Helium lambda point

Lipa J A, Swanson D R, Nissen J A, Chui TCP and Israelsson U E 1996 Heat capacity and thermal relaxation of bulk helium very near the lambda point Phys. Rev. Lett. 76 944-7... 

Another unique phenomenon exhibited by Hquid helium II is the Rollin film (62). AH surfaces below the lambda point temperature that are coimected to a helium II bath are covered with a very thin (several hundredths llm) mobile film of helium II. For example, if a container is dipped into a helium II bath, fiUed, and then raised above the bath, a film of Hquid helium flows up the inner waH of the container, over the Hp, down the outer waH, and drips from the bottom of the suspended container back into the helium II bath. SinHlady, if the empty container is partiaHy submerged in the helium II bath with its Hp above the surface, the helium film flows up the outer waH of the container, over its Hp, and into the container. This process continues until the level of Hquid in the partiaHy submerged container reaches that of the helium II bath. 

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. 

MSE.12. 1. Prigogine et J. Philippot, Theorie moleculaire du point lambda de I helium liquide, (Molecular theory of the lambda point of liquid helium), Physica 18, 729—748 (1952). 

MSE.14. I. Prigogine et J. Phihppot, Sur la theorie mol ulaire de I Helium hquide, IV. Le caractere cooperatif de la transition du point lambda (Molecular theory of hquid helium, IV. The cooperative character of the lambda point transition), Physica 19, 508—516 (1953). 

Ehrenfest s concept of the discontinuities at the transition point was that the discontinuities were finite, similar to the discontinuities in the entropy and volume for first-order transitions. Only one second-order transition, that of superconductors in zero magnetic field, has been found which is of this type. The others, such as the transition between liquid helium-I and liquid helium-II, the Curie point, the order-disorder transition in some alloys, and transition in certain crystals due to rotational phenomena all have discontinuities that are large and may be infinite. Such discontinuities are particularly evident in the behavior of the heat capacity at constant pressure in the region of the transition temperature. The curve of the heat capacity as a function of the temperature has the general form of the Greek letter lambda and, hence, the points are called lambda points. Except for liquid helium, the effect of pressure on the transition temperature is very small. The behavior of systems at these second-order transitions is not completely known, and further thermodynamic treatment must be based on molecular and statistical concepts. These concepts are beyond the scope of this book, and no further discussion of second-order transitions is given. 

Superfluid. Liquid helium (more precisely the 2He4 isotope) has a "lambda point" transition temperature of 2.17 K, below which it becomes a superfluid ("Helium-II"). This superfluid, or "quantum liquid," stays liquid down to 0 K, has zero viscosity, and has transport properties that are dominated by quantized vortices thus 2He4 never freezes at lbar. Above 25.2 bar the superfluid state ceases, and 2He4 can then freeze at 1K. The other natural helium isotope, 2He3, boils at 3.19 K and becomes a superfluid only below 0.002491 K. 

At even lower temperatures, some unusual properties of matter are displayed. Consequently, new experimental and theoretical methods are being created to explore and describe chemistry in these regimes. In order to account for zero-point energy effects and tunneling in simulations, Voth and coworkers developed a quantum molecular dynamics method that they applied to dynamics in solid hydrogen. In liquid helium, superfluidity is displayed in He below its lambda point phase transition at 2.17 K. In the superfluid state, helium s thermal conductivity dramatically increases to 1000 times that of copper, and its bulk viscosity drops effectively to zero. Apkarian and coworkers have recently demonstrated the disappearance of viscosity in superfluid helium on a molecular scale by monitoring the damped oscillations of a 10 A bubble as a function of temperature. These unique properties make superfluid helium an interesting host for chemical dynamics. 

Standard liquid helium cryostats can be used at any temperature above the lambda point of helium, 1.5K, and specialised types of cryostat routinely operate as low as 0.05K. For most samples of chemical interest, there is no practical difference between spectra recorded at 4.2K and at 20K (unless phase transitions occur), thus the additional expense and complexity of very low temperatures cannot be justified. 

The following data were obtained by a critical evaluation of all existing experimental measurements on liquid helium, using a fitting procedure described in the reference. All values refer to liquid helium at saturated vapor pressure temperatures are on the ITS-90 scale. Several properties show a singularity at the lambda point (2.1768 K). 

