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 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

Quantum evaporation of 4He atoms by phonons and rotons in liquid 4He is measured for a wide range of conditions. The results confirm that an atom is evaporated in a single-excitation to single-atom process and that the boundary conditions of conservation of energy and parallel momentum are obeyed. Excitations in the liquid are generated by pulse heating a thin metal film heater, and the evaporated atoms are detected by the energy yielded on condensation at the surface of a superconducting transition edge bolometer. The heater and bolometer can be rotated about a common axis in the liquid surface, and the collimation of the excitations and atoms into beams allows the angles of incidence and evaporation to be defined. It is first shown that the input power and pulse length must be carefully chosen to produce beams of phonons and rotons that are fully ballistic. The time of flight from the heater to the bolometer is measured, and the angular distribution of the evaporated atoms is determined for different angles of incidence. In particular, the wavevector dependence of the roton to atom pulse shape can be seen. The authors see no sign of Pitaevskii roton decay over the long liquid path lengths involved ( approximately 6 mm), and there is no indication that ripplons are created in the evaporation process.

The surface boundary conditions for quantum evaporation in 4He

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

Thermal wave propagation through nanofilms in ballistic-diffusive regime by Monte Carlo simulations

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

A detailed description of a newly developed experimental technique for measuring the angular distribution of phonons radiated from the surface of a solid, heated to a few K, into liquid helium 4 at T<or approximately=0.1K is given. The relevance of such measurements to the Kapitza boundary conductance problem is discussed and examples of measured angular distributions from cleaved (100) faces of sodium fluoride crystals and from gold films evaporated on glass substrates are presented to illustrate the possibilities of the technique.

The angular distribution of phonons radiated from a heated solid surface into liquid 4He. I. Measurement principles and techniques

Measurements have been made of the angular spreading of initially well defined beams of phonons of energies h(cross) Omega /kB or=17 bar. The decay lengths of the processes giving rise to this spreading are found to be approximately 1 mm. Various scattering mechanisms are considered and it is concluded that the results are consistent with a spontaneous three-phonon decay process allowed when the phonon dispersion curve initially deviates upward from its asymptotic linear form.

N G Mills

Papers

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

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

The angular distribution of phonons radiated from a heated solid surface into liquid 4He. I. Measurement principles and techniques

The angular spreading of phonon beams in liquid 4He: upward phonon dispersion