translator’s note.

complex hysteresis curves (the work of Sizoo, de Haas, and Kamerlingh-Onnes^40^). With regard to such cases it may be supposed that differently oriented crystals undergo the transition to superconductivity at different values of the magnetic-field strength. Consequently, here the influence of one or another direction of the crystalline axes already becomes appreciable.

How the critical value of the magnetic field \(H\), which removes a metal from the state of superconductivity, depends on temperature is shown again for the case of a single crystal of tin in Fig. 17 (according to de Haas and Voogd^36^). By the critical value here is meant first of all the critical value of the longitudinal magnetic field (points denoted by squares \(\square\)). For the transverse magnetic field the graph also contains the critical values of the field strength at which superconductivity disappears (points \(\Delta\)). The third line (points \(\nabla\)) gives those values of the field strength at which the residual resistance is completely restored. As we see, in all three cases the critical values of the magnetic-field strength for single crystals of tin are in a rectilinear dependence on the absolute temperature. How these curves behave in the immediate vicinity of the normal conditions of superconductivity (a very small external magnetic field, very small currents) will generally be clarified only after still more careful investigation. Practically, however, in any case it may be considered that within a certain limited range of values of the current strength and the externally applied field it is impossible to notice any change in the transition temperature, and this compels one to admit that the curves in Fig. 17, when approaching the point \(H=0\), would have to run parallel to the vertical axis (the field \(H\)). Likewise, the linear character of the dependence of the critical field strength on temperature is observed by no means in all substances. Fig. 18 gives

Fig. 16. Hysteresis loops of the conductivity for mercury at \(3.8^\circ\) abs.

Fig. 17. Dependence of the critical value of the magnetic field on temperature for a single crystal of tin.

for example, curves of linear dependence for mercury and thallium, according to the work of de Haas and Foogle[^32].

For all pure metals studied up to the present time, the slope of the curve of critical values with respect to the temperature axis has proved to be approximately the same; therefore, for example, already at \(1^\circ\) abs., for all metals the order of magnitude of the critical field strength is one and the same. And since this critical value reaches only a few hundred gauss, this means that, using superconductors made of pure metals, one cannot obtain strong magnetic fields without the onset of Joule heat evolution.

As the investigations of de Haas and Voogd[^33],[^35],[^38] have shown, alloys behave better in this respect. Table 9 gives a summary of the critical values of the magnetic field for alloys. \(H\) (\(t_2\)) is the value of the field strength at which half of the normal resistance is restored. The largest critical value has been established for an alloy of lead with bismuth (35 atomic percent Bi). Such an alloy permits excitation of magnetic fields of about 23,000 gauss already at \(3^\circ\) abs., while still remaining a superconductor, since there is no evolution of Joule heat. This remarkable effect is due, on the one hand, to the fact that the normal transition temperature (in the absence of a magnetic field) of this alloy is relatively high (\(8.7^\circ\) abs.), and, on the other hand, to the fact that for this alloy the curve of the critical field value is very steeply inclined with respect to the temperature axis, in comparison with the curves for pure metals. Let us represent approximately the equation of this curve in the form:

Fig. 18. Dependence of the critical value of the longitudinal magnetic field on temperature for mercury and thallium.

\[ H = a(T_c - T), \]

where \(H\) is the critical value of the magnetic field strength at temperature \(T\), \(T_c\) is the normal transition temperature of the electrical conductivity jump in the absence of a magnetic field, and \(a\) is a constant characterizing the steepness of the curve with respect to the \(T\) axis. Then, as experiment shows, for example for tin \(a = 20\), while for the lead–bismuth alloy (35 atomic percent Bi) \(a \approx 4000\).

Some influence on the transition temperature is exerted not only by the magnetic field, but also by the mechanical stresses experienced by the material. According to the experiments of Sizoo, de Haas, and Kamer-

TABLE 9

Critical values of the magnetic field for alloys

Alloy and reference number in the bibliography	Temperature in ° abs.	Critical value of the magnetic field \(H\) (1/2) in gauss	Temperature of the jump in the absence of a magnetic field, in ° abs.
\(\mathrm{Bi}_5\mathrm{Tl}_3\)	4.23	4080	6.4
(33)	4.04	4360	6.4
(33)	3.87	4680	6.4
(33)	3.59	5150	6.4
(33)	3.35	5560	6.4
\(\mathrm{Sn—Bi}\) \((E)\)	3.59	95	3.8
(33)	3.48	130	3.8
\(\mathrm{Sn—Cd}\) \((E)\)	3.48	17.5	3.61
(33)	3.35	36	3.61
(33)	1.85	266	3.61
\(\mathrm{Sb}_2\mathrm{Sn}_3\)	3.79	69	4.00
(35)	3.69	101	4.00
(35)	3.58	134	4.00
\(\mathrm{Au—Bi}\) \((E)\)	1.54	95	1.80
(38)	1.25	149	1.80
\(\mathrm{Pb—Hg}\) (15.3 atomic percent Hg)	4.23	6800	6.75
(38)	2.93	10300	6.75
\(\mathrm{Pb—Tl}\) (40 atomic percent Tl)	4.23	3050	5.8
(38)	2.93	5000	5.8
\(\mathrm{Pb—Tl}_3\) (66.6 atomic percent Tl)	3.97	132	4.05
(35)	3.90	242	4.05
\(\mathrm{Pb—Bi}\) (7 atomic percent Bi)	3.06	5350	7.7
\(\mathrm{Pb—Bi}\) (10 atomic percent Bi)	3.06	7400	7.95
\(\mathrm{Pb—Bi}\) (20 atomic percent Bi)	4.24	9400	8.15
(35)	3.06	12000	8.15
\(\mathrm{Pb—Bi}\) (35 atomic percent Bi)	4.22	18450	8.15
(38)	3.36	22000	8.7
(38)	2.94	23450	8.7
(38)	2.43	24300	8.7
(38)	1.93	25700	8.7
\((E)\)	1.88	26250	8.7
\((E)\)	4.24	16000	8.7
(35)	3.35	22000	8.7
(35)	2.61	23600	8.7
(35)	1.91	26700	8.7

\((E)\) indicates that the given alloy was taken as eutectic.

…lingh Onnes ^{110,111,113}, elastic stretching in the direction of the dark current raises the jump temperature, while at the same time the residual resistance increases somewhat. Conversely, hydrostatic compression somewhat lowers the jump temperature. In both cases the jump temperature generally changes very little. For example, hydrostatic compression of \(300\ \mathrm{kg}/\mathrm{cm}^{-2}\) lowers the jump temperature by only approximately \(10^{-2^\circ}\). It is perhaps with this influence of elastic stretching that the rise in the jump temperature may be connected which Meissner, Franz, and Westerhoff ^{86} obtained upon supercooling a mixed crystal of an indium–thallium alloy, because upon supercooling very strong internal tensions also arise in the material.

Of course, the effects of a magnetic field and of elastic stretching may be combined, and then especially complex ^{111} phenomena are obtained; but we cannot dwell on this here in greater detail.

5. Experiments Aimed at Elucidating the Nature of Superconductivity

Certain premises for conclusions about the essence of the phenomenon of superconductivity are already contained in the experimental results discussed in the preceding paragraphs. But over a number of years a whole series of experiments was also carried out whose immediate aim was to reveal the very nature of superconductivity. First of all, the question was posed whether the superconducting current is merely a variety of ordinary electric current, or whether here we are dealing with some other, entirely new phenomenon. To clarify this, it was necessary first of all to know whether the state of superconductivity is determined by a surface or by a volume effect. That under certain conditions there may be some process in the boundary layer between a conductor and an insulator is, in general, a quite conceivable possibility also from the standpoint of modern wave mechanics. To resolve this question, Meissner ^{74} carried out experiments which are a direct continuation of Kamerlingh Onnes’s experiments ^{96}. Kamerlingh Onnes’s experiment consisted in the following. A steel capillary was filled with mercury. A current was passed to the ends of the capillary, and platinum wires for measuring the potential difference were immersed in the mercury. It turned out that in most cases superconductivity occurs exactly as if a thread of mercury were enclosed in glass. But in some cases the superconducting state was not established in any way; Kamerlingh Onnes ascribed this to the fact that the mercury thread had ruptured somewhere. But in general there was also another possibility of explaining this. Since mercury does not wet steel, it is always possible that, in Kamerlingh Onnes’s experiment,

SUPERCONDUCTIVITY

there remained between the steel and the mercury a gap, the shell of the gas. Kamerlingh Onnes himself carried out his experiments for quite different reasons, on which we shall dwell further below. In any case, he did not intend by his experiment to prove the impossibility of a surface effect.

