Superfluids

Helium provides an interesting variant of normal liquid behaviour. When 4He is cooled at atmospheric pressure, the gas liquefies to He I at 

On further cooling a second-order transition to He II, another liquid form, occurs at 2.2 K. This form persists down to as close to 0 K as can be attained. To form solid helium, a pressure of 25 atm is required at 

The mass of the 4He atom is low and the intermolecular interactions are very weak. This means that the motion of the helium atoms is unusually large, too large in fact for a solid-like structure to persist 

The density of He I at the boiling point at 1 atm is 125 kg m 3 and the viscosity is 3 x 10 6 Pa s. As we would anticipate, cooling increases the viscosity until He II is formed. Cooling this form reduces the viscosity so that close to 0 K a liquid with zero viscosity is produced. The vibrational motion of the helium atoms is about the same or a little larger than the mean interatomic spacing and the flow properties cannot be considered in classical terms. Only a quantum mechanical description is satisfactory. We can consider this condition to give the limit of De-+ 0 because we have difficulty in defining a relaxation when we have the positional uncertainty for the structural components. 

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Grebenev S, Toennies J P and Vilesov A F 1998 Superfluidity within a small helium-4 cluster the microscopic andronikashvili experiment Soienoe 279 2083... 

Jasny J, Sepiol J, Irngartinger T, Traber M, Renn A and Wild U P 1996 Fluorescence microscopy in superfluid helium single molecule imaging Rev. Sc/. Instrum. 67 1425-30... 

Obviously 9 =0 corresponds to the SmA phase. This transition is analogous to the nonnal-superfluid transition in liquid helium and the critical behaviour is described by the AT model. Further details can be found elsewhere [18, 19 and 20]. 

Besides being used as a tool for scientific research, siUca aerogels can be the cause for new scientific phenomena. For example, the long-range correlations of the disorder in siUca aerogels are beheved to be responsible for the intriguing observations of the superfluid transitions in He and He and on the ordering of He— He mixtures (75). 

There is assumed to be no interaction between the superfluid and normal components, thus the superfluid component can diffuse very rapidly to a heat source where it absorbs energy by reverting to the normal state. It thereby produces the very high effective thermal conductivity observed in helium II. 

When the superfluid component flows through a capillary connecting two reservoirs, the concentration of the superfluid component in the source reservoir decreases, and that in the receiving reservoir increases. When both reservoirs are thermally isolated, the temperature of the source reservoir increases and that of the receiving reservoir decreases. This behavior is consistent with the postulated relationship between superfluid component concentration and temperature. The converse effect, which maybe thought of as the osmotic pressure of the superfluid component, also exists. If a reservoir of helium II held at constant temperature is coimected by a fine capillary to another reservoir held at a higher temperature, the helium II flows from the cooler reservoir to the warmer one. A popular demonstration of this effect is the fountain experiment (55). 

Superfluid helium can pass easily through openings so small that they caimot be detected by conventional leak detection methods. Such leaks, permeable only to helium II, are called supedeaks. They can be a source of fmstrating difficulties in the constmction of apparatus for use with helium II. 

Fig. 3. Phase diagram for helium-3 where A, B, and A1 represent the three superfluid phases and PCP is the polycritical poiat. The dashed lines iadicate the...

Below about 0.5 K, the interactions between He and He in the superfluid Hquid phase becomes very small, and in many ways the He component behaves as a mechanical vacuum to the diffusional motion of He atoms. If He is added to the normal phase or removed from the superfluid phase, equiHbrium is restored by the transfer of He from a concentrated phase to a dilute phase. The effective He density is thereby decreased producing a heat-absorbing expansion analogous to the evaporation of He. The He density in the superfluid phase, and hence its mass-transfer rate, is much greater than that in He vapor at these low temperatures. Thus, the pseudoevaporative cooling effect can be sustained at practical rates down to very low temperatures in heHum-dilution refrigerators (72). 

Helium Purification and Liquefaction. HeHum, which is the lowest-boiling gas, has only 1 degree K difference between its normal boiling point (4.2 K) and its critical temperature (5.2 K), and has no classical triple point (26,27). It exhibits a phase transition at its lambda line (miming from 2.18 K at 5.03 kPa (0.73 psia) to 1.76 K at 3.01 MPa (437 psia)) below which it exhibits superfluid properties (27). 

Liquid helium-4 can exist in two different liquid phases liquid helium I, the normal liquid, and liquid helium II, the superfluid, since under certain conditions the latter fluid ac4s as if it had no viscosity. The phase transition between the two hquid phases is identified as the lambda line and where this transition intersects the vapor-pressure curve is designated as the lambda point. Thus, there is no triple point for this fluia as for other fluids. In fact, sohd helium can only exist under a pressure of 2.5 MPa or more. 

Specific heat measurements [1] of " He layers on Fe203 have shown the dependency of the onset of superfluidity on the width of the film thickness. 

Many interesting quantum effects appear at low temperatures due to the effect of quantum statistics. Very interesting PIMC studies of such effects have been done for structural phase transitions in adsorbed " He and He layers [90-91] and for the superfluidity of H2 layers [92]. For studies of related systems and additional information see Sec. IV D 2. 

Permutations of this type have to be considered in PIMC simulations if a full account of the quantum statistics is intended in the study and required by the physical effect under consideration, which means that additional permutation moves have to be done in the simulation. In this way quantum statistics has been included in a few PIMC simulations, in particular for the study of superfluidity in He [287] and in adsorbed H2 layers [92], for the Bose-Einstein condensation of hard spheres [269], and for the analysis of... 

We have remarked that a temperature of zero on the absolute temperature scale would correspond to the absence of all motion. The kinetic energy would become zero. Very interesting phenomena occur at temperatures near 0°K (the superconductivity of many metals and the superfluidity of liquid helium are two examples). Hence, scientists are extremely interested in methods of reaching temperatures as close to absolute zero as possible. Two low temperature coolants commonly used are liquid hydrogen (which boils at 20°K) and liquid helium (which boils at 4°K). Helium, under reduced pressure, boils at even lower temperatures and provides a means of reaching temperatures near 1°K. More exotic techniques have been developed to produce still lower temperatures (as low as 0.001°K) but even thermometry becomes a severe problem at such temperatures. 

Sun, data on, 119, 444, 447 Superconductivity, 58 Superfluidity, 58 Symbols, chemical, 30 not from common names, table, 31 System, 70... 

Helium is an interesting example of the application of the Third Law. At low temperatures, normal liquid helium converts to a superfluid with zero viscosity. This superfluid persists to 0 Kelvin without solidifying. Figure 4.12 shows how the entropy of He changes with temperature. The conversion from normal to superfluid occurs at what is known as the A transition temperature. Figure 4.12 indicates that at 0 Kelvin, superfluid He with zero viscosity has zero entropy, a condition that is hard to imagine.v... 

The phase diagram for helium is shown here, (a) What is the maximum temperature at which superfluid helium-II can exist (b) What is the minimum pressure at which solid helium can exist (c) What is the normal boiling point of helium-I ... 

The noble gases are all found naturally as unreactive monatomic a sc Helium has two liquid phases the lower-temperature liquid pha.<< xhibits superfluidity. 

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