1 The Discovery of Superconductivity¹

1.1 Liquefaction of Gases

Superconductivity was not discovered simply by chance or by luck. Certainly it had not been predicted, but the extremely low temperatures ($\sim$4K) necessary for superconductivity prevented its discovery from being mere happenstance. The story of superconductivity begins nearly 100 years prior to its discovery with the development of the means for achieving extremely low temperatures: the liquefaction of gases.

Michael Faraday liquefied chlorine gas in 1823, and over the next twenty-five years he liquefied all the known gases except for six gases he termed ``permanent'' gases. In 1869, Thomas Andrews discovered why Faraday had been unable to liquefy these six remaining gases: a gas cannot be liquefied at a temperature greater than its critical temperature $(T_{c})$, because the gas' kinetic energy will overcome the intermolecular forces that cause condensation (see figure 1).

Figure 1: Pressure-volume phase diagram. The solid lines are isotherms; the dashed line is the gas-liquid phase transition. At temperatures above $T_{c}$, regardless of the pressure, the material will be in the gas phase.
Source: Vidali (1993), page 20.

After Faraday's liquefaction work ended in the 1840's, little progress was made until Louis Paul Caillitet's accidental discovery in 1877: one day Caillitet noticed a capillary leaking and that mist was briefly forming on the glass walls. Caillitet realized that the mist was condensed vapor and made a great discovery: when a gas expands from a region of high pressure to low pressure, its temperature decreases. Caillitet soon put his discovery to use and became the first person to liquefy oxygen and achieved a record temperature of 90K. Caillitet's achievement ended a 30-year standstill in cryogenic progress and sparked a race to liquefy the remaining five ``permanent'' gases.

Caillitet, however, was unable to produce enough liquid oxygen for practical applications. In 1883, by combining evaporative cooling - pumping the hotter gas molecules out of the system - with Caillitet's method of cooling a gas through expansion, Sigmund von Wroblewski and Karol Olszewski of the University of Cracow were able to produce large quantities of liquid oxygen ``boiling quietly in a test tube'' (Dahl: 1992, p.6). That same year they used liquid oxygen to liquefy nitrogen at 77K.

The next gas to liquefy was hydrogen. But with a critical temperature of 33K - a fifth of that of oxygen - liquefying hydrogen would prove much more difficult. James Dewar, in part racing against Kamerlingh Onnes, realized that to liquefy hydrogen, he needed a way to store cold liquids and in 1893, Dewar invented a flask that could do just that. The flask, now called a dewar, had a double wall with the space between the two walls evacuated to thermally isolate a gas from its environment. Using the dewar and other advancements, Dewar first liquefied hydrogen in 1896 and by 1898 he could produce large quantities of the boiling liquid. The following year Dewar produced solid hydrogen from further evaporative cooling and achieved a record temperature of 12K.

Meanwhile, Kamerlingh Onnes was also trying to liquefy gases and conduct low-temperature physics research. Unlike Dewar, who was very competitive, Onnes was more interested in using low temperatures to, for example, test van der Waals' equations of state, than to set record temperatures. Onnes developed a reputation throughout Europe for his detailed work in low temperature physics that included measuring magnetic, magneto-optic, radioactive and electrical properties of gases and liquids at low temperatures. Because of the scope of the research in Onnes' lab, the dedication to precision measurements, and a host of experimental mishaps, Onnes was far behind Dewar in liquefying hydrogen.

After succeeding with hydrogen, Dewar began trying to liquefy helium, an element only discovered in 1869 by William Ramsay and with a critical temperature of 5K - five times lower than hydrogen. With Wroblewski's untimely death from an overturned kerosene lamp in his lab, and Olszewski's limited financial resources, the only competition for Dewar was from Kamerlingh Onnes. Dewar, however, was unable to liquefy helium. His failure came from his inability to obtain pure samples of the then-rare element. At the time, Ramsay was one of the few people in England able to obtain sizable quantities of helium, which was disastrous for Dewar, whose longstanding feud with Ramsay forced him to find another source of helium. Dewar was able to find helium, but was unable to purify it. Onnes, however, had more success obtaining helium: his brother, the head of the Office of Commercial Intelligence at Amsterdam, was able to cheaply get large quantities of sand from America that contained helium. Unlike with hydrogen, Onnes' slow, methodical research style proved advantageous for the quick liquefaction of helium. Because of the low critical temperature of helium, a system of regenerative expansion and cooling was needed to sufficiently cool helium, but conveniently Onnes had already used this technique to produce large quantities of liquid hydrogen. Onnes' hydrogen plant was operational in 1906 - ten years after Dewar liquefied hydrogen - but only two years later, on July 10$^{th}$ 1908, Onnes liquefied helium and achieved a record low temperature below 5K.