In Meissner’s experiments a tin thread was fused into a tube made of Neusilber, which is not superconducting down to \(1.2^\circ\) abs. All measures were taken to ensure that direct contact was established between the Neusilber and the tin through a continuous surface layer of alloy. It turned out that the tin in the Neusilber tube remains superconducting, and it makes no difference—whether the wires carrying current to the Neusilber and those serving to measure the potentials are connected to the tin, or vice versa. Analogous experiments\({}^{126}\) with a tantalum wire in a tin sheath and with lead in a tin sheath led to the corresponding result. In both cases superconductivity always appeared at the temperature characteristic of the jump in electrical conductivity of that one of each pair of substances whose transition temperature lies higher. And this despite the fact that the superconductor with the higher transition temperature was enclosed inside a superconductor with a lower transition temperature. True, the recorded transition temperature in all the cases cited proved to be somewhat lower than for pure tin, or, correspondingly, pure tantalum or lead; however, this undoubtedly occurred on account of the properties of the boundary surface alloy. This can also be verified with complete clarity by cutting open the Neusilber tube with tin (tin with tantalum wire, tin with lead); then there is found to be a genuine internal adhesion between the tin and the Neusilber (the tin with the tantalum, with the lead). Consequently, it is quite unambiguously proved by these experiments that the superconducting current does not flow along the surface layer between the superconductor and the insulator, and that there can be no question of any surface effect in the indicated sense. By this, of course, it is in no way asserted that the current is distributed uniformly over the entire cross-section of the superconductor. In all the experiments described it could perfectly well flow inside the metal in such a way that its density was greatest near the very surface of the metal, exactly as occurs with high-frequency currents owing to the skin effect.

In contrast to Meissner, Kamerlingh Onnes pursued by his experiment an entirely different aim. He wanted to verify whether the electrons, which by their motion constitute the superconducting current, could pass from the superconductor into ordinary conductors. In the latter case one might have expected that in two parallel metals firmly connected with one another, of which one is a superconductor and the other is not, there would always have to be

there should exist some resistance, since the electrons that have entered the simple conductor can no longer move in it without resistance. Since the experiment with the steel capillary, as was already said above, did not give an unambiguous answer to the question posed, Kamerlingh Onnes also tested a constantan ribbon covered with a thin layer of tin. The result of this experiment was entirely analogous to the already described results of Meissner’s experiments: in this case too, superconductivity was excellently observed. Consequently, from the experiments of Kamerlingh Onnes and the experiments of Meissner one may draw the further conclusion that the electrons—carriers of current in a superconductor—do not pass from the superconductor into the adjacent ordinary metal, internally connected with it (for example by alloying), which is not in the superconducting state.

Fig. 19. Constancy and stability of the current in a superconducting hollow sphere.

The experiments of Kamerlingh Onnes and Tuyn[^99_118] then showed that a superconducting current, once for some reason established in a superconductor along a definite trajectory, cannot change its direction and not in the least depart from the path once taken, so long as the conductor remains superconducting. The experiment was as follows (Fig. 19). A lead ring was placed in liquid helium, and inside the ring, concentrically with it, a hollow sphere, likewise made of lead. The sphere was suspended on a thread attached to a sufficiently long glass rod, which in turn was suspended from a torsion spring with a rotating head. A small mirror was attached to the glass rod, opposite which, in an armored tube, there was a point. In the ring and the sphere, previously cooled to a temperature below the transition point for lead, a superconducting current was excited in the following way: with the aid of an electromagnet an external magnetic field was created, whose direction was perpendicular to the plane of the lead ring. At that moment the field was so strong that the superconducting properties of the lead were immediately destroyed. When the magnetic field was switched off and passed through the critical value of the field strength, there arose in the lead ring and the hollow lead sphere a superconducting current;

SUPERCONDUCTIVITY

a current which did not cease so long as the lead was maintained in the superconducting state. After obtaining such an “inertial” current in the ring and the same kind in the sphere, the constancy of these currents was verified by simply twisting the spring, leaving it in its new position. Then the sphere inside the fixed ring was turned through a certain angle, and, with the aid of a telescope and a scale reflected in a small mirror, it remained to observe whether the initial orientation of the sphere with respect to the head would begin to be restored. It turned out that, after a small initial deflection, the total, large deflection remained constant within the limits of possible observational errors—for the whole time during which the lead ring and the hollow sphere were surrounded by liquid helium and, consequently, up to the moment when both of them ceased to be superconductors at all. The small initial deflection noted can be explained by the fact that, when the magnetic field is decreased, upon reaching the critical value of the field strength, the resistance does not disappear at once and not simultaneously in the ring and in the hollow sphere2. The observation continued for 6 hours. And only after the evaporation of the liquid helium was completely ending did the deflection change appreciably. This means that during all this time between the ring and the sphere, or rather between the two currents induced in the ring and in the sphere, considerable forces of interaction were acting. These forces would have been entirely absent if the lines of electric current had shifted inside the lead in the hollow sphere2. Consequently, this experiment shows quite unambiguously that the superconducting current continues to flow stubbornly along that very circuit which it has gone around at least once. Lorentz3, on the basis of this experiment, also inferred theoretically that a superconducting current cannot be carried by free electrons, but that one should rather accept the hypothesis developed by Kamerlingh Onnes4, de Haas5, and Einstein6. According to this hypothesis, the electrons carrying the current in a superconductor pass from atom to atom, from one quantum orbit to another. In general, these arguments of Kamerlingh Onnes, de Haas, and Einstein were of a purely qualitative character. Kretschmann’s calculations7, on the contrary, led to the result that in a superconductor the electric current should not be noticeably displaced in a magnetic field, even if it were carried by free electrons. However, since the calculations of Lorentz and Kretschmann were made on the basis of classical statistics (in Kretschmann’s, to be sure, the quantum conceptions were taken into account), the conclusions of Lorentz and Kretschmann can no longer be considered binding.

In any case, it remains a firmly established experimental fact that the superconducting current flowing in a superconductor cannot be appreciably shifted into the interior of the superconducting substance by applying a magnetic field. In full agreement with this, there is no Hall effect in superconductors[^103].

Even earlier, Kamerlingh Onnes[^98] carried out an experiment quite analogous to that just described, except that instead of the inner hollow sphere a second lead ring was used. This experiment showed that the residual resistance in lead at \(4.2^\circ\) abs. is less than \(10^{-12}\) of the resistance possessed by lead at room temperature. These same experiments made it possible to determine an upper limit for the damping coefficient. Taking into account the self-inductance of the circular current, one could calculate, on the basis of the experimental data, an upper limiting value for the resistance. The value \(10^{-12}\) is precisely only the upper possible limit. However, the existence of some residual resistance in a superconductor could finally be proved by carrying out further experiments. For example, one might try to measure the rise in temperature in an adiabatically insulated superconductor through which a current flows. But such measurements have so far yielded nothing particularly significant. This is understandable, since any resistance smaller than \(10^{-12} R_0\) can be successfully neglected not only from the practical point of view, but also in any theoretical consideration. For the present it may be assumed that the resistance of a metal in the superconducting state is indeed equal to zero. Incidentally, this also agrees with the value of the resistance for temperatures lying immediately below the transition point. Meissner’s measurements[^88], in which the resistance was determined in general merely by the ordinary method in a compensation circuit, showed that the resistance of lead in the temperature region immediately adjoining the transition temperature from below is in any case less than \(10^{-9} R_0\).

It already follows from the foregoing that, from the moment the superconducting state sets in, not only does any residual resistance disappear, as Kapitza[^44,^45] supposed, but also any dependence of the resistance on temperature. Indeed, taking into account the low characteristic temperature of lead, that part of the resistance which depends on temperature should have, at \(7^\circ\), and also at \(4.2^\circ\) abs., a still quite measurable value if, of course, disregarding reality, one were to suppose that the superconducting state at these temperatures had not yet set in. This was also pointed out by Grüneisen[^14]. From this point of view, \(7^\circ\) abs. for lead is the same...

the same as \(27^\circ\) abs. for copper. However, there is also the possibility of directly measuring the magnitude of this term of the total resistance—the term that would depend on temperature if the superconducting state did not occur. This was shown by Meissner8. He investigated the resistance of lead below the transition point in the presence of a magnetic field, as a function of its intensity and at different temperatures. Extrapolating each of the isotherms thus obtained down to the abscissa (magnetic-field intensity) equal to zero, we obviously obtain the value of the resistance (ordinate) that would exist in the metal in the absence of a magnetic field and without the appearance of superconductivity at the temperature of each of the available isotherms. In this way as many points are obtained as there were isotherms taken. All these points lie on one curve, serving as the natural continuation of the curve of the normal values of the resistance plotted for temperatures above the transition point. Extrapolating then once more this newly obtained curve down to absolute zero temperature \(T = 0\), we find the residual resistance of the lead under investigation, which the lead would have at \(T = 0\) in the absence of superconductivity. The extremely pure lead investigated in this way showed a residual resistance of only the order of \(1.5 \cdot 10^{-4} R_0\), while at the same time the resistance depending on temperature (after subtraction of the residual resistance), in the immediate vicinity of the transition point (slightly below it), proved to be equal to \(6 \cdot 10^{-4} R_0\), i.e. four times greater than the residual resistance.

After all this there can no longer be any doubt that, after the metal becomes superconducting, neither the residual resistance nor that component of the resistance which depends on temperature can remain in it. Both resistances are destroyed abruptly and without trace.

