Low Temperatures

(also cryogenic temperatures), usually, temperatures below the boiling point of liquid air (about 80°K). Such temperatures are customarily given in degrees above absolute zero (—273.15°C, or 0°K) and expressed in kelvins (K), or degrees Kelvin (°K). In 1971, the Thirteenth Congress of the International Institute of Cryogenics accepted a recommendation to define temperatures below 120°K as cryogenic temperatures. However, the recommendation has not yet been generally accepted. Temperatures below about 80°K are dealt with in this article.

Production. Liquefied gases are customarily used to produce and maintain low temperatures. The constant temperature T_N of the normal boiling point of the coolant is maintained with adequate accuracy in a Dewar flask containing a liquefied gas that vaporizes at atmospheric pressure. The following coolants (liquefied gases) are used in practice: air (T_N = 80°K), nitrogen (T_N = 77.4°K), neon (T_N = 27.1°K), hydrogen (T_N = 20.4°K), and helium (T_N = 4.2°K). Liquid gases are produced in special liquefaction units, in which highly compressed gas is cooled and condenses upon expansion. Liquefied gases may be stored for prolonged periods of time in Dewar vessels and cryostats with good thermal insulation (powdered and porous thermal insulators, such as foam plastics).

The pressure above the liquid may be reduced—and its boiling point lowered—by pumping off the vaporizing gas from the sealed vessel. Thus, the temperature may be controlled by varying the vapor pressure above the boiling liquid. In this case, natural or forced convection and good thermal conductivity of the coolant ensure uniformity of temperature throughout the volume of the liquid. This makes it possible to cover a wide interval of temperatures by using liquid nitrogen from 77° to 63°K, liquid neon from 27° to 24°K, liquid hydrogen from 20° to 14°K, and liquid helium from 4.2° to 1°K. The use of the evacuation method to attain temperatures below the triple points of the respective coolants is impossible. At lower temperatures the material solidifies and loses its properties as a coolant. Intermediate temperatures, which are between the intervals mentioned above, are attained in special cryostats. The object being cooled is thermally insulated from the coolant—for example, by placing it in a vacuum chamber immersed in a liquefied gas. A small controlled evolution of heat in the chamber (it contains an electric heater) causes the temperature of the object under study to rise with respect to the boiling point of the coolant; this temperature may be maintained with a high degree of stability at the required level. In another method of achieving intermediate temperatures, the sample to be cooled is placed over the surface of the evaporating coolant, and the rate of evaporation of the liquid is controlled by a heater. In this case, heat is removed from the object under study by the flow of gas being pumped off. A cooling method is also used in which the cold gas produced during the evaporation of a coolant is passed through a heat exchanger (usually a copper tube shaped into a spiral, or a porous copper block), which is in thermal contact with the object being cooled.

At atmospheric pressure, helium remains liquid down to absolute zero. However, evacuation of ⁴He vapor usually does not permit attainment of temperatures substantially below 1°K, even using very powerful pumps, because of the superfluidity of ⁴He and the extremely low pressure of the saturated ⁴He vapor. For this reason, temperatures of the order of tenths of a kelvin are produced using the isotope ³He (T_N = 3.2°K), which does not exhibit superfluidity at these temperatures. The temperature of the liquid may be lowered to 0.3°K by evacuation of the evaporating ³He.

The temperature region below 0.3°K is usually called the superlow temperature region. Various methods are used to attain such temperatures. Temperatures of the order of 10^-3°K are produced by means of the adiabatic demagnetization method (magnetic cooling), which uses a paramagnetic salt as the cooling system. Temperatures of the order of 10 ^-6°K have been attained using the paramagnetism of atomic nuclei. The main problem area in the adiabatic demagnetization method (which is also the case in all other methods for the generation of low temperatures) is the achievement of a good thermal contact between the cooling system and the object being cooled. This is particularly difficult to attain in a system using atomic nuclei. The aggregate of atomic nuclei may be cooled to superlow temperatures, but it is not yet possible to achieve the same degree of cooling in the substance containing the nuclei.

