Heat Capacities of SubmonolayerHe3andHe4Adsorbed on Ar-Plated Copper

Abstract

Extending the earlier study by Goodstein, McCormick, and Dash, we have measured the heat capacities of ${\mathrm{He}}^3$ and ${\mathrm{He}}^4$ films absorbed in Ar-plated copper, at coverages $x$ ranging from 0.1 to 0.8 monolayer from 0.5 to 4.2 °K. The broad features of the results include the following: $C\left(T\right)\mathrm{}$ for ${\mathrm{He}}^4$ resembles the temperature dependence of two-dimensional Debye solids, but with characteristic temperatures ${\Theta }_D$ which decrease as $T$ falls; ${\Theta }_D$ at high coverage agrees with the value 28 °K obtained by Goodstein et al.; ${\Theta }_D$ decreases at lower $x$, but is surprisingly large (16 °K) at $x=0.1\mathrm{}$; ${\mathrm{He}}^3$ heat capacities at high coverage are quite similar to ${\mathrm{He}}^4$ films at the same areal density; at intermediate and lower coverages, $C(x,T)\mathrm{}$ of ${\mathrm{He}}^3$ is significantly different from that of ${\mathrm{He}}^4$ and displays a small peak or offset at $T\simeq 2$ °K. The data are compared with several microscopic models: localized adsorption, two-dimensional gases, noninteracting particles in a two-dimensional tunneling band, and two-dimensional solids. Each is shown to be inadequate to account for the observed variations with $T$, $x$, and isotopic mass. The data are then compared with the behavior of a two-phase film, and this is found to agree with the data on ${\mathrm{He}}^4$ over a substantial range of $x$, but it fails at low $x$. We are forced, by general arguments, to invoke surface inhomogeneity to resolve the paradox, and we examine an ad hoc model (due to Peierls) of a substrate consisting of two distinct regions, on which the helium is clustered into dense monolayer patches. The two-patch model is quite successful for ${\mathrm{He}}^4$, yielding two-dimensional characteristic temperatures ${\Theta }_1=16\mathrm{}$ °K, ${\Theta }_2=28\mathrm{}$ °K for the two species, the ${\Theta }_D$ values and the areas belonging to each fraction of the substrate being practically independent of $T$. Agreement with the two-patch model implies that much of the substrate is substantially bare of adatoms, and hence that adatoms are strongly bound in the dense surface phases. The latent heat for two-dimensional vaporization is estimated to be at least 15°. This value is about 8° greater than the heat of vaporization of bulk liquid ${\mathrm{He}}^4$, implying a large enhancement due to interactions with the substrate. We propose a possible mechanism for the enhancement; namely, a local depression of the...