If one adopts the point of view that the current inside a metal in the superconducting state is carried by the motion of electrons passing from atom to atom along quantum orbits, then, as Kretschmann9 has shown, one can indicate the smallest value for the superconducting current which in any case must exist, since the velocities of rotation of electrons in solids are of approximately the same order as in the free atom of the given metal. According to Kretschmann’s calculations9, the elementary linear current produced in this way by electrons running along quantum orbits must be at least \(0.3\ \mathrm{mA}\). This, of course, would also be valid in the case when the current flows not parallel to the axis of the wire or along any axis at all, but proceeds in the conductor along zigzag paths. Still weaker currents, according to this theory, must flow discontinuously, i.e. the current in a superconducting

a conductor must break off, reappear, and so forth. Using an ordinary galvanometer, this cannot be noticed, since the current pulses follow one another too rapidly. Meissner and Adelsberger[^71] nevertheless attempted to detect, with the aid of cathode amplifiers, such a discontinuity of the current, by observing measurements of the voltage applied to a superconductor. In these experiments the ends of the superconductor were connected to an amplifier, at the output of which there was a detector circuit into which a very sensitive armored galvanometer (ballistic) was included. The arrangement made it possible to vary things in any way desired, so that both slow and the fastest oscillations or current pulses could be detected at will. It turned out that no changes in the readings of the armored galvanometer were observed, whether a large current, or a very weak one, or no current at all passed through the superconductor. Consequently, this experiment argues that the electrons participating in the superconducting current, if only they really do move along quantum orbits, must in any case possess much smaller velocities than when moving along the orbits of a free atom. Therefore there can be no question of “normal” quantum orbits.

The result of an experiment carried out by Holm and Meissner[^41],[^42] is also in agreement with this. Here the resistance of contacts between two superconductors was investigated. If it were found that the contact between two different superconductors also possesses the property of superconductivity, then, as Einstein[^8] pointed out, the existence of such a superconducting contact would in essence present a considerable difficulty for its understanding, if one adheres to the notion that the superconducting current is created by electrons running along quantum orbits. Kamerlingh Onnes[^97] had already shown that, with the aid of lead contacts, one can make a switch possessing superconducting properties. However, there was no complete certainty that in this case we were not dealing with a peculiar welding of both pieces of lead forming the contact; moreover, Kamerlingh Onnes did not investigate whether this contact really possessed the properties characteristic of superconductors. In Leiden, Tuyn[^118] also carried out experiments on the study of contacts between two different superconductors. In a ring composed of pieces of lead and tin, an inertial current was excited. However, these experiments, even in the opinion of their author himself, cannot be called convincing for two reasons. First, the pieces of lead and tin were alloyed with one another, and, according to what has already been said above, alloys of lead with tin, in any case by themselves, possess all the properties of superconductors. On the other hand, the inertial current could also be maintained in the case where in each separate

part of the ring, which is a single piece of one metal, closed separate currents would arise. Indeed, even in a ring cut at some place, so that the conductor assumes a horseshoe shape, an inertial current could be observed. The experiments of Holm and Meissner were carried out with contacts that moved relative to one another during the measurement. Thus there was already a complete guarantee that there was no welding, which in general can lead to “sintering” even at relatively small currents. Then the superconductivity of the contacts was also investigated with respect to its dependence on the applied current strength. It turned out that not only contacts between two identical superconductors, but also between two different ones, possessed all the properties of a typical superconductor.

From the moment superconductivity appears, not only does the resistance to the passage of current within the contacting metals themselves disappear, but so does the contact resistance (when the current passes from one piece of metal into the neighboring one). Yet this latter resistance is considerably greater than the former and is probably due to the presence of a very thin shell of gas, having nothing in common with an oxide film. The jump in electrical conductivity occurs at the temperature at which the metal among those in contact whose transition temperature is lower becomes superconducting. The dependence of the resistance on the strength of the current passing through the contact and on the intensity of the magnetic field is exactly the same as for any superconductor. Therefore it may be regarded as an established fact that contacts between two different superconductors not alloyed with one another also possess superconductivity, independently of the existence of a boundary contact layer which may perhaps be a mixed crystal composed of one or another gaseous phase and the pure metal. These same experiments, in any case, contradict the view that the electrons carrying the current in the superconducting state of a conductor pass from atom to atom simply from one normal quantum orbit to another.

On the other hand, free electrons as well (in the ordinary sense of the word) apparently cannot serve as carriers of the superconducting current. Already the experiments of MacLennan, MacLeod, and Wilhelm[^63] showed that fast electrons (β-particles) do not penetrate through lead foil in the superconducting state. And this could hardly have been expected, since such fast electrons, after they have entered the metal, possess velocities in any case far exceeding the velocities of conduction electrons. Therefore these fast electrons behave quite differently from the electrons responsible for superconductivity. However, Meissner and Steiner[^90] carried out their experiments with very slow...

by electrons. A beam of electrons fell upon tin foil that was in the superconducting state; the velocity of the electrons could be reduced to zero. These slow electrons, after entering the metal, however, in general always still possessed at least such velocities as corresponded, first, to the work function of the electrons, of which one can form an idea from thermoelectron emission, and, second, to the internal potential of the lattice. Such velocities, if one proceeds from the modern electron theories of metals developed by Sommerfeld, Bloch, and Nordheim, are possessed by only very few of all the electrons present in the metal, on which ordinary conductivity depends. (These modern theories take into account the influence of the atoms inside the metal on the propagation of electron waves.) Meissner and Steiner, in any case, succeeded in establishing beyond doubt that electrons with velocities of the indicated order do not pass through tin foil cooled to the superconducting temperature. It therefore nevertheless appears improbable that the electrons which produce the current in the case of superconductivity move in a manner entirely analogous to those free electrons which, according to modern electron theories, are considered responsible for the phenomenon of ordinary electric current.

The question of the distribution of the superconducting current over the cross-section of a conductor is highly essential for elucidating the nature of superconductivity. But this question has been so little investigated experimentally that it is as if no experiments at all had been performed. In § 3 it has already been mentioned that the form of the transition curve to superconductivity remains exactly the same whether one is speaking of the transition from the normal state to the superconducting state upon lowering the temperature or, conversely, of the reverse transition upon raising the temperature, provided only that the change in the current is in fact accompanied by a jump. This obviously indicates that the distribution of current density in both cases is one and the same and that, if we are dealing at all with a measurable resistance, the current is distributed over the transverse section of the conductor just as in the case of the most ordinary direct current; the distribution does not change if we gradually move away from the superconducting state. However, this does not mean that, upon reaching the superconducting state itself, the same distribution will remain, even if one proceeds gradually from the ordinary non-superconducting state to the superconducting one. In any case, one condition must be fulfilled: under any change whatsoever of the current distribution, the available store of magnetic energy of the superconducting current must remain unchanged, if radiation is not taken into account (and there are no other possibilities for transformations of this energy). This proposition was brilliantly confirmed by Silsbee’s experiments, in which the distribution of current in two superconductors connected in parallel was investigated ^110. The experiments

were carried out in the following manner (Fig. 20): in liquid helium two wire rectangles made of tin (in nature of exactly the same size) were fastened parallel to one another. The diameter of the wire used to make one of them was \(0.24\) mm, and of the other—\(0.49\) mm. These two rectangles were connected so that they were traversed by current in opposite directions: if through one the current went clockwise, then through the other—counterclockwise. From the liquid helium two leads were brought out for supplying the current. The magnetic needle shown in Fig. 20 indicated the resultant magnetic field, whose intensity is proportional to the difference of the two currents in one rectangle and the other. The following was observed:

1. At temperatures above the jump point the magnetic needle is deflected, as was to be expected, in proportion to the difference of the two antiparallel currents.

2. When the temperature is lowered below the jump point, the deflection of the needle undergoes no change and, consequently, the distribution of the current over the two wires connected in parallel remains as before.

Fig. 20. Distribution of current in tin wires connected in parallel.

1. If the current is now switched off, the deflection of the needle again does not change. But the current now flows both through the one and through the other rectangle in the same direction, on one and the same side. Consequently, in one of them it must have changed its former direction to the opposite. The current must be equal to

\[ \frac{I_1-I_2}{2}, \]

if \(I_1\) and \(I_2\) were the magnitudes of the current in the first and second rectangle before the applied voltage was switched off.

1. If the current is switched on for the first time when, judging by the temperature, the state of superconductivity has already certainly been reached, then no deflection of the needle at all is observed.

2. After this, raising the temperature above the jump point causes the needle to set itself in the most normal manner, giving the deflection that should be expected.

All this, in its essential features, is quite naturally explained by the fact that the magnetic energy of superconducting currents must remain constant and equal to that which the current once possessed. In the case of the 4th experiment the picture is further supplemented by the fact that even the weakest magnetic field, in the process of its arising, weakens one of the two currents, while the other, antiparallel to the first, strengthens; as a result, such a distribution of currents is automatically established for which the total field is equal to zero.