A more convenient method, the dissolution of liquid ³He in liquid ⁴He, is widely used for generating temperatures of the order of several thousandths of a degree Kelvin (millikelvins). The apparatus used for this purpose is called a dilution refrigerator (Figure 1). The operation of a refrigerator of this type is based on the fact that ³He retains a finite solubility (about 6 percent) in liquid ⁴He down to absolute zero. For this reason, ³He atoms will pass into solution on contact of almost pure liquid ³He with a dilute solution of ³He in ⁴He. This process will be accompanied by the absorption of the heat of solution, and the temperature of the solution will decrease. Dissolution occurs at one location in the apparatus (in the solution chamber), and the removal of ³He atoms from the solution by evacuation is performed in a different location (vaporization chamber). The continuous circulation of ³He, which is achieved by a system of pumps and heat exchangers, makes it possible to maintain temperatures of the order of 10–30 millikelvins in the solution chamber for unlimited periods of time. The cooling output of such refrigerators is determined

Figure 1. (a) Diagram of operation of a dilution refrigerator based on dissolution of ³He in ⁴He: ³He vapor is pumped out by the diffusion pump (1) and conveyed by the rotary pump (2) into the solution chamber (8) after preliminary cooling in the liquid nitrogen bath (3) and the helium bath (4). The ³He vapor is condensed in front of the capillary (5). Liquid ³He, which is cooled further in the heat exchanger (7), passes into chamber (8). From there, atoms diffuse through the solution of ³He in ⁴He into the vaporization chamber (6), and the cycle is repeated. Legend: (T) temperature, (p) pressure, (ν) concentration of ³He, (Θ) capacity of the pumping system, (b) Main low-temperature part of the dilution refrigerator: (1) and (2) pipelines for pumping out ³He and ⁴He, (3) vaporization chamber, (4) dissolution chamber, (5) heat-exchange units.

by the capacity of the pumps, and the minimum attainable temperature (several millikelvins) is determined by the efficiency of heat exchangers and by the elimination of parasitic heat flux. Helium ³He may be cooled even more by using the Pomeranchuk effect. Liquid ³He solidifies at pressures above 30 bars. An increase in pressure in the temperature region near 0.3°K (in the range up to 34 bars) is accompanied by absorption of heat and a decrease in the temperature of the equilibrium mixture of the liquid and solid phases (solidification is accompanied by heat absorption). This method was used to generate temperatures of the order of 1–2 millikelvins.

Measurement. The primary thermometric device for determination of thermodynamic temperatures down to 1°K is the gas thermometer. Other types of primary thermometer are the acoustic and noise thermometers, whose operation is based on the relationship of the thermodynamic temperature to the speed of sound in a gas and to the intensity of thermal voltage fluctuations in an electric circuit, respectively. Primary precision thermometers are mainly used for the determination of the temperatures of easily reproducible phase equilibriums in one-component systems (called the reference points), which are used as the reference temperatures of the International Practical Temperature Scale (ITPS-68). The temperature reference points in the low-temperature region are as follows: the triple point of equilibrium hydrogen (13.8°K), the equilibrium point between the liquid and gaseous phases of equilibrium hydrogen at 25/76 of a normal atmosphere (17.042°K), the boiling point T_N of equilibrium hydrogen (20.28°K), T_N of neon (27.102°K), the triple point of oxygen (54.36°K), and T_N of oxygen (90.188°K).

To reproduce any value of temperature between 630.74°C and 13.81°;K with an accuracy of the order of 0.001°K, a platinum resistance thermometer is specified by ITPS-68. Temperatures determined according to ITPS-68 differ in the low-temperature range by no more than 0.01°K from the true value. The ITPS-68 scale has not yet been extended below 13.8°K because of the lack of a secondary thermometer for this range of low temperatures that would have the same sensitivity, precision, and reproducibility of readings as the platinum resistance thermometer at higher temperatures. Low-temperature thermometry in the range 0.3°-5.2°K is based on the relationship between the pressure P_s, of the saturated helium vapor and the temperature T, which is established by the use of the gas thermometer. This relationship was accepted as the basis for an international temperature scale in the ranges from 1.5° to 5.2°K (⁴He scale, 1958) and 0.3° to 3.3°K (³He scale, 1962). The dependence P_S ((T) in these temperature ranges cannot be represented by a simple analytical formula and is therefore tabulated; the tabular data ensure precise determination of temperature that is accurate down to 0.00°K.

