Brief history of superconductivity

To cool a gas down you need to lower the volume or the pressure: pV=kT

In practice it is easier to keep a volume constant and decrease the pressure: i.e. cold and vacuum go together.

at constant temperature, the absolute pressure and the volume of a fixed amount of gas are inversely proportional: p ~ 1/V

Boyle’s vacuum pump was made of a spherical glass globe with a diameter of 38 cm and a brass pumping cylinder connecting with it. The globe had an opening on the top. Objects used in experiments could be transferred into the globe through this opening and later sealed by a brass cap and lute. The air pumping process was controlled by the valve connecting the pump and globe and a small brass plug on the pump, as shown graphically below (please pay attention to the colored component in each step).

The air in the bulb expands at higher temperatures, which lowers the liquid level in the tube.

The device established fixed points but does not measure specific quantity, although it can tell when something is warmer than another thing.

It was Torricelli (one of his pupils) who experimenting with mercury columns for thermometers and barometers realized that the space on the top closed end of the column was vacuum.

1805 Oliver Evans patents a refrigeration machine (he never built)

1810 John Leslie freezes water using an air pump

1822 Caignard de la Tour observes critical points in fluids

1823 Faraday (accidentally) liquifies Cl2

The tube is sealed at one end (a) and bent in the middle (b).The gas-evolving material is placed in the closed end (c), and the other end, which has been left open for the introduction of the material, is closed by melting the glass with a blow-pipe and burner flame. There exist two main ways to carry out the experiment: (i) the gas-evolving material is a salt, whose thermal decomposition involves the development of a gas, and decomposition is induced by keeping the closed leg (c) in a water or oil bath; (ii) gas is produced by a chemical reaction, typically involving a liquid and a solid as reactants, mixed in leg (c). As the gas is evolved it produces pressure in the tube, and (i) if the pressure becomes great enough, and/or (ii) if the temperature of the empty end of the tube is cool enough, it liquefies and collects there in the liquid state.

1824 Sadi Carnot develops the Carnot cycle

1834 Émile Clapeyron - ideal gas law pV=nRT

Jacob Perkins patents the first gas compression refrigerator

In thermodynamics, the Joule–Thomson effect (also known as the Joule–Kelvin effect or Kelvin–Joule effect) describes the temperature change of a real gas or liquid (as differentiated from an ideal gas) when it is forced through a valve or porous plug while keeping it insulated so that no heat is exchanged with the environment.

The cause of the Joule-Thomson effect lies in the interaction of gas particles. Since the particles attract each other at greater distances (see van der Waals forces), work has to be done when increasing the particle distance. The particles slow down and the gas cools down. However, when the distance is small, the particles repel each other, causing them to accelerate when they can move away from each other, and the gas heats up. The ratio of the two effects depends on the temperature and the pressure. The predominantly effective effect determines the sign of the Joule-Thomson coefficient.

1869 Thomas Andrews observes critical points

1873 van Der Waals equation

atoms or molecule have their own proper volume and exert reciprocal attraction

a and b, the van der Waals constants, have positive values and are characteristic of each individual gas. If a gas behaves ideally, both a and b are zero, and van der Waals equation coincides with the ideal gas law pV=nRT.

The pressure of a gas results from the collisions of its particles on the walls of the container. However, the frequency of the collisions is reduced by the attractive interactions between the gas molecules. Thus, to obtain the ideal pressure, the corrective term [(n/V)2×a] has to be added to the measured pressure p. The constant a reflects the tendency of the particles to interact each other, which is related to the polarity and to the polarizability of the molecule.

The measured volume of the container, V, is not the volume available to the gas, because molecules are material particles and have their own volume. Thus, V must be corrected. In particular, van der Waals considered that when two molecules (imagined as hard spheres of radius r) interact after collision, coming as close as to touch each other, they will not allow any other molecule to enter that volume of space.

Ideal gas particles are free; they do not exert any attractive or repulsive forces on one another. Only elastic collisions take place between the wall and the particle and between particles.