*

The experiments of McLennan, Burton, Pitt, and Wilhelm[^52][^53][^60], as well as the experiments of Silsbee, Scott, Cook, and Brickwedde[^109], then showed that superconductivity is also preserved in the case of alternating currents; this was verified up to a frequency of \(10^6\) Hz. In this connection it turned out that there is a slight lowering of the transition temperature; the reasons for such a lowering have not yet been fully clarified.

The next question, likewise extremely important for elucidating the nature of superconductivity, is the question of whether any abrupt change is also undergone by the other physical properties of a superconductor in passing through the temperature below which the region of superconductivity begins. According to all experiments performed up to the present, no such sharp change has been detected in any of the physical properties of a superconductor. This especially compels one to see in superconductivity a somewhat mysterious phenomenon. De Haas and Kinoshita[^27] studied the change of the torsion modulus in passing through the transition point; Kamerlingh Onnes and Holst[^102], and also de Haas and Bremmer[^25], investigated the thermal conductivity from this point of view; McLennan, Allen, and Wilhelm[^58] investigated the coefficient of thermal expansion and magnetostriction; Keesom and van den Ende[^47], and also Mendelssohn and Simon, investigated the specific heat; Meissner and Steiner[^90] studied the work function of electrons; McLennan, Hunter, and McLeod[^62], the photoelectric emission; Borelius, Keesom, Johansson, and Linde[^1a], the thermoelectromotive force and the Thomson effect. From this list it is evident how deeply one must penetrate into the essence of the metallic state in general if the nature of superconductivity is to be clarified at all.

In substance, only one positive feature may be noted in the result of all these experiments: in the above-mentioned experiments of de Haas and Bremmer[^25], although it was not possible to detect any jump in the thermal conductivity at the temperature at which superconductivity appears, the following phenomenon was discovered: below the transition point of the electrical conductivity, the influence of the magnetic field on the thermal conductivity immediately ceases—at least if the field strength is not too great. If, however, one then begins gradually to strengthen the external magnetic field (while all the time keeping the temperature below the normal transition point of the electrical conductivity) and brings the field strength up to the moment when superconductivity is destroyed, then the thermal conductivity increases considerably. Meanwhile, if the strength of the magnetic field is increased at temperatures above the transition point of the electrical conductivity, then the thermal conductivity of the dark substance decreases. At the transition point itself the influence of the magnetic field on the thermal conductivity is vanishingly small; it grows as the temperature is lowered. We shall return, in the next paragraph, to this established fact, in which an idea of enormous significance is evidently hidden.

Further, the experiments of Borelius, Keesom, Johansson, and Linde¹ᵃ led with sufficiently high probability to the result that both the thermoelectromotive force and the Thomson effect in lead, already at temperatures somewhat higher than the point of the jump in electrical conductivity, rather rapidly—if not discontinuously—fall to zero. That, at the temperature of the jump in electrical conductivity itself, the thermoelectromotive force in superconductors is equal to zero had already been established earlier by Meissner⁷³.

In Charlottenburg, experiments are being set up to study the distribution of intensity along individual lines of X-ray patterns taken from superconductors, and also to investigate the continuous background above and below the temperature at which superconductivity appears. It is to be hoped that in this way it will be possible to establish whether the distribution of electrons in a metal changes upon passing through the point of the jump in electrical conductivity.

6. Conclusions concerning the nature of superconductivity and the question of its theory

Let us pose the quite general question: how is superconductivity realized from the point of view of the electron theory? Two possible answers to this question come to mind:

1. The current carriers in the phenomenon of superconductivity are the very same electrons, or a part of the electrons, that also produce the ordinary electric current at temperatures above the jump point. From the moment the state of superconductivity appears in the metal, the stream of these electrons, which at first provided ordinary conductivity, acquires, at the expense of the external electric field, so large an increase in kinetic energy that the electrons no longer have time to give it up to the atoms; thus between any two points of the superconductor the potential difference is equal to zero. The stream of these electrons, moreover, must possess also the property that the superconducting current inside the metal would be “absolutely” immobile under attempts to disturb it by a magnetic field. As to how, in greater detail, the transfer of energy to the atom takes place, whether or not there occurs at the same time an exchange of the electrons carrying the current with the electrons bound to the atom, molecule, or crystal lattice—nothing definite can yet be said about this. Such an exchange may also be taken into consideration in investigating the state of superconductivity. In the case of superconductivity, the only essential point is that any transfer of energy whatever from a mobile electron to the atomic lattice is absolutely impossible.

2. After the state of superconductivity has set in, new electrons become active, for example those freed by atoms, by their core, or by the entire crystal lattice. These electrons then produce an “inertial,” long-lasting—

an electric current in the phenomenon of superconductivity, encountering no resistance and not displaced by the magnetic field from the path chosen by it in the metal.

After this superconducting current begins to flow, it as it were short-circuits the ordinary current carried by electrons, which are still active in the temperature range up to the transition point. Therefore the ordinary current, in the presence of the superconducting one, no longer plays any role as regards electrical conductivity.

This second possible variant of the answer to the question posed corresponds approximately to the views at which Grüneisen arrived on the basis of his investigation of the law of isotherms[^13].

The presence of foreign atoms in mixed crystals creates for the ordinary current a certain resistance at absolute zero. And in both the first and the second of the variants given, the presence of the same foreign atoms can, in principle, have no influence whatever on the current of superconductivity. To explain this last proposition, it is evidently sufficient to consider a metal at absolute zero temperature.

Starting from the first variant, it is difficult to imagine why, at the transition point of electrical conductivity, the coefficient of thermal conductivity does not also change. Since the electrons carrying the ordinary electrical conductivity, below the conductivity transition temperature, can no longer transfer their kinetic energy to the crystal lattice, it follows that they evidently also cannot carry heat with them from points of higher temperature to points of lower temperature. According to all that we know, there can be no doubt that, at least in good metallic conductors, heat transfer is effected mainly by the very same electrons which carry electricity, producing a current. Consequently, contrary to what experiment shows, at the transition point of electrical conductivity one should simultaneously expect a sharp change in thermal conductivity. The experiments of de Haas and Bremmer described show that the thermal conductivity everywhere below the temperature at which superconductivity appears generally again and appreciably decreases, but gradually, in no way resembling a discontinuity in the smoothness of its fall. This strong decrease of thermal conductivity can quite well be explained by impurities, about which still further experiments would help to draw conclusions. Moreover, it sets in somewhat earlier than the transition temperature is reached. Consequently, in order to remove the difficulty with thermal conductivity in the first variant, one could assume that, in the phenomenon of superconducting current, far from all take part, but only an insignificant fraction of all those electrons which make possible the most ordinary electric current in general.

If one proceeds from the second version, then this whole difficulty with thermal conductivity does not arise at all, since the ordinary electrons of normal conductivity, in the absence of current, also carry heat. Here, however, too, a natural question arises: why do the electrons that at once become so active (in the sense of carrying electricity) upon passing through the transition point behave in this respect quite differently from the electrons “responsible” for the ordinary electrical conductivity above the transition point. One possible explanation of this is perhaps the following. Let the superconducting state have only just been established. The electrons which have only just begun to manifest their capacity for action (“electrons of superconductivity”) cannot be imagined as free in quite the same sense as ordinary “electrons of normal conductivity”: no, here the matter concerns electrons which still belong to the crystal lattice, but which at the transition point are to some extent in unstable equilibrium, and therefore even the weakest external electric field is sufficient to transfer each such electron from one atom to a neighboring one. In order to take into account Kretschmann’s objection as well, one must further assume that at temperatures below the transition point and in the absence of an external electric field these “electrons of superconductivity” in the metal are almost at rest and, consequently, in all probability form a kind of electron lattice. In particular, the idea of an electron lattice was used in their works by F. A. Lindemann and Haber. At all temperatures above the transition point, the “electrons of superconductivity” can describe quantum orbits in the crystal lattice. Nevertheless, it remains incomprehensible and strange that the unstable state continues to exist even at temperatures below the transition point, if one approaches absolute zero, since, for example, in the case of lead the thermal vibrations near the transition temperature are still by no means ceasing. Below the transition point there still exists a noticeable change in the sizes of atoms, in the lattice constant, etc. Then it still requires explanation why the “electrons of superconductivity,” when they move, producing a current, cannot be deflected by a magnetic field from the path once adopted by them. It seems especially difficult to understand superelectrical conductivity in mixed crystals.

In favor of the second version, however, the following perhaps speaks. Considering Table 1, we notice that among all superconductors so far found there is not a single chemical element in whose free atoms (for example, in the gaseous state), besides a single valence electron, upon which falls the role of carrier of the ordinary current, there would still be, at the periphery of the atom, only a quantum shell completely filled with electrons. If such atoms had

if superconductivity were observed, then it would at least be difficult to imagine whence the new “electrons of superconductivity” would come upon attainment of the transition temperature. Here one may object first of all that our knowledge of the structure of electron shells applies only to free atoms and does not extend unconditionally to atoms that are in the bound state in a solid. In this direction, however, Juom-Rosery has already carried out many rather profound investigations.^127 He succeeded in establishing the following: there exists a mathematical dependence connecting with one another 1) the distance \(d\) between two nearest-neighbor atoms in a solid, 2) the principal quantum number \(n\) of the outermost of the completely filled electron shells of the free atom and, finally, 3) the limiting frequency \(\nu\) corresponding to the transition of some electron from the outermost of the completely filled electron shells of the free atom to the very periphery.

