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. 

Thermomolecular pressure difference is present in vapour pressure with any gas. In the case of 4He, additional problems occur above the lambda point (see Section 2.2.4.1), the result is that the temperature above the surface may be a few millikelvin lower than that... 

Household appliances can also benefit from improvements in other areas. For example, oxygen sensors that measure the 02-concentations in exhaust gas have been developed that combine a Nernst type lambda gauge (which can measure only the ( -concentration at one lambda-point) with an amperometric 02-pumping cell. 

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. 

The Ehrenfest17 classification of phase transitions (first-order, second-order, and lambda point) assumes that at a first-order phase transition temperature there are finite changes AV 0, Aft 0, AS VO, and ACp VO, but hi,lower t = hi,higher t and changes in slope of the chemical potential /i, with respect to temperature (in other words (d ijdT)lowerT V ((9/i,7i9T)higherT). At a second-order phase transition AV = 0, Aft = 0, AS = 0, and ACp = 0, but there are discontinuous slopes in (dV/dT), (dH/<)T), (OS / <)T), a saddle point in and a discontinuity in Cp. A lambda point exhibits a delta-function discontinuity in Cp. 

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. 

To reach temperatures below 4.2 K, one can partially evacuate a He reservoir using a high-capacity vacuum pump this works down to the lambda point of liquid He (2.1768 K) below this temperature the 2He4 turns into a superfluid quantum liquid, which cannot be cooled any further. The minority isotope, 2He3 remains a normal fluid down to 0.002491 K this allows cooling down to about 1K. 

The existence of a critical point in the pressure-volume-temperature (PVT) diagram (actually, a point in the planar PV projection, but a critical line in a three-dimensional representation), a critical point (Curie temperature) in ferromagnetism, a critical point (Neel point) in antiferromagnetism, a critical temperature in superconductivity, and a critical point (lambda point) in liquid 2He4 are physical descriptions of the onset of a sudden macroscopic collective transition. If one approaches the critical point very closely, dimensionless parameters, defined to describe this approach, are common to all these disparate phenomena the approach to criticality, or to a phase transition, are really the same. 

Inspection of Fig. 3.16.5, where we have set w - 2RTA, shows that as the temperature rises there is a marked increase in heat capacity, with a sharp drop off back to zero at T - TA. This figure has approximately the shape of the Greek capital letter A and hence is frequently called a A anomaly TA is known as the lambda point. What Fig. 3.16.5 once more illustrates is... 

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. 

The solid is not stable at one atmosphere, and can only be obtained at elevated pressures. In the range from 0° to 1° K., the required pressure is reported by Simon and Swenson (304) as 25 atmospheres. At a pressure of 103 atmospheres, Keesom (174) reports the melting point to be 3.5 K., with an associated heat of 5 cal./gram atom. Keesom also reports the second order transition (lambda point) at 2.186 K., and the normal boiling point at 4.216 K. with the associated heat of vaporization of 20 cal./gram atom. Thermodynamic prop>erties for the ideal monatomic gas have been calculated at the National Bureau of Standards (395). Kobe and Lynn (193) report the critical temperature as 5.3 K. and the critical pressure as 2.26 atmospheres. 

In 1938 London proposed [120] that Bose-Einstein condensation provides a microscopic explanation for superfluidity in liquid " He. When Eq. (6) is naively applied to bulk He, a rather reasonable estimate of T 3 K is obtained, which is close to the experimental result for the lambda point temperature of... 

For He below the lambda point, v(r) represents the velocity of the superfluid. The wavefunction [Eq. (11)] corresponds to a complex local order parameter [130-135] associated with the macroscopic occupation of the Bose-Einstein condensate. 

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