Ideal gas particles themselves do not occupy any volume in their space.

Ideal gas particles do not rotate or vibrate. Their energy is exclusively the kinetic energy of the translational movement in space.

A dewar is a mirrored, double-walled, evacuated vessel made of glass or stainless steel. The Dewar provides good thermal insulation of the substance stored in it from the environment and therefore represents an adiabatic closed system.

A Dewar reduces the three possible heat transfer processes: heat conduction, heat radiation and convection. Heat conduction is influenced by both the choice of material (glass has a very low thermal conductivity) and the shape of the vessel. Since the inner part of the vessel is only connected to the outer via the upper edge, the heat has to be transferred over a relatively long distance, which limits heat conduction. Heat transport through radiation is reduced by mirroring the container walls. Evacuation prevents heat transport through convection. The heat transport through particle collisions is only reduced when the mean free path of the remaining gas particles in the vacuum becomes longer than the distance between the limiting surfaces. Therefore, a significantly higher vacuum is created than would be necessary to prevent convection.

1895 von Linde patents the Hampson-Linde cycle

The cooling cycle proceeds in several steps:

1. The gas is compressed, which adds external energy into the gas, to give it what is needed for running through the cycle. Linde's US patent gives an example with the low side pressure of 25 standard atmospheres (370 psi; 25 bar) and high side pressure of 75 standard atmospheres (1,100 psi; 76 bar).

2. The high pressure gas is then cooled by immersing the gas in a cooler environment; the gas loses some of its energy (heat). Linde's patent example gives an example of brine at 10°C.

3. The high pressure gas is further cooled with a countercurrent heat exchanger; the cooler gas leaving the last stage cools the gas going to the last stage.

4. The gas is further cooled by passing the gas through a Joule–Thomson orifice (expansion valve); the gas is now at the lower pressure.

   The low pressure gas is now at its coolest in the current cycle.

   Some of the gas condenses and becomes output product.

5. The low pressure gas is directed back to the countercurrent heat exchanger to cool the warmer, incoming, high-pressure gas.

6. After leaving the countercurrent heat exchanger, the gas is warmer than it was at its coldest, but cooler than it started out at step 1.

7. The gas is sent back to the compressor, mixed with warm incoming makeup gas (to replace condensed product), and returned to the compressor to make another trip through the cycle (and become still colder).

In each cycle the net cooling is more than the heat added at the beginning of the cycle. As the gas passes more cycles and becomes cooler, reaching lower temperatures at the expansion valve becomes more difficult.

In 1860 Carl Siemens had introduced resistance thermometers (usually Pt or Au) which were calibrated using gas thermometers. These resistance thermometers were introduced in Onnes lab in 1902.

1901 lord Kelvin: as the electrons freeze on the atoms and resistance goes to infinity

1900 Paul Drude: free electron gas model - resistance goes down to zero linearly with decreasing temperature

After liquifying He Onnes set out to study his Pt resistive sensor

The results seemed to point that Lord Kelvin was wrong: the electrons do not freeze as the resistance drops to a constant residual value (no infinity).

However, Onnes (based on Drude’s result) hypothesizes that the resistance of Pt and Au wires should go to zero at absolute zero if they were of high enough purity.

To test this hypothesis he chooses to measure Hg: it can be obtained at much higher purity than Pt or Au.

The first measurement of Hg (08.04.1911): As the vapor pressure of He was dropped to achieve temperatures below 4.2 K, they observed a sudden extremely sharp drop of the resistance to (what looked like) zero.

During the same experiment (as they reached 1.8 K) they observed the superfluid transition of He at 2.2 K. It was only in October that they realized that what they measured in April was a new phenomenon which Onnes called supraconductivity.

In 1913 he was awarded the Nobel prize: “for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium”

Already in 1912 they were studying the magnetic properties of superconductors and realized that the samples became normal conductors if too much current was put - there was a threshold current (and therefore a threshold field).