If \(R\) is the Rydberg constant and \(Z\) the atomic number, then, on the one hand, there is the equality:

\[ \frac{\nu}{R} = (bZ)^y \]

and, on the other hand,

\[ \frac{d}{n} = \frac{1}{(aZ)^x}. \]

Let us mentally pass from element to element, moving along the row of any one, for example the third, period. Let us begin, for example, with group 1a. Then for the first groups encountered the relation \(y = 2x\) will at first hold. When subsequently the outermost “octet” electron shell becomes filled, the value of \(y\) changes. The value of \(x\), however, also changes in passing to other values of \(Z\). This is evidently a sign that in solids the filling of the octet shell of the electron cloud begins at a different value of \(Z\) than in the free atom. Therefore the octet shell—or, more precisely, its filling—determines the regular change of the quantity \(d\). Suppose that, with the given initial filling of the octet shell, the atomic number \(Z\) increases, changing each time by one unit. Then, also for atoms situated inside the metal, beginning with a certain definite value of \(Z\), there are places in the periodic system where \(y = 2x\) (with other values of \(y\) than in the first groups). Thus here, for the atom entering into the composition of the metal, the structure of the electron cloud turns out to be the same as that of the free atom. Juom-Rosery discovered these relations between \(\nu\) and \(d\) for all the a-subgroups of the third and fourth periods. In the first groups of the first period \(x = 1\), in the same groups of the second period \(x = 2\), and so on, up to \(x = 4\). Further,

up to the sixth group \(x\) is approximately equal to \(1/3\). In the b-subgroups this is also justified in a first approximation. All these ratios are empirical and have not yet been studied experimentally to the end; there is as yet no theoretical interpretation of them. However, even these discovered regularities undoubtedly make it possible to draw certain conclusions about the distribution of electrons in the solid state of matter. In Table 1, as far as possible, the numbers of electrons filling the \(K\)-, \(L\)- and \(M\)-shells, obtained in this way, are given; these numbers are placed under the corresponding numbers valid, according to Hund \(^{12}\), for free atoms. Where the accuracy of the value given cannot be vouched for, a question mark is placed. Then in Table 1, next to the indication of the crystal system, the coordination numbers are also given, each of which represents the number of atoms—the nearest neighbors to any given atom of the lattice, situated at equal distances from it on a sphere. The second number, enclosed in parentheses, also denotes the number of neighbors, but not the nearest ones; rather, “neighbors of the second order,” situated on a certain sphere somewhat larger than the first. At the center of this sphere there is again the same, arbitrarily chosen atom of the crystal lattice: the two spheres are concentric.

From Table 1 we now see that all superconductors always have more than one valence electron, and consequently, in the atom of any superconductor, besides the completely filled shells, there are in an unfinished shell two or even more electrons. F. London assumes that in the a-subgroups all these valence electrons are free. Such an assumption, however, is not necessary; it is enough that these valence electrons no longer belong to individual atoms and that they no longer determine the magnitude \(d\). They may, for example, partly run along orbits belonging simultaneously to several atoms of the compound. In the b-subgroups the valence electrons not enclosed in parentheses probably belong to individual atoms. It is especially interesting that Nb, whose atom in the free state has in the outermost shell only one valence electron, when in the metal already has five valence electrons and provides the excellent superconductivity of metallic niobium. In the case of Mo, on the contrary, the number of electrons in the last shell in passing from the free atom to the metallic one increases not at all more strongly than in Nb; this, apparently, is what was reflected in the fact that the jump point of the electrical conductivity in Mo, at the temperatures reached, could not be directly established. It is very possible that in Th there is the same strong change in the distribution of the outer electrons in passing from the free atom to the Th atom in the solid state as in Nb.

Thus, a detailed study of the distribution of electrons in metals, although it leads to results still full of all sorts of gaps, at least agrees fully with the second of the proposed variants of the fundamental explanation of the basic facts concerning superconductivity. This study must be recognized as necessary for establishing the laws that determine the position of the jump point on the temperature scale.

It seems to me that the strong increase in thermal conductivity caused, according to the works of de Haas and Bremmer^25, by a magnetic field at superconducting temperatures also speaks in favor of the second of the possible variants. Indeed, once the superconductivity of the “electrons of superconductivity” is destroyed, it remains for them to take part in the transfer of heat and to enhance it. From the point of view of the first variant, an increase in thermal conductivity could occur only to a very slight extent, owing to the small number of electrons that carried out superconductivity before its loss.

It remains to be seen to what extent future experimental investigations in the region of still lower temperatures will confirm the second variant and the possibilities it predicts for the discovery of new superconductors. For example, Meissner and Voigt found, at the lowest attainable temperatures, distinct indications of the beginning of a rapid drop in the resistance curve of rhodium, Rh. In the event that further investigations do indeed reveal that rhodium can be a superconductor, and that the superconductivity cannot be ascribed to the presence of impurities, this would evidently constitute some difficulty for the view set forth regarding the propensity of one or another element toward superconductivity and regarding the possibility that, upon reaching the jump point, new “electrons of superconductivity” may appear. To verify whether such new “electrons of superconductivity” actually appear or not, experiments on the distribution of the intensities of X-ray diffraction lines and on the change in this distribution on passing through the jump point of electrical conductivity will be of decisive importance. Such experiments have already been begun.

In connection with the study of the distribution of electrons in solids there are investigations devoted to the question of the dependence of valence on the structure of the solid. Friedrich has directed his work along these lines^120, ^131.

Without doubt, the problem of superconductivity is closely connected with the magnetic properties of the metal. In this respect mention should be made of Gerlach’s hypothesis^11, according to which the temperature of the jump in electrical conductivity is identified with the Curie point for ferromagnets. This hypothesis has not yet been developed and in general has not been subjected to experimental verification.

One difficulty confronting the development of Gerlach’s idea is that at the jump point no ...

although even an indication of a jump in the change of the energy reserve, whereas at the Curie point noticeable thermal effects would have to be expected.

Kikoin and Lazarev[^49] established that the coefficient \(R\) in the Hall-effect formula, and especially the quantity \(R\sigma\) (\(\sigma\)—the electrical-conductivity coefficient), are substantially smaller for superconductors than for ordinary conductors. In doing so, however, both for \(R\) and for \(\sigma\) they used values referred to room temperature, whereas, in any case, the corresponding temperatures should have been used. The value of Kikoin and Lazarev’s conclusions, of course, depends entirely on whether many new superconductors will not still be discovered after sufficiently low temperatures have been reached.

Even a slight Hall effect in superconductors would indicate some weak ability of the superconducting electrons to be deflected under the action of an external magnetic field. Neither the former nor the latter exists in metals that are in the superconducting state[^103].

Sizoo[^110] pointed out the fact that the transition temperatures of the first superconductors studied in Leiden form a sequence of values regularly connected with the sequence of values of the magnetic susceptibility of the same metals. Here too, however, unfortunately, the comparison of the two sequences of values was based on the magnetic susceptibility at room temperature. If one considers all the superconductors now known and recalculates their magnetic susceptibility per gram-molecule, we shall see that no parallels at all can be drawn between the sequence of values for the transition temperatures of electrical conductivity and the sequence of values for the susceptibility coefficients; consequently, Sizoo’s observation has lost its force.

Epstein[^10] attempts to establish another regularity in the properties of various superconductors. For a whole series of superconductors—lead, mercury, tin, indium, and thallium, as well as for many other chemical elements—he calculates the magnitude of the ratio \(\dfrac{\alpha \nu^{2/3}}{\varkappa}\), where \(\alpha\) is the expansion coefficient, \(\varkappa\) the compressibility coefficient, and \(\nu\) the atomic volume. As the characteristic temperature he chose, instead of some fractional part of the corresponding temperature, one half of the melting-point temperature. According to Epstein, for superconductors this ratio has values differing from its mean value by no more than 8%. At the same time, the values of this ratio for other metals considered by Epstein (excluding Cd) prove to be either considerably larger or considerably smaller in comparison with the mean value. Clusius4 showed that the value for the recently discovered superconductor Ga is an exception. For Nb, Th, and Ti insuffi-

…provides data for calculating the Einstein ratio. Einstein also attempts to form an idea of the origin of superconductivity. His views here are close to the standpoint of Kamerlingh Onnes, de Haas, and others, and develop this standpoint. In conclusion he arrives at the result that the relation \(\frac{a}{x}\cdot v=\mathrm{const}\), which is valid for all metals and is derived from the approximate formulas of Einstein and Alterthum, must be replaced for superconductors, in view of their specific features,* by the above-mentioned empirical relation.