1.2 Low-Temperature Electrical Conductivity

One reason for seeking low temperatures and the liquefaction of gases was to measure the electrical properties of metals at low temperatures. In 1892, Dewar proclaimed that his task was to ``complete the examination of the change of conductivity with diminished temperature for all the metals in a state of the greatest chemical purity.'' (Dahl: 1992, p.17) With the advent of liquid helium and temperatures as low as 1K, Onnes was able to test the conductivity of metals at unprecedented temperatures. His motivation was two-fold: the utilitarian goal of replacing gas thermometers with more convenient metal thermometers based on calibrated conductivity measurements, and the scientific goal of testing different theories of electrical conductivity near absolute zero (see figure 2).

Figure 2: Resistance vs. temperature predictions. Curve #1 is Drude's and Lorentz's prediction that as the temperature goes to zero, the resistance would go to zero. Curve #2 predicts that the resistance is minimized at absolute zero. Curve #3 is Lord Kelvin's prediction based on a conducting electron gas.
Source: Buckel (1991), page 1.

One theory, proposed by Lord Kelvin, treated conduction electrons as a gas. As the electron gas cooled, the electrons would have less energy and would collide less so the metal's resistance would decrease, but at sufficiently low temperatures, the electron gas would condense onto the atoms and, lacking any free electrons to conduct current, the metal would turn into a perfect insulator. At some low temperature, an equilibrium between these processes would be reached and the resistance would be minimized. Another theory, proposed by Paul Drude and later modified by Hendrik Lorentz, proposed that electrical resistance was caused by thermal agitation between the metal and the conduction electrons, so the resistance would decrease as the temperature got lower, and a metal would achieve perfect conductivity at absolute zero. While some theories predicted a finite resistance at absolute zero, other theories, supported by parabolic curve-fitting, predicted that the resistance of a metal would go to zero at a temperature above absolute zero.

To test these theories, Onnes needed highly pure metals since impurities would make theories of conductivity more complicated and maybe mask important results. Mercury, being the only element that is a liquid at room temperature, was chosen because it was easy to purify through repeated distillations. On June 9$^{th}$ 1911, while measuring the resistance of mercury at very low temperatures made possible by liquid helium, Onnes discovered what he quickly termed superconductivity: the resistance of mercury suddenly dropped to an immeasurably small resistance (see figure 3).

Figure 3: The discovery of superconductivity: Onnes' original plot of the resistance of mercury vs. temperature.
Source: Onnes (1911), reproduced in Vidali (1993, p.33)

Even though some theories predicted zero resistance at finite temperatures, Onnes realized that his data was not what anyone predicted:

``The experiment left no doubt that... the resistance disappeared. At the same time something unexpected occurred. The disappearance did not take place gradually but abruptly [his underlining].'' (Vidali: 1993, p.32)

Certainly many were surprised that mercury had zero resistance, but even more shocking was the abruptness of the transition between finite and infinite conductivity. Onnes correctly suspected that the developing theory of quantum mechanics held the key for explaining superconductivity and its sharp transition, but such a solution was not to be found for nearly 50 years.

Footnotes

... Superconductivity¹

Much of the specifics for the history of the liquefaction of gases and the discovery of superconductivity comes from the thorough introduction in Dahl (1992, p.1-22). A broader survey comes from the second chapter of Vidali (1993, p.13-38). Some of the dates are not consistent between the two sources, but the time-line presented here is based on Dahl's more exhaustive research.