Phases ofHe3andHe4Monolayer Films Adsorbed on Basal-Plane Oriented Graphite

Abstract

Heat capacities of ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ monolayers adsorbed on Grafoil graphite substrates at low temperatures are qualitatively different from previous results using other adsorbents. The present study consists of a detailed survey of many samples conducted in two similar but independent calorimeters: the fractional coverages ranged from 5 to 115% of a completed first layer and the temperature range extended from 0.04 to above 10\ifmmode^\circ\else\textdegree\fi{} K. Several distinct thermodynamic regimes are seen, some of which correspond closely with well-known theoretical models as well as others that had not been predicted. At moderate densities and temperatures the behavior resembles that of two-dimensional gases. Departures from ideality are correlated with quantum-mechanical virial corrections for interacting molecules. In this range of coverages the ${\mathrm{He}}^{4}$ specific heats begin to rise at $T\ensuremath{\lesssim}{3}^{\ensuremath{\circ}}$ K, forming strong rounded peaks near 1\ifmmode^\circ\else\textdegree\fi{}K. ${\mathrm{He}}^{3}$, on the other hand, shows a monotonic decrease with falling temperature until $T\ensuremath{\simeq}{0.2}^{\ensuremath{\circ}}$ K, then (for a narrow range of coverages) reversing the trend to form rounded maxima near 100 m\ifmmode^\circ\else\textdegree\fi{}K. At the lowest temperatures the ${\mathrm{He}}^{3}$ appears to enter a two-dimensional ($2D$) Fermi-liquid regime. At higher coverage both ${\mathrm{He}}^{3}$ and ${\mathrm{He}}^{4}$ undergo second-order phase transitions to regular arrays in registry with the substrate. In the critical region that heat capacities have symmetric peaks of logarithmic shape, with coefficients in close quantitative agreement with exact $2D$ Ising models. Above critical density the ordering peaks disappear and $2D$ liquid and solid behavior is seen. ${\mathrm{He}}^{4}$ at high density and low $T$ is Debye-like, with characteristic temperatures ${\ensuremath{\Theta}}_{2D}$ equal to ${\ensuremath{\Theta}}_{3D}$ of hcp solid ${\mathrm{He}}^{4}$ of the same interatomic spacing. At higher $T$ the $2D$ solid appears to transform to a $2D$ fluid by a continuous process, and pronounced heat-capacity peaks associated with