Some properties of liquid helium at very low temperatures

Measurements hare been made of the thermal conductivity of gaseous 3He and 4He and of liquid 3He and 4He by using a modified parallel plate arrangement of small volume (0.12 ccs.) which is capable of measuring conductivities of the order of 5.10-6 watt units. Before this work could be carried out, the tritium with which the 3He gas was contaminated was removed by passing the gas through a copper trap immersed in liquid helium. The thesis includes a description of the apparatus used in cleaning this 3He and the techniques employed in transporting the gas from the storage container to the measuring apparatus. Comparatively small quantities of gas were available so that all apparatus had to be of small volume, and of a robust construction to reduce the possibility of loss.
The transport properties of gases at low temperatures are of interest because of the appreciable quantum effects, and, of all gases, helium is the most suitable since it is monatomic, light and remains in the gas phase to very low temperatures. There are also the advantages that it exists in two isotopic forms so that the effect of statistics may be studied, and that the interaction potential between two helium atoms which is used in the calculation of the transport properties should be a simpler function of distance than the potential between more complicated atoms.
No measurements have bean reported tor 3He gas, and in view of the considerable difference in the conductivity of the two isotopes suggested by the theoretical calculations (see de Boer 1955), it was decided to sake these measurements. For comparison purposes and in order to check that the apparatus was behaving correctly, measurements were also made on gaseous 4He. Values were obtained for both gases in the temperature range 1.5 - 4.0°K. The conductivity of 4He gas at these temperatures has been measured by Ubbink and de Haas (1943) and the results of the present work are in good agreement with their values. The results for 3He gas are significantly different from those of 4He confirming the predictions, and the values for both gases are compared with the theoretical values of Keller (1957) when it is found that the agreement obtained is good for 4He and moderate for 3He. A comparison is also made with the conductivities derived from the viscosity data using the expression K = 5⁄2μCv.
The conductivity of liquid 3He is found to be of the same order of magnitude as that of gaseous 3He and, as it also rises with temperature like a gas, some sort of gas-model would seem appropriate. The results we obtain are slightly below those of Lee, Donnelly and Fairbank (1957) and we attribute this to a boundary resistance which is present in our cell though not in theirs. This conclusion has recently been confirmed by some experiments of H.A. Fairbank and Lee (1957) and our values for the conductivity of 4HeI indicate that a boundary resistance is also present in this liquid.
A resistance of the same order of magnitude is known to exist at surfaces in contact with 4HeII when it is referred to as the Kapitza resistance (Kapitza 1941) and the present demonstration of its existence in 4HeI would appear to rule out explanations based on the peculiar properties of helium below the λ-point. A theory independent of these properties is by Khalatnikov (1952) who considers the vibrations of the surface of a solid in contact with liquid helium and attributes the resistance to the acoustic mismatch of the phonons, or quantised vibrational motions, in the solid at the interface. We suggest that this theory should be modified in some way to account for the dense adsorbed layer of helium at this interface; the thickness of the layer is of the same order of magnitude as that of the dominant wavelength of the sound radiated into the helium and it would appear that this invalidates the assumption that the helium is a continuous medium of constant density right up to the interface. The wavelengths just above the dominant wavelength will be of the order of the interatomic distances so that the concept of wave motion for the energy radiated at these wavelengths is becoming a less useful one.
The conductivities of liquid 3He and liquid 4HeI together with their viscosities have been discussed briefly in the light of the model proposed to describe the behaviour of these liquids and they have been compared with other simple liquids such as liquid argon and nitrogen.
Measurements have also been made on the velocity of sound in liquid 3He. A method has been need in which the time taken for a pulse of ultrasonics to travel a known distance (to a reflector and back again) is measured. Before the completion of this work, two independent sets of values were reported (Laquer, Sydoriak and Roberts 1957, and Flicker and Atkins 1957) and in view of this, only a few measurements were made; these lie between the values obtained by the two groups of workers mentioned above. From this velocity, we calculate the ratio of the specific heats Cp/Cv from thermodynamic formulae and hence show that Csat which has hitherto been used for Cv in calculations of the entropy, differs appreciably from Cv above 1.5°K.