Measurements of the conduction of heat between solids and liquid helium-Kapitza conductance-point to the existence of an anomalously large acoustic transmission coefficient at high frequencies ( approximately 100 GHz). The dependence of this coefficient on frequency and on the properties of the solid are discussed together with recent theoretical work on this problem.

https://iopscience.iop.org/article/10.1088/0022-3719/7/3/005/pdf

Kapitza resistance and acoustic transmission across boundaries at high frequencies

We report here the process for the evaporation of He atoms from the surface of liquid 4He. It is a particularly simple quantum process: a phonon inthe liquid with energy ħω > EB, the binding energy, propagates to the free surface where it is either reflected or gives all its energy to an atom on the surface. This energy is used to overcome the binding forces and the balance, ħω − EB, is carried away by the atom as kinetic energy.

Quantized evaporation from liquid helium

We have measured the effect of colliding two phonon sheets together at different angles. At small angles they interact strongly and a hot line is formed along the line of intersection of the two sheets. At angles between ~13? and ~27? the interaction becomes weaker and less energy goes into the hot line. At angles greater than ~27? there is no interaction between the sheets and they pass through each other. By delaying one sheet with respect to the other, the path of the hot line can be shifted laterally. Using this behaviour, we show that the sensitive area of the bolometer is around 10?2?mm2. We have measured the profile of the hot line and find that its width, typically 1?mm, varies as 1/sin(?/2), where ? is the angle between the two sheets. We analyse the data and estimate that the typical angle between two phonons interacting by the three phonon process varies between 8.4? and 12.5?, depending on their energy. We model the formation of the hot line when the sheets are strongly interacting. From the model and the measured data, we find that the temperature of the hot line decreases, and the cone angle and energy density of the hot line increases, with both increasing energy density in the sheets and increasing angle ?.

http://iopscience.iop.org/article/10.1088/1367-2630/8/8/128/pdf

Interactions between phonon sheets in superfluid helium

REVIEW ARTICLE: Phonon spectroscopy

For pt.I see ibid., vol.8, 289 (1975). Detailed measurements of the angular distribution of phonons radiated from the cleaved (100) faces of sodium fluoride crystals pulse heated to 0.9K or approximately=85%) of the energy flux across the interface at all source temperatures, and its variation with source temperature T1 corresponds well to the temperature dependence of the excess Kapitza conductance observed in steady heat flow experiments for a wide variety of materials. This temperature dependence is consistent with a threshold energy for transmission into the background of approximately 5K.

The angular distribution of phonons radiated from a heated solid surface into liquid 4He. II. Cleaved sodium fluoride (100) faces

Various experiments on the propagation of high-frequency phonons in liquid $^{4}\mathrm{He}$ at $T=0.1$ K lead to the conclusion that there is a critical wave vector ${q}_{c}$ such that phonons with wave vector $ql{q}_{c}$ have very short mean paths while those with $qg{q}_{c}$ have very long ones. As ${q}_{c}$ is adjustable over a wide range we recognize the possibility for phonon spectroscopy, using the helium as a tuneable high-pass phonon filter.

Liquid 4 He: A Tunable High-Pass Phonon Filter

We have measured the angular distribution of phonons radiated from a cleaved (100) face of a sodium fluoride crystal, pulse heated to $T\ensuremath{\sim}0.5$ K, into liquid $^{4}\mathrm{He}$ at $Tl0.1$ K. The distribution shows a sharp peak superimposed on a low-amplitude background extending to \ensuremath{\sim}35\ifmmode^\circ\else\textdegree\fi{} to the normal. The peak width is consistent with a critical cone ${\ensuremath{\theta}}_{c}={4.25}^{\ensuremath{\circ}}$ calculated under the assumption of conservation of phonon wave vector parallel to the interface.

ANGULAR DISTRIBUTION OF PHONONS RADIATED FROM A HEATED SOLID INTO LIQUID $sup 4$He.

Measurements have been made of the angular spreading of initially well-defined beams of phonons of energies $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{{k}_{B}}\ensuremath{\lesssim}12$ K in liquid $^{4}\mathrm{He}$ at $T\ensuremath{\sim}0.1$ K and at pressures between saturated vapor pressure and 24 bars. The spreading is consistent with three-phonon decay processes and the results strongly suggest that in the dispersion relation $\ensuremath{\omega}=cq(1\ensuremath{-}\ensuremath{\gamma}{\ensuremath{\hbar}}^{2}{q}^{2})$ the constant $\ensuremath{\gamma}$ is negative at $p\ensuremath{\lesssim}17$ bars and positive at higher pressures.

Evidence for upward phonon dispersion in liquid $sup 4$He from the angular spreading of phonon beams

The angular variation of the acceptance of phonons by a cleaved NaF crystal from liquid $^{4}\mathrm{He}$ has been measured as a function of heater temperature and compared with the angular emission through the same interface. There are clearly two channels for transmission in both directions but their dependences on heater temperature are quite different and it appears that the transmission process is asymmetric.

R. A. Sherlock

Papers

Liquid 4 He: A Tunable High-Pass Phonon Filter

ANGULAR DISTRIBUTION OF PHONONS RADIATED FROM A HEATED SOLID INTO LIQUID $sup 4$He.

Evidence for upward phonon dispersion in liquid $sup 4$He from the angular spreading of phonon beams

Angular acceptance of phonons in /sup 4/He by NaF

Measurement of the group velocity of 93 GHz phonons in liquid 4He