After all that has been set forth above, it is hardly surprising that the construction of a true theory of superconductivity encounters great difficulties; for this, evidently, requires a very deep penetration into the essence of the metallic state in general. For this reason we shall not dwell on Thomson’s old theory of superconductivity\(^{114}\) or on Kretschmann’s interesting theory.\(^{50}\)** The new electronic theories of metals created after these works, belonging to Bloch, Nordheim, and Peierls, were constructed on the foundation of wave mechanics, Fermi–Dirac statistics, and Sommerfeld’s work. However, even these theories, as the authors themselves emphasize, have not yet been able to encompass the phenomena of superelectrical conductivity. It should perhaps also be said that the theory of superconductivity probably cannot be constructed on the basis of quantum mechanics alone; the problem may prove soluble only with the aid of quantum electrodynamics. Meanwhile, quantum electrodynamics has not yet crystallized to a sufficient degree.

The beginnings of a theory of superconductivity have nevertheless quite recently been given by Schachenmeier\(^{106}\) (the author himself considers his work preliminary). At the basis of his reasoning he assumes that an atom, when in a metal, possesses, in addition to the outermost shell itself, completely filled with electrons, one especially distant “series” electron and then one more mobile conduction electron. The number of conduction electrons is thus equal to the number of ions in the lattice, as in Sommerfeld’s theory. The atomic core has an effective charge \(2e\), if \(e\) is the elementary charge, since the “series” electron is still farther from the nucleus than the conduction electron. Proceeding from these assumptions, Schachenmeier, using the apparatus of wave mechanics, calculated the exchange forces

* In the abstract made by the author in “Physik. Ber.” this point of Einstein’s work did not find its proper expression.

** Already after the present review had been submitted for publication, a new electronic theory of electrical conductivity and superconductivity by Kretschmann appeared (“Ann. d. Phys.,” V, 13, 564, 1932). The basic premises of this theory are, in a known sense, the opposite of the assumptions laid down as the basis of Schachenmeier’s work, which appeared almost simultaneously. The fundamental difference lies in the manner of conducting the reasoning (see the end of this paragraph).

interactions between conduction electrons and “series” electrons.

In the course of his calculations he then made a simplified assumption, approximately corresponding to the first Einstein theory of specific heat. Namely, he assumes that in the crystal lattice, besides slow thermal vibrations, only vibrations with a single frequency \(\nu_m\) are possible. The frequency of the process of exchange interaction between the conduction electrons and the “series” electrons depends on the amplitude of these vibrations with frequency \(\nu_m\), and this amplitude depends on the temperature \(T\). At the temperature at which the frequency of the exchange interactions is equal to \(\nu_m\), the resonance has an effect on the resistance. Below this temperature of the jump the resistance is vanishingly small, notwithstanding the phenomena of exchange between the conduction electrons and the “series” electrons. In the conclusion of his work, Schachenmeier writes an expression for the jump temperature \(T_c\), which in the first approximation has the following form:

\[ T_c = A \Theta^{7/4} m^{1/4} a^{-1/2}, \]

where \(\Theta\) is the characteristic temperature, \(m\) is the mass of the atom, \(a\) is the lattice constant, and \(A\) is a constant, but not an arbitrary one: it is calculated from universal physical constants. For lead, Schachenmeier in this way found the value \(T_c = 1.4^\circ\) abs. instead of the actually observed value \(7.3^\circ\) abs.

It remains to be seen how close to reality, in its further development, Schachenmeier’s theory will come in explaining the real course of the resistance curve above the jump point of electrical conductivity, in connection with thermal conductivity, in clarifying the fact of the stability of the superconducting current with respect to external magnetic influences, etc.

Finally, mention should be made of a note by Elsasser,\(^{9}\) which also appeared quite recently. In this work, on the basis of Dirac’s theory of the electron, a connection is established between one relativistic correction and the phenomenon of superconductivity.

LITERATURE*

1. Van Aubel E., de Haas W. J., and Voogd J., Superconductivity of the compounds \(\mathrm{Sb}_2\mathrm{Sn}_3\) and \(\mathrm{Bi}_5\mathrm{Tl}_3\); resistance of the compounds \(\mathrm{Cu}_3\mathrm{Sn}_3\), \(\mathrm{Ag}_3\mathrm{Sn}\), and \(\mathrm{Bi}_5\mathrm{Tl}_3\), Comm. Leiden, Nr. 193, 1928.

1a. Borelius G., Keesom W. H., Johansson C., and Linde J. O., Thermoelectromotive force and Thomson effect in Pb rapidly cooled below the temperature of the electrical-conductivity jump, Proc. Amsterdam, 34, 1365, 931; Comm. Leiden, Nr. 217, 1932.

1. Choubine S., Theory of superconductivity, C. r. Acad. Sci. Paris, 192, 1021, 1931.

* After the authors’ surnames, for the most part, what is given is not a translation of the title of the work, but only its main content concerning superconductivity.

1. Clusius K., Review on superconductivity, Z. Elektrochemie, 38, 312, 1932.
2. Crommelin, C. A., Report on superconductivity, Phys. Z., 21, 274, 300, 331, 1920.
3. Crommelin C. A., Review on superconductivity, Chem. Weekblad. Deel, 18, 1921.
4. Crommelin C. A., Review of investigations devoted to superconductivity in the work of the Leiden laboratory; jubilee volume in honor of Kamerlingh-Onnes, p. 401, Leiden, 1922.
5. Review devoted to the work of Kamerlingh-Onnes at the Fifth International Congress on Refrigeration, Comm. Leiden Suppl., Nr. 63, 1928.
6. Einstein A., The essence of superconductivity, volume dedicated to the memory of Kamerlingh-Onnes, p. 429, Leiden, 1922.
7. Elsasser W., An attempt to explain superconductivity from the standpoint of Dirac’s theory of the electron, Z. Physik, 75, 129, 1932.
8. Epstein Z., The essence of superconductivity, Z. Physik, 62, 401; 63, 640, 1930.
9. Gerlach E., The Curie point and superconductivity, Metallwirtschaft, 10, 1006, 1930.
10. Grüneisen E., Article on metallic electrical conductivity, Handbuch d. Physik, 13, 22, 1928.
11. Grüneisen E., Explanation of the Wiedemann–Franz–Lorenz law and the law of isothermal straight lines, Z. Physik, 51, 652, 1928.
12. Grüneisen E., The Kaluza hypothesis, the resistance of Pb, Leipziger Vorträge, p. 46, 1930.
13. De Haas W. J., The essence of superconductivity, Proc. Amsterdam, 22, 1110, 1914.
14. De Haas W. J., The essence of superconductivity, J. Physique et Radium (6), 9, 265, 1928.
15. De Haas W. J., New superconductors and the theory of superconductivity, Nature, 123, 130, London 1929.
16. De Haas W. J., Abstract on metals and superconductors, Metallwirtschaft, 9, 149, 1930.
17. De Haas W. J. and van Alphen P. M., Resistance of graphite, thorium, titanium, and titanium–zirconium in the temperature interval from 20.4° abs. to 1.1° abs.; superconductivity of thorium and titanium, Comm. Leiden, Nr. 212, 1931.
18. De Haas W. J., van Aubel E. u. Voogd J., Superconductivity of the eutectic AuBi, Comm. Leiden, Nr. 197, 1929.
19. De Haas W. J., van Aubel E. u. Voogd J., Superconductivity of the alloys SnBi, SnZn, SnCd, TlCd, TlAu, PbAg, PbCd, PbSb, PbBi, Comm. Leiden, Nr. 197b, 1929.
20. De Haas W. J., van Aubel E. u. Voogd J., Superconductivity of AuBi alloys (90–20% Bi); fall of resistance in alloys with 99.5 and 97.5% Bi, Comm. Leiden, Nr. 197c, 1929.
21. De Haas W. J., van Aubel E. u. Voogd J., Superconductivity of AuPb₂, Pb₂Tl; resistance of Cu₄Sn, Comm. Leiden, Nr. 197d, 1929.
22. De Haas W. J., van Aubel E. u. Voogd J., Temperature of the discontinuity in Hg₅Tl₂, PbTl₂, and the alloy AgTl, Comm. Leiden, Nr. 208a, 1930.
23. De Haas u. H. Bremmer, Thermal conductivity of lead and tin down to 2° abs.; influence of the magnetic field, Comm. Leiden, Nr. 214d, 1931.
24. De Haas u. Jurrianse F., Dependence of the superconductivity of the alloy AuBi on the compound Au₂Bi, Naturwiss., 19, 33, 706, 1931.
25. De Haas u. Kinoshita M., Torsion modulus of Sn and Hg above and below the point of the jump in electrical conductivity, Comm. Leiden, Nr. 187b, 1927.
26. De Haas u. Sizoo G. J. u. Voogd J., Gray tin is not a superconductor, Comm. Leiden, Nr. 187d, 1927.
27. De Haas u. Tuyn W., Sizoo G. J. u. Voogd J., Review of investigations devoted to superconductivity for the period 1924–1928, Comm. Leiden. Suppl., Nr. 66d, 1928. Rapports et Communic. V Congrès int. du froid, I Comm., Rome 1928.

