Superfluid phase

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]. 

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. 

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. 

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. 

Table 2.2 clearly shows the strong differences between the two quantum liquids . It is worth noting that both isotopes have very low boiling and critical temperatures and a low density (the molar volume is more than the double than that corresponding to a classic liquid). Figure 2.4 shows the p-T phase diagrams besides the presence of a superfluid phases it is to be noted for both isotopes the missing of a triple point. 

Fig. 2.9. Specific heat of liquid 4He at temperature closed to its normal superfluid phase transition. 

When temperature decreases, a second transition to a distinct superfluid phase B is observed. The latter is first-order transition at T — 1.948 mK at the melting pressure. 

D. Vollhard, P. Woelfle The Superfluid Phases of Helium-3, Taylor Francis, London (1990)... 

Fig. 5.5. Per cent of remaining liquid 4He after pumping the bath down to the temperature T. Note the step around 2.2 K due to the transition to the superfluid phase with a peak in the specific heat... 

Figure 6.1 shows the x-T phase diagram of the 3He-4He mixture at saturated vapour pressure. Some important characteristics of these mixture are to be noted. In the dilution of 4He with 3 He, the temperature of the superfluid phase transition of the former is lowered and the transition disappears for 3He concentration above 67.5%. At such concentration... 

Superelectrons, 23 819-820 Superfibers, 24 624 Superficial filtering velocity, 26 710 Superficial velocity, 11 766 Superfilling, 9 774 Superfinishing stones, 1 19 Superflex catalytic cracking butylenes manufacture, 4 417 Superfluid helium, 17 353-354 Superfluid phases, of helium-3,17 354-355 Superfluids, 17 352-354 Superfractionation, 23 333-334 Superfund Amendments and... 

The commonly accepted pulsar model is a neutron star of about one solar mass and a radius of the order of ten kilometers. A neutron star consists of a crust, which is about 1 km thick, and a high-density core. In the crust free neutrons and electrons coexist with a lattice of nuclei. The star s core consists mainly of neutrons and a few percents of protons and electrons. The central part of the core may contain some exotic states of matter, such as quark matter or a pion condensate. Inner parts of a neutron star cool up to temperatures 108iT in a few days after the star is formed. These temperatures are less than the critical temperatures Tc for the superfluid phase transitions of neutrons and protons. Thus, the neutrons in the star s crust and the core from a superfluid, while the protons in the core form a superconductor. The rotation of a neutron superfluid is achieved by means of an array of quantized vortices, each carrying a quantum of vorticity... 

The inclusion of both three and four-particle correlations in nuclear matter allows not only to describe the abundances oft, h, a but also their influence on the equation of state and phase transitions. In contrast to the mean-field treatment of the superfluid phase, also higher-order correlations will arise in the quantum condensate. 

To complete our discussion of non-relativistic superfluids let us briefly mention some of the alternatives to the LOFF and DFS phases. One possibility is that the system prefers a phase separation of the superconducting and normal phases in real space, such that the superconducting phase contains particles with the same chemical potentials, i.e. is symmetric, while the normal phase remains asymmetric [20, 21],... 

Finally we d like to give a comment about fluctuations. In this talk we have completely discarded fluctuations and been only concerned with the mean-held. It would be reasonable to study the phase transition, at least qualitatively. However, we know some fluctuations or correlations between relevant operators should have some effects even before the phase transitions. In particular the axial and magnetic suscephbilihes in normal quark matter would be interesting they might have important consequence,e.g., for quark-quark pairing correlation as in 3 He superfluidity [17]. 

Von Bavel et al. [55] have developed a solid phase carbon trap (PX-21 active carbon) for the simultaneous determination of polychlorodibenzo-p-dioxins and polychlorodibenzofurans also polychlorobiphenyls and chlorinated insecticides in soils using superfluid extraction liquid chromatography for the final determination. Supercritical fluid extraction with carbon dioxide has been applied to the determination of dioxins in soil [114],... 

Figure 7.4 illustrates the phase diagram of the 4He isotope in the low-temperature condensation region. The thermodynamic properties of 4He are fundamentally distinct from those of the trace isotope 3He, and the two isotopes spontaneously phase-separate near IK. Both isotopes exhibit the spectacular phenomenon of superfluidity, the near-vanishing of viscosity and frictional resistance to flow. The strong dependence on fermionic (3He) or bosonic (4He) character and bizarre hydrodynamic properties are manifestations of the quantum fluid nature of both species. 3He is not discussed further here. 

Figure 7.4 Phase diagram of 4He, showing the solid, gas, and two liquid phases (He-I, superfluid He-II), the A-line (dashed) of liquid-liquid transitions (upper terminus 1.76K, 29.8 atm lower terminus 2.17K, 0.0497 atm), and the gas-liquid critical point (circle-x 5.20K, 2.264 atm).

From the slopes of the phase boundaries, one can judge [using the Clapeyron mnemonic (7.32)] that pSoiid > Pi, Pii (i.e., a high-pressure ice cube of frozen helium will sink in either He-I or He-II) and that pn> Pi (i.e., the low-T He-II superfluid floats on the high-T He-I normal fluid). One can also judge from its placement at lower T that He-II is more highly ordered than He-I (5n < Si), despite its superfluid proclivities. 

As we go to press, reports are coming in that superfluid water might exist in other words, water may also have two liquid phases. 

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