Practical thermometry in the low-temperature region uses mainly resistance thermometers (copper down to 20°K and carbon thermometers in the range of hydrogen and helium temperatures, down to 1 millikelvin; the resistance of the latter thermometers increases with decreasing temperature). Resistance thermometers fabricated from pure germanium are also used. High stability and adequate sensitivity make them convenient instruments for temperature measurements below 100°K.

There are a number of other devices that are sensitive to changes in temperature and may be used as secondary thermometers for measurements in the low-temperature range: thermocouples, thermistors, semiconductor diodes, and transducers made of superconducting alloys (in the ranges of helium and hydrogen temperatures).

Gas thermometers are virtually useless below 1°K. Magnetic and nuclear methods are used for temperature determination in this range. Magnetic thermometry uses the concept of the magnetic temperature T*, which is determined from measurements of the magnetic susceptibility X of a paramagnetic salt. Curie’s law states that ξ~ one/T* at sufficiently high temperatures. The law is also valid in the helium temperature range for many salts. The magnetic temperature is determined, as a quantity proportional to the inverse of the susceptibility, by extrapolating the Curie relationship into the superlow temperature range. To obtain accurate results, various secondary factors, such as the anisotropy of magnetic susceptibility and the geometric shape of the sample, must be taken into account. The temperature range in which the magnetic temperature scale is sufficiently close to the thermodynamic scale depends on the specific salt. The material most widely used for the measurement of superlow temperatures down to 6 millikelvins is cerium-magnesium nitrate, for which the discrepancy between the scales is less than 0.1 millikelvin at the above temperature.

The nuclear methods of measurement are based on the principle of quantum statistical physics, according to which the equilibrium population of discrete energy levels of a system depends on the temperature. One such method uses measurement of the intensity of the nuclear magnetic resonance lines, which is determined by differences in the population of the nuclear magnetic moment levels in a magnetic field. Another method determines the temperature-dependent ratio of the intensities of components arising from the splitting of the resonance gamma radiation (the Mössbauer effect) in the internal magnetic field of a ferromagnet.

A method analogous to thermometry based on the saturated vapor pressure measurements in the region of superlow temperatures is the determination of temperatures in the range from 30 to 100 millikelvins according to the osmotic pressure of ³He in a ³He-⁴He mixture. The absolute accuracy of measurement is about 2 millikelvins; the sensitivity of the osmotic thermometer is of the order of 0.01 millikelvin.

Low-temperature physics. The use of low temperatures has played a decisive role in the study of the condensed state. A particularly large number of new and fundamental facts and relationships was discovered during studies of various materials at helium temperatures. This led to the development of a special branch, low-temperature physics. A decrease in temperature leads to peculiarities in the properties of materials that are related to the existence of interactions that at normal temperatures are suppressed by the strong thermal motion of atoms. New relationships discovered at low temperatures may be logically explained only on the basis of quantum mechanics. In particular, the uncertainty principle in quantum mechanics and the existence of zero-point vibrations at absolute zero, which arises from it, explain the fact that helium remains liquid down to 0°K.

Quantum relationships are most strongly manifested at low temperatures in the phenomena of superfluidity and superconductivity. The study of these phenomena is an important area of low-temperature physics. Beginning in the 1960’s, a number of interesting effects were discovered in which the spatial coherence of wave functions over macroscopic distances is of special importance (superconductive tunneling and the Josephson effect). Of great importance is the study of the properties of liquid helium He, which is an example of a neutral Fermi fluid. It is now known that ³He undergoes a phase transformation at about 3 millikelvins and 34 bars, accompanied by a significant decrease in viscosity (it passes into the superfluid state).

