Heat Capacities of Submonolayer He 3 and He 4 Adsorbed on Ar-Plated Copper

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 \ifmmode^\circ\else\textdegree\fi{}K. The broad features of the results include the following: $C(T)$ for ${\mathrm{He}}^{4}$ resembles the temperature dependence of two-dimensional Debye solids, but with characteristic temperatures ${\ensuremath{\Theta}}_{D}$ which decrease as $T$ falls; ${\ensuremath{\Theta}}_{D}$ at high coverage agrees with the value 28 \ifmmode^\circ\else\textdegree\fi{}K obtained by Goodstein et al.; ${\ensuremath{\Theta}}_{D}$ decreases at lower $x$, but is surprisingly large (16 \ifmmode^\circ\else\textdegree\fi{}K) at $x=0.1$; ${\mathrm{He}}^{3}$ heat capacities at high coverage are quite similar to ${\mathrm{He}}^{4}$ films at the same areal density; at intermediate and lower coverages, $C(x,T)$ of ${\mathrm{He}}^{3}$ is significantly different from that of ${\mathrm{He}}^{4}$ and displays a small peak or offset at $T\ensuremath{\simeq}2$ \ifmmode^\circ\else\textdegree\fi{}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 ${\ensuremath{\Theta}}_{1}=16$ \ifmmode^\circ\else\textdegree\fi{}K, ${\ensuremath{\Theta}}_{2}=28$ \ifmmode^\circ\else\textdegree\fi{}K for the two species, the ${\ensuremath{\Theta}}_{D}$ 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\ifmmode^\circ\else\textdegree\fi{}. This value is about 8\ifmmode^\circ\else\textdegree\fi{} 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 surface by the adatoms: a "mattress effect." The two-patch model is successful in describing $C(T)$ for ${\mathrm{He}}^{3}$ at high coverage, but $C(T)$ at low coverage and the $x$ dependence over the entire range shows that ${\mathrm{He}}^{3}$ is significantly different from ${\mathrm{He}}^{4}$, but we have no explanation for the difference.