Title: Experimental and theoretical studies in low temperature physics: sublimation and vapor pressure of ³⁶Ar and the combined effects of phonon attenuation and impedance matching on Kapitza resistance

The sublimation and vapor pressure of Ar³⁶ were measured in the temperature range 23.752-87.375 K. Pressures below 1 Torr were measured with a McLeod gauge and corrected for effects of thermal transpiration and mercury streaming. The estimated accuracy of these pressure measurements ranges from 1% near 1 Torr to 10% near 10 Torr. Above 1 Torr ^-5 a calibrated Bourdon gauge was used to give pressures to ±0.03 Torr. Temperatures were measured to ±3 mK with a N.B.S.-calibrated Pt resistance. thermometer. A liquid helium bath was used throughout the temperature range for which the experiment was done. The data were fit to theoretical sublimation pressure curves to obtain values for the static lattice energy, lattice vibrational energy, and geometric mean frequency of the phonon spectrum. The data were also compared with theoretical calculations of others based on an anharmonic selfconsistent phonon theory. Equivalent sublimation-pressure data on normal Ar are compared with our Ar³⁶ data in the temperature range 62.315-84.503 K. This comparison yields vapor-pressure ratios which are in reasonable agreement with theory and other experiments. Thermodynamic properties of normal Ar and of Ar calculated from these data 36 are also compared. It is found that several of the differences in MASTER properties may be qualitatively understood in terms of the increased zero-point energy of Ar³⁶ compared to normal Ar. The Kapitza resistance, RK(T), is calculated for a Cu-He⁴ interface using the acoustic mismatch theory of Khalatnikov and of Mazo and Onsager. Included in the calculation are the effects of: phonon attenuation in the copper as well as impedance matching due to the increased He density near the interface. We calculate R (T) for several K values of attenuation in the Cu; detailed calculations are displayed for the case of equal attenuations for longitudinal and transverse waves in the solid. Also considered are different attenuation profiles in the Cu. We use a density profile, for the He, calculated from compressibility data and the van der Waals attractive force between He and the Cu substrate. Our model includes the effect of a solid layer of He at the copper surface, i.e. in such a He layer both longitudinal and transverse waves are allowed. Included in our calculations are the effects of different density profiles for the He. The calculations indicate that for suitable choices of the physical parameters, the theoretical results for R_K(T) agree in magnitude as well as T dependence with the experimental data. Unfortunately, the important physical properties have not yet been experimentally determined and a definitive test of this theory must await such data.