What is cryogenic constant

Low temperature physics

The thermal conductivity determines how a system can be cooled down. It therefore becomes the construction of Cryostats (Cryogenics) often stainless steel used because its relatively low thermal conductivity ideally complements the high mechanical stability. In insulating solids, the phonon gas carries the heat through the material. The number of phonons is strongly temperature-dependent and proportional to at low temperatures T3. The exponent decreases at higher temperatures as the phonons increase Scattering processes (Scatter) are subject to. In metals, the free conduction electron gas makes an additional contribution to the thermal conductivity, which becomes dominant at low temperatures. Metals have a very high thermal conductivity. The electrons with an energy kT / E.F. at the Fermi edge (Fermi energy) contribute to 3k / 2 to the specific heat capacity cel at, cel = 3nk2T / 2E.F., in which n the number of free electrons per mole, E.F. the Fermi energy and k are the Boltzmann constant. So overall it applies ctotal = AT + BT3 (A., B.: corresponding constants).

The electrical conductivityρ of metals decreases proportionally up to approx. 10 K 1 / T. Below the so-called Debye temperature, it sinks more slowly because the phonon populations, which limit the conductivity, also do so T3 fall off and their ability to scatter electrons is reduced. In most metals, the electrical resistance does not drop to zero, but reaches a final value that depends on impurities V and phonons P: ρ = ρV. + ρP.. Materials that are electrically non-conductive remain so even at low temperatures. Metals and semiconductors, on the other hand, show interesting phenomena at low temperatures, which can be traced back to the behavior of the free electron gas. The special electrical properties are e.g. Temperature measurement used.

The thermoelectric power, from which the temperature dependence of the thermoelectric effects follows, depends strongly on the nature of a material. It goes against zero for T → 0. In some materials it assumes a maximum below 50 K, which corresponds to the so-called. Phonon drag going back.

Below a critical temperature, many metals and alloys become superconducting, i.e. the electrical resistance becomes zero. In semiconductors, the electrical resistance decreases towards low temperatures according to an exponential law, if Hop line (Hopping mechanism) is present. The electron contribution to the specific heat capacity is small in semiconductors because the conduction electron density in them is much smaller than in metals. On the other hand, the thermoelectric effects can be very large, so that the Peltier effect is used in semiconductor compounds as a basis for local cooling.

In MOS field effect transistors, in which the electrons are bound in a 2-3 nm thick surface layer, the quantum Hall effect can be observed, which only occurs at low temperatures.

Superconductivity and superfluidity

One of the most prominent low-temperature phenomena, which at the same time also contains the most promising possible applications, is Superconductivity. The ›application hopes‹ not only include loss-free current conduction, but also the miniaturization of components, supercomputers, high field magnets, magnetic levitation trains or applications in the field of nuclear fusion.

At a so-called transition temperatureTc some metals become superconducting, i.e. they suddenly lose their electrical resistance, and the Meißner-Ochsenfeld effect occurs. Superconductivity can be seen as a manifestation of superfluidity, with the conduction electrons of the metal forming the “liquid” (ribbon model).

The currently highest transition temperatures reached for conventional superconductors are 23.2 K in Nb3Ge and for high temperature superconductors at 137 K (-136 ° C) for Hg-1223. Most other exotic superconductors (heavy fermion superconductors, organic superconductors, fullerenes) have relatively low transition temperatures. The main progress, which lies in the higher transition temperatures, is that they are above the temperature of boiling nitrogen (77.4 K) and are therefore much easier to handle technologically. (Superconductivity and superfluidity)

Quantum Liquids and Quantum Solids

The quantum fluids3Hey and 4He does not become solid under its own vapor pressure up to the absolute zero point of the temperature and is therefore unique among all substances. The reason for this behavior lies in their large zero-point energies, which make macroscopic quantum effects visible. Below the λ line (2.19 K at normal pressure) 4He superfluid, a condition in which frictionless flow occurs.

At significantly lower temperatures, the rare isotope also becomes 3He superfluid. It also has interesting magnetic and orbital effects. In the superfluid phase, the liquids have a very high thermal conductivity, which by far exceeds that of metals, they show strange film flow behavior and unusual sound and transport properties. In rotating liquids, quantized flow tubes can form at certain speeds, and above a critical speed, friction sets in. With rotating superfluid 4He can test theories about vortex dynamics.