1. De Haas and Voogd J., Hysteresis phenomena in a magnetic field in the superconductors Sn, Pb, Tn, Tl, Comm. Leiden, Nr. 191d, 1928.

2. De Haas, Superconductivity of Ca, Comm. Leiden, Nr. 193b, 1928.

3. De Haas, Hafnium and zirconium at low temperatures, Comm. Leiden, Nr. 194c, 1928.

4. De Haas, Transition point in Bi₅Tl₃; influence of the magnetic field on the superconductivity of Bi₅Tl₃, SnBi, SnCd, Comm. Leiden, Nr. 199c, 1929.

5. De Haas, Transition point in Ga, Comm. Leiden, Nr. 199d, 1929.

6. De Haas, Magnetic threshold for superconductivity in alloys: PbTl₂, Sb₂Sn₃, PbBi, PbSnBi, PbSnBiCd, Comm. Leiden, Nr. 208b, 1930.

7. De Haas and Voogd J., Magnetic threshold for tin single crystals; hysteresis loop; various cases of longitudinal and transverse field; dependence of the magnetic threshold on temperature, Comm. Leiden, Nr. 212c, 1931.

8. De Haas and Voogd J., Resistance of indium, thallium and gallium; dependence of the threshold on temperature for Tl and Hg, Comm. Leiden, Nr. 212d, 1931.

9. De Haas and Voogd J., Magnetic threshold for PbBi 35%, PbTl 40%, PbHg 15% and for the eutectic AuBi, Comm. Leiden, Nr. 214b, 1931.

10. De Haas and Voogd J., Discontinuous transition to superconductivity in a tin single crystal; the transition temperature does not depend on the direction of the current, Comm. Leiden, Nr. 214c, 1931.

11. De Haas, Sizoo G. J. and Kamerlingh-Onnes H., Hysteresis phenomena in Hg in the superconducting state, Comm. Leiden, Nr. 180d, 1925 and 1926.

12. Holm R. and Meissner W., Contacts made of the superconductors PbPb, SnSn, PbSn, Z. Physik, 74, 715, 1932.

13. Holm R. and Meissner W., Yield point at low temperatures, Z. Physik, 74, 736, 1932.

14. Kapitza P., Influence of a magnetic field on metals, Proc. Roy. Soc., 123, 292, 342, London (A) 1929.

15. Kapitza P., Superconductivity and residual resistance, Nature, 123, 870, London 1929.

16. Kapitza P., Influence of a magnetic field on the resistance of Au; on the nature of superconductivity, Proc. Roy. Soc., 126, 683, London (A) 1930.

17. Keesom W. H., Obituary for Kamerlingh-Onnes, Discovery of superconductivity, Comm. Leiden Suppl., Nr. 57, 1926.

18. Keesom W. H. and van den Ende J. H., Absence of anomalies in the value of the characteristic temperature of lead at transition temperatures, Comm. Leiden, Nr. 203d, 1930; Nr. 213c, 1931.

19. Keesom W. and Kamerlingh-Onnes H., Crystalline state above and below the transition point in superelectrical conductivity, Comm. Leiden, Nr. 174b, 1924.

20. Kikoin and B. Lasarew, Hall constant and superconductivity, Nature, 129, 57, London 1932.

21. Kretschmann E., Theory of superconductivity and long-duration currents, Ann. Physik (4), 74, 405, 448, 1924; 80, 109, 1926; 86, 914, 1928.

22. Kretschmann E., Review of electronic theories, Physik Z., 28, 565, 1927.

23. McLennan J. C., Superconductivity and high-frequency currents; superconductivity and the polarization effect, Nature, London 1931, August 29.

24. McLennan J. C., Superconductivity at high-frequency currents, “Trans. Roy. Soc. Canada,” 25 III, 191, 1931.

25. McLennan J. C., Allen J. F. and Wilhelm J. O., Superconductivity of ruthenium, Trans. Roy. Soc. Canada, 23 III, 283, 1929.

26. McLennan J. C., Allen J. F. and Wilhelm J. O., Superconductivity in BiPb, PbSb, Bi₅Tl₃, Rose’s metal (Bi₂SnPb), Newton’s metal (Bi 50 Sn 19, Pb 31%), Wood’s metal (Sn 12.5, Pb 25, Bi 50, Cd 12.5%), Trans. Roy. Soc. Canada, 24, III, 1930.

27. McLennan J. C., Allen J. F. and Wilhelm J. O., Superconductivity of Sb₂Tl₇, PbAg, PbAsBi, PbBiSb, PbBiSbAs, PbP, PbAu, PbAg, PbCa, PbLi, SnAs, PbS; resistance of PbCu, Trans. Roy. Soc. Canada, 24, III, 1930.

1. McLennan J. C., Allen J. F. and Wilhelm J. O., Numerous alloys and compounds which did not exhibit superconductivity, Philosophic. Mag. 10, 500, 1930.

2. McLennan J. C., Allen J. F. and Wilhelm J. O., Absence of a jump in thermal expansion and magnetostriction near the transition to superconductivity, Trans. Roy. Soc. Canada, 25, III, 1931.

3. McLennan Allen J. and Wilhelm J., Absence of superconductivity in ruthenium and ruthenium carbide at 1.96° abs.; superconductivity in W₂C at 2.05° abs., Trans. Roy. Soc. Canada, 25, III, 1931.

4. McLennan, Burton A. C., Pitt A. and Wilhelm J. O., Absence of superconductivity in high-purity mercury, Philosophic. Mag. 12, 707, 1931.

5. McLennan, Howlett L. E. and Wilhelm J. O., Superconductivity of Na₂, Pb₅, Ta; resistance of Mo, U, Hf, Zr, W, Mg, Nb, Tl, a rare-earth alloy, Sb–Cd eutectics at temperatures down to 2.4° abs., Trans. Roy. Soc. Canada, 23, III, 287, 1929.

6. McLennan, Hunter R. C. and McLeod J. H., Photoelectric effect in lead and mercury at various temperatures down to the point of the jump of electrical conductivity in lead and below; absence of a jump in photoelectric emission at the point of appearance of superconductivity, Trans. Roy. Soc. Canada 24, III, 269, 1929.

7. McLennan, McLeod, H. and Wilhelm J. O., Scattering and absorption of fast electrons as they pass through lead to the temperature of the jump and below it, ibid., 23, III, 269, 1929.

8. McLennan and Niven C. D., Measurements of the resistance of Pb, Cd, In, Be, Cr, Rb, Th at low temperatures, Philosophic. Mag., 4, 386, 1927.

9. McLennan, Niven C. D. and Wilhelm J. O., Influence of Cd impurities on the superconductivity of Pb, Trans. Roy. Soc. Canada 6, 678, 1928.

10. McLennan, Niven C. D. and Wilhelm J. O., Resistance of As and Sb, ibid., 6, 666, 1928.

11. McLennan, Niven C. D. and Wilhelm J. O., Resistance of Cs, Cr, Co, ibid., 6, 672, 1928.

12. Lippmann G., Induction of persistent currents in superconductors, C. R. Acad. Sci. Paris 168, 73, 1919.

13. Lorentz H. A., Current in a spherical shell in a magnetic field, Comm. Leiden, Suppl. Nr. 50b, 1924.

14. Meissner W., Constantan, lead, tin, single crystals of gold in the interval from 273.2° to 1.6° abs., Physik. Z. 26, 689, 1925.

15. Meissner W., Single crystals and wires of Au, Zn, Cd; wires of Pt, Ni, Fe, Ag in the interval from 273.2° to 1.3° abs., Z. Physik 38, 647, 1926.

16. Meissner W., Au, Zn, Cd, Pt, Ni, Fe, Ag at low temperatures, Physik. Z. 27, 725, 1926.

17. Meissner W., Pure metals at low temperatures, thermoelectromotive force of an alloy of superconductors, Z. Kälte-Ind. 34, 197, 1927.

18. Meissner W., Cu, Al, Fe, Be, Co, Mo, Rh, Pt, W, Li, Sb, nickel silver, carbon at low temperatures; experiments with Sn in a nickel-silver tube and on establishing the lower limit of the superconducting current; superconductivity of tantalum, Physik. Z. 29, 897, 1928.

19. Meissner W., Superconductivity of Th, Naturwiss. 17, 390, 1929.

20. Meissner W., Superconductivity of CuS, Z. Physik. 58, 570, 1929.

21. Meissner W., Superconductivity of Ti, ibid., 60, 181, 1930.

22. Meissner W., Superconductivity of Ta and Th, ibid., 61, 191, 1930.

23. Meissner W., Superconductivity of niobium, carbides and nitrides, Z. Kälte-Ind. 37, 174, 1930.

24. Meissner W., State of research on superconductivity, Metallwirtschaft 10, Nr. 15 u. 16, 289—295, 310—313, 1931.

25. Meissner W., Resistance of lead in a magnetic field; residual resistance of lead; Kamerlingh’s hypothesis; Grüneisen’s formula for resistance, Ann. Physik (5), 13, 641, 1932.