The development of low-temperature physics has to a considerable degree promoted the development of quantum solid-state theory, particularly the general theoretical framework, according to which the state of matter at low temperatures may be regarded as a superposition of the ideally ordered state, corresponding to 0°K, and a gas of elementary excitations (quasiparticles). The introduction of various quasiparticles (phonons, holes, magnons, and so on) makes possible description of the variegated nature of the properties of materials at low temperatures. The thermodynamic properties of a gas of elementary excitations define the observable macroscopic equilibrium properties of matter. The methods of statistical physics, in turn, permit prediction of the properties of a gas of excitations based on the nature of the relationship between the momentum and energy of quasiparticles (dispersion law). The study of the heat capacity, thermal conductivity, and other thermal and kinetic properties of solids at low temperatures provides an opportunity to obtain the dispersion law for phonons and other quasiparticles. The temperature dependence of the magnetization intensity of ferromagnets and antiferromagnets may be explained within the framework of the dispersion law for magnons (spin waves).

The study of the dispersion law for electrons in metals is another important branch of low-temperature physics. The weakening of thermal lattice vibrations and the use of pure materials made possible the elucidation of the special features in the behavior of electrons in metals (galvanomagnetic phenomena, the de Haas-van Alphen effect, and cyclotron resonance). The use of low temperatures plays an important role in studies of various types of magnetic resonance.

Cooling to superlow temperatures is used in nuclear physics to generate targets and sources in studies of the anisotropy of scattering of elementary particles. For example, such sources have made possible the performance of decisive experiments concerning the problem of the nonconservation of parity. Low temperatures are used in studies of semiconductors, optical properties of molecular crystals, and so on.

Technical applications. One of the principal areas of application of low temperatures in technology is the separation of gases. Production of oxygen and nitrogen in large quantities is based on the liquefaction of air, with subsequent separation in rectification columns to give nitrogen and oxygen. The uses of liquid oxygen and nitrogen are many. In particular, liquid oxygen is used as an oxidizer in rocket propellants. Low temperatures are also used in the production of high vacuum by the method of adsorption on activated carbon or zeolite (adsorption pump) or by direct condensation on the metal walls of a vessel containing a coolant (cryopump; Figure 2). High vacuum and cooling to low temperatures make possible imitation of conditions characteristic of outer space and the testing of materials and instruments under these conditions. Cooling to the temperatures of liquid air or nitrogen has found important applications in medicine. The use of instruments capable of producing local freezing of tissues makes possible treatment of brain tumors and urological and other diseases. There is also the possibility of long-term storage of living tissue at low temperatures.

Figure 2. Diagram showing operation of a cryopump: the heat shields (2) and (3), which are at the temperature of liquid nitrogen (77°K), are located in the housing (1). The shields protect the reservoir (4), containing liquid helium, from external thermal influences. Helium vapor is pumped out through a pressure-regulation system (5) by a pump (6). As a result, the temperature in the reservoir (4) is decreased, and the molecules of gas in the working volume are frozen out. (7) Pump for preliminary evacuation, (8) and (9) sensors of the levels of liquid nitrogen and helium, (10) automatic electronic regulation and control system, (11) external envelope, which is heated to prevent the device from becoming covered with frost during operation.

Another trend in the technical application of low temperatures is associated with the uses of superconductivity. In this case, the most important role is played by the generation of strong magnetic fields (of the order of 10³ kilooersteds), which are required for particle accelerators, tracking instruments (such as bubble chambers), magnetohydrodynamic generators, and a great variety of laboratory studies. The phenomenon of superconductive tunneling is the basis for the development of superconductive quantum interference devices, which are capable of measuring extremely low voltages (of the order of 10^-4 V), as well as recording very small variations of magnetic fields (of the order of 10 ^-11 oersted). Low temperatures are also of great importance in quantum electronics.