The explanation for this behavior is given in 4Hey the Bose-Einstein statistics with a Bose-Einstein condensation in the ground state. Liquid 3He, on the other hand, follows the Fermi-Dirac statistics, so that its low-temperature behavior differs from that of 4Hey makes a difference. 3He changes into the superfluid phase at normal pressure at 0.93 mK. It has three different sub-phases, which can be explained by the magnetic and non-magnetic triplet pairing that occurs here.

If a strong pressure of approx. 30 atm is applied, the barrier that forms the zero point energy is overcome, and solid phases also form in helium. The zero point movements are also particularly large in these quantum crystals. The consequence of these vibrations is an overlap of the wave functions with those of neighboring lattice sites and an associated increased quantum mechanical tunneling probability (tunnel effect), i.e. the atoms are delocalized quantum mechanically. The effect is in 3Hey most pronounced. It is decisive for the unusual nuclear magnetism of the isotope with order temperatures around 10-3 K, an unusually high temperature (oriented nuclei). Spin diffusion measurements with NMR and measurements of the magnetic susceptibility have confirmed this interpretation.

In 3He an order temperature with a transition into a solid phase with antiferromagnetic order is found at approx. 1 mK, which is also assigned to these many-body interactions.

Low dimensionality

If you reduce the dimensionality of a group of substances, e.g. in the case of carbon compounds of diamond (3-dimensional) via graphite (2-dimensional) and various 1-dimensional chain substances to fullerenes (0-dimensional), interactions come to light that are not visible in the higher-dimensional systems (see Fig. 2). In practice, these systems can often not be implemented, but you have to quasi-two-dimensional or quasi-one-dimensional speak, i.e. there are weak inter-chain or inter-layer couplings that falsify the pure character of the system.

The great strength - seen from the point of view of basic research - of these materials is that in some cases there are concrete predictions of the theory about the properties of these systems and that these theories, which can then also be transferred to higher-dimensional solids, can be verified on them. In addition, there are also a number of highly interesting application possibilities that can be addressed with low-dimensional systems. These include e.g. synthetic metalsthat could be used to develop lightweight, durable cables, electromagnetic shielding, field shielding in cables, antistatic sleeves, polymer batteries, solar cells, LEDs and much more.

Low-dimensional magnetism tries to derive the basic problems of three-dimensional systems from an understanding of one-dimensional systems. The Ising model and the Heisenberg model should be mentioned here in particular.

The low-dimensional materials also include the modern research areas of spin conductors and spin chains, the issues of which are linked to the field of high-temperature superconductors.

Other phenomena

This group includes effects that often only become noticeable at low temperatures, such as the Kondo effect, the Jahn-Teller effect, the Peierls instability, the Spin-Peierls transition and materials such as heavy fermions, as well as integer and the fractional quantum Hall effect.

Principles of refrigeration

The techniques used to generate low temperatures can be divided into three categories:

1) Range up to 1 K:

Cryogenic gases are liquefied for a temperature range of up to 1 K. A liquefied gas can be used to maintain constant temperatures between its triple pointTtp and the critical pointTkr to adjust. The temperature of a liquid gas left to itself is set at its boiling pointTS. a. On theirs boiling point these liquids represent a temperature bath of good constancy. The gases most frequently used for this purpose are 4Hey (Tkr = 5.2 K, TS. = 4.2 K) and N2 (Ttp = 63.2 K at 0.12 atm, Tkr = 126.1 K at 33.5 atm, TS. = 77.4 K). As from the phase diagram for 4He can be seen owns 4Hey no triple point. The temperature can be varied by changing the vapor pressure above the liquid by pumping on its surface. Since the flow of heat to such a cold bath cannot be completely suppressed, the liquid slowly boils away and must be topped up regularly if the low temperature is to be maintained. Gas liquefaction takes place either by utilizing Joule expansion by compression or by passing a gas at constant pressure through a cascade of cooler cooling stages. The lowest temperatures at which a liquid bath can be used in practice are 0.3 K (3Hey). The range of cooling temperatures that can be realized in this way shows gaps at 5-14 K and 44-55 K because there are no cryogases that cover this temperature range. These loopholes can be used with cyclical (steady, slow temperature drift) or non-cyclicalRefrigerating machines (constant temperature) are filled.