26. Meissner W. and Franz H., Superconductivity of Nb., Z. Physik 63, 558, 1930.

SUPERCONDUCTIVITY

1. Meissner W. u. Franz H., Superconductivity of carbides and nitrides; resistance of oxides, Naturwiss. 18, 418, 1930; Z. Physik, 65, 30, 1930.

2. Meissner W., Franz H. u. Westerhoff, H., Resistance of barium, indium, thallium, graphite and titanium at low temperatures, Ann. d. Phys. (5), 13, 555, 1932.

3. Meissner W., Franz H. u. Westerhoff, Superconductivity of carbides, nitrides, borides and silicides, Z. Physik, 75, 521, 1932.

4. Meissner W., Franz H. u. Westerhoff, Investigation of the superconductivity of alloys of various concentrations InPb, PbHg, SnTl, InTl, MoC, Ann. Physik (5), 13, 505, 1932.

5. Meissner W., Franz H. u. Westerhoff, Investigation of the superconductivity of alloys of various concentrations PbTb, PbBi, ibid. (5), 13, 967, 1932.

6. Meissner W. u. Scheffers, H. Influence of the magnetic field on Au at low temperatures; hypothesis of Kalischer on superconductivity, Physik Z. 30, 827, 1929; 31, 574, 1930.

7. Meissner W. u. Scheffers H., Influence of the magnetic field on superconductivity, Naturwiss., 18, 110, 1929.

8. Meissner W. u. Steiner K., Copper electrons do not pass through a superconducting sheath, Z. Physik, 76, 201, 1932.

9. Meissner W. u. Voigt B., Resistance of most metals at low temperatures; value of the characteristic temperature of metals, Ann. Physik (5), 7, 761, 892, 1930.

10. Mendelsohn K. u. Simon F., Absence of heat-capacity anomalies at the transition point—greater than 3% of the specific heat, or \(10^{-3} RT\), Z. phys. Chem. (B), 16, 72, 1932.

11. Kamerlingh-Onnes H., Superconductivity of Hg, Comm. Leiden, No. 122b, 124c, 1911; No. 133a, 133c, 1913.

12. Kamerlingh-Onnes H., Superconductivity of Hg; influence of current strength and magnetic field; Nobel lecture, ibid., Suppl., Nr. 35b, 1913.

13. Review of superconductivity at the Third International Congress on refrigeration, ibid., Suppl., Nr. 34b, 1913.

14. Kamerlingh-Onnes H., Influence of current in Hg; experiments with Hg in a steel tube and with constantan (with Sn admixture); on the nature of superconductivity; superconductivity of the alloys Hg—Au, Hg—Cd, Hg—Sn and of pure Sn and Sb, ibid., Nr. 133a—133d, 1913.

15. Kamerlingh-Onnes H., Superconducting switch made of Pb, ibid., Nr. 141b, 1914.

16. Kamerlingh-Onnes H., Limit for residual resistance in superconducting lead; nature of superconducting currents, Rep. u. Comm. IV International Congress on Refrigeration, London 1924.

17. Kamerlingh-Onnes H., Non-decaying currents in superconductors; absence of displacement of current in a superconducting spherical shell; equivalence of the critical value of the magnetic field and temperature; influence of elastic deformation; classes of superconductors; atoms of superconductors; on the nature of superconductivity, Comm. Leiden, Suppl., Nr. 50a, 1924.

18. Kamerlingh-Onnes H., Experiments on superconductivity; on the nature of superconductivity, Rapp. et Discuss. d. IV Conseil Solvey. Paris Gauthier-Villars, 1927, S. 251.

19. Kamerlingh-Onnes H. u. Clay J., Bismuth, Comm. Leiden, Nr. 99c, 1907.

20. Kamerlingh-Onnes H. u. Hof K., “Absence of the Hall effect in superconducting tin and lead,” ibid., No. 142b, 1914.

21. Kamerlingh-Onnes H., Holst G., Hg, Sn, Cd, Cu, Fe up to 272° abs.; specific heat and thermal conductivity of mercury at the transition point, ibid., Nr. 142a, 142c, 1914.

22. Kamerlingh-Onnes H. u. Tuyn W., Superconductivity in thallium; transition point in Pb and uranium Pb, ibid., Nr. 160a u. b, 1922.

23. Kamerlingh-Onnes H., Summary of the resistance of metals at low temperatures, ibid., Suppl. Nr. 58, 1926.

1. Schachenmeier R., Theory of superconductivity on the basis of wave mechanics, Z. Physik, 74, 503, 1932.

2. Silsbee F. B., Relation between the critical value of the current and the magnetic field in superconductivity, J. Washington Acad. Sci. 6, 597, 1916; Sci. Pap. Bur. Stand., 14, Nr. 307, S. 305, 1917.

3. Silsbee F. B., Theory of the experiments of Tuyn and Kamerlingh-Onnes, performed to test Silsbee’s hypothesis, Proc. nat. Acad. Sci. U. S. A. 13, 516, 1927; Sci. Pap. Bur. Stand., Nr. 556, 1927.

4. Silsbee F. B. and Scott R. B., Cook J. W. and Brickwedde F. G., Superconductivity at high frequencies well confirmed, up to a frequency of \(1.4 \cdot 10^6\) hertz, Phys. Rev. (2), 39, 379, 1932.

5. Sizoo G. J., Influence of tension and all-round compression on superconductivity and the magnetic threshold in tin and indium; hysteresis of the critical value of the magnetic field in tin and mercury; superconductivity of thin layers; distribution of current in parallel wires of Sn, Diss. Leiden, 1926.

6. Sizoo G. J., de Haas W. J. and Kamerlingh-Onnes H., Magnetic field and elastic deformations in superconducting In; hysteresis phenomena, Comm. Leiden, Nr. 180c., 1926.

7. Sizoo G. J. and Kamerlingh-Onnes H., Superconducting thin films, ibid., Nr. 180a, 1925.

8. Sizoo G. J. and Kamerlingh-Onnes H., Influence of elastic deformation on superconductivity in Sn and In, ibid., Nr. 180b, 1925.

9. Thomson J. J., Theory of superconductivity in a solid electron lattice; collision time approximately equal to the period of atomic vibrations, Philosophic. Mag. (6), 44, 657, 1922.

10. Tuyn W., Resistance of metals and alloys at the temperature of liquid helium; critical value of the magnetic field and current strength, Diss. Leiden, 1924.

11. Tuyn W., Influence of a magnetic field on the superconductivity of Tl, Conn. Leiden, Nr. 191b, 1928.

12. Tuyn W., Resistance of Cd, Cu, Au, In, Pb, Pt, Tl, Sn and Zn at low temperatures, ibid., Nr. 196b, 1929.

13. Tuyn W., Experiments on obtaining persistent currents in superconductors and in conductors made of Pb and Zc, ibid., Nr. 98a, 1929.

14. Tuyn W. and Kamerlingh-Onnes H., Superconductivity of indium, ibid., Nr. 167a, 1923.

15. Tuyn W. and Kamerlingh-Onnes H., Critical value of the magnetic field for indium, tin and lead; critical value for the current in tin and lead; superconducting tin cylinder in a magnetic field of coaxial alternating current, ibid., Nr. 174a, 1925.

16. Tuyn W. and Kamerlingh-Onnes H., Compilation of data on superconductivity of alloys: Hg, Sn, Pb, uranium, Pb, Tl, In, Cd, Zn, Ga, Ge, Pt, Au, Cu, Fe, Ag, Ni, Be, K, Na, Li, Pb Sn, ibid., Nr. 181, 1926.

17. Schenck R., Kurzen F. and Wesselkock H., Z. Anorg. u. allg. Chem. 203, 181, 1931.

18. Becker K. and Ebert F., Z. Physik 31, 268, 1925.

19. Ibid.

20. Westgren W. and Phragman W., Z. anorg. u. allg. Chem. 156, 27, 1925.

21. Meissner W., Activity report of the Phys.-Techn. Reichsanstalt, Z. Instrumentenkunde 49, 166, 1929.

22. Hume-Rothery, Metallic state, Philosophic. Mag 9, 65, 1930; 11, 649, 1931, Oxford 1931.

23. Hund E., Line spectra and the periodic system of the elements, Berlin, Julius Springer, 1927.

24. Friederich E., Techn.-wissenschaft. Ab. a. d. Osrem-Konzern 1, 335, 1930.

25. Friederich, Fortschr. Chem. Phys. u. phys. Chem. 18, 713, 1926; Z. Physik 31, 813, 1925.

26. Friederich and L. Sittig, Z. anorg. u. allg. Chem. 145, 251, 1925.

27. Frenkel Ya. I., Theory of superconductivity, Journal of Experimental and Theoretical Physics, vol. III, 1933.

1. Ergebnisse der exakten Naturwiss., Vol. XI, 1932. Translation by V. V. Bobin. ↩

2. Until coincidence with the plane of the ring. Translator’s note. ↩↩

3. 79 ↩

4. 96, 98, 99 ↩↩

5. 15, 16 ↩

6. 8 ↩

7. 50, 51 ↩↩