FIGURE 4.13 The heat capacity of liquid helium at the lambda point temperarnre. The lambda point temperature depends on pressure, with values from 1.763 K at 3.01 MPa to 2.172 K at 5.04 kPa. 

Helium-4 is by far the more common of the two isotopes. Ordinary helium gas contains about 1.3 x 10 " percent helium-3, so that when we speak of helium or liquid helium, we normally are referring to helium-4 (molecular weight 4.0026). Liquid helium-4 has a normal boiling point of 4.224 K and a density at the normal boiling point of 124.96 kg/m, or about one-eighth that of water. Liquid helium has no solidification point at normal atmospheric pressure. In fact, liquid helium does not solidify under its own vapor pressure even if the temperature is reduced to absolute zero. Saturated liquid helium must be compressed to a pressure of 2.53 MPa before it will solidify. Liquid helium-4 is odorless and colorless and somewhat difficult to see in a container, since its index of refraction is so near that of the gas ( = 1.02 for liquid He). The heat of vaporization of liquid He at the normal boiling point is 20.73 kJ/kg, which is only 1/110 that of water. Table 2.7, prepared by McCarty, presents densities for helium-4 at the critical point, normal boiling point, lower lambda point, and upper lambda point. 

Stance see Fig. 2.2. The most striking properties, however, are those exhibited by liquid helium at temperatures below 2.17 K. As the liquid is cooled below this temperature, instead of solidifying, it changes to a new liquid phase. The phase diagram of helium thus takes on an additional transition line separating the two phases into liquid He I at temperatures above the line and liquid He II at lower temperatures. The low-temperature liquid phase, called liquid helium II, has properties exhibited by no other liquid. Helium II expands on cooling its conductivity for heat is enormous and neither its heat conduction nor viscosity obeys normal rules (see below). The phase transition between the two liquid phases is identified as the lambda line, and the intersection of the latter with the vapor-pressure curve is known as the lambda point. The transition between the two forms of liquid helium, I and II, is called the X... 

Helium II is often referred to as a superfluid. Immediately below the lambda point, the flow of liquid through narrow slits or channels becomes very rapid. Figure 2.4 shows the viscosity of liquid helium when measured by an oscillating disk. Helium I has a viscosity of about 3 x 10 Pa s, whereas this experiment indicates that Hell has a viscosity of about 10 Pas at... 

To resolve the viscosity paradox, assume that at the lambda point all the fluid is normal fluid with a normal viscosity, and at absolute zero all the fluid is superfluid with zero viscosity. In the thin channel experiment described above, only the superfluid atoms, which have zero entropy and do not interact, can flow through the slit. On the other hand, the oscillating disk is damped by the normal fluid and thus accounts for the shape of the viscosity curve below the lambda point. The flow of helium II through very thin channels is accompanied by two very interesting thermal effects called the thermomechanical effect and the mechanocaloric effect. ... 

Sound can be propagated in liquid helium II by at least three mechanisms. First, or ordinary, sound is the transfer of energy by a pressure wave. Second sound is a temperature wave caused by out-of-phase oscillations of superfluid and normal components of the helium II. The velocity of second sound is zero at the lambda point and rises to a value of about 20 m/s between 1 and 2 K. 

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). 

The mysteries of the helium phase diagram further deepen at the strange A-line that divides the two liquid phases. In certain respects, this coexistence curve (dashed line) exhibits characteristics of a line of critical points, with divergences of heat capacity and other properties that are normally associated with critical-point limits (so-called second-order transitions, in Ehrenfest s classification). Sidebar 7.5 explains some aspects of the Ehrenfest classification of phase transitions and the distinctive features of A-transitions (such as the characteristic lambda-shaped heat-capacity curve that gives the transition its name) that defy classification as either first-order or second-order. Such anomalies suggest that microscopic understanding of phase behavior remains woefully incomplete, even for the simplest imaginable atomic components. 

The triple-point temperature of air is the solidification temperature of the liquid (see Reference 2 for details). The boiling-point temperature for air is the bubble-point temperature (i.e., the temperature at which boiling begins as the pressure of the liquid is lowered). The dew-point (vapor) properties of air at 101.325 kPa are calculated at a temperature of 81.72 K the liquid and vapor properties of these two state points are not in equilibrium. The triple-point properties of helium are given at the temperature of the lambda line (change from normal-to-superfluid helium) for the saturated-liquid state. 

---