2) Range up to 2 mK:

With 3He-4He separation cooling can be achieved between 0.003 and 0.3 K. The method is based on the special properties of 3He-4He mixtures. Both Helium-I and Helium-II become superfluid, and the remaining normal liquid phase together with the Kapiza resistance limits the cooling that can be achieved. With Pomeranschuk cooling, the adiabatic compression of solid-liquid 3He mixtures, 0.002-0.05 K are achieved. Between 0.003 and 1 K, the adiabatic demagnetization of paramagnetic ions is used in solids.

3) Range up to nK:

With magnetic cooling, in which paramagnetic salts such as CMN are used, the change in entropy associated with the process of magnetic order is used for cooling. With core demagnetization, temperatures of 0.001-0.005 mK can be achieved after appropriate pre-cooling (see Fig. 3 for thermometers for different temperature ranges).

Safety aspects of refrigeration technology

Sources of danger

When dealing with cryogenic gases and refrigeration technology, there are three main sources of danger: physiological danger, physical danger and chemical danger.

To the physiological hazards include chilblains (gradually depending on the exposure to cold and blood circulation in the area; the body gives off approx. 5-8 W heat to its surroundings) and breathing problems. Even small amounts of cryogenic liquids can take up considerable volumes through evaporation (spontaneously evaporated 65 l of liquid hydrogen displace the oxygen content of approx. 150 m in 5 s3 Air to a dangerous level). Heavy noble gases have an anesthetic effect on the body. At concentrations above approx. 60 vol%, even oxygen can become a problem. Oxygen-rich atmospheres also encourage infections.

To the physical hazards count the Phase transitionsthat can take place during cooling. The complete evaporation of cryogenic liquids leads to considerable pressures (a container with 1 atm of liquid helium experiences 100 atm at 27 K and 1,000 atm at 270 K; for a half-filled container the value for 270 K is 400 atm.). If cryogenic liquids are spilled, explosive evaporation can occur because additional energy is supplied to the system from the atmosphere and the surfaces in contact.

The durability of materials also changes at low temperatures. Many materials become brittle when exposed to atomic hydrogen. It penetrates into them and forms molecular hydrogen in cavities, the accumulation of which leads to material fragility. When material surfaces are cooled below 82 K, an oxygen-rich air condensate forms on them (approx. 50% oxygen, 50% nitrogen).

To the chemical hazards count the flammability of substances and combustion reactions.

General precautions

When operating cryogenic systems, measures must be taken to prevent the formation of shock-sensitive mixtures - such as liquid oxygen and charcoal if liquid nitrogen is used in a cold trap or cryopump. Organic materials should not be cooled below 82 K in the presence of air. If glass systems are used, shielding should be planned, as glasses often contain organic condensate.

Overfilling of cryogenic liquids should be done through double-walled, evacuated transfer tubes. Frozen condensate (e.g. air) can cause blockages, which can lead to explosions. In many cases, inserting a copper rod on a regular basis can help. If a blockage cannot be removed, the container must be moved to a screened area, provided the pressure is not too high for transport.

Special precautions are also necessary when using flammable liquids, gases and vapors. All sources of ignition (open flames, hot surfaces, unsecured electrical connections) must be removed from the flow area. There is a tendency for all flammable fumes to fall to the floor.

Liquid fluorine, ozone and CO should never be handled in rooms that are also used by personnel. Liquid oxygen reacts with many substances that are typically used in a laboratory, and some materials even form explosive mixtures with it!

Inert gases can, in principle, be released directly into the atmosphere. It should be noted that they cannot accumulate in closed volumes. In the case of flammable gases, scarfing is usually preferred. Depending on the type of gas, by-products can arise which make it necessary to design an individual disposal. Due to the risk of fire, special care must be taken when disposing of oxygen vapors which are heavier than air and which can accumulate in clothing, for example.


The large number of Nobel Prizes that have been awarded in the field of low-temperature physics are impressive proof of the potential that is hidden in this area. The possible applications that may be realized in the future, e.g. from superconductivity and low-dimensional materials, can fundamentally change the world as we know it today. With the reaching of ever lower temperatures, one can finally see the maps better and better from the point of view of basic research into nature.

Low temperature physics 1: Some fixed points of the ITS-90 temperature standard (Ttp: Triple points).

Low temperature physics 2: Density of states n(E.) at the tape edge in 1D, 2D and 3D electronic systems.

Low temperature physics 3: Thermometers of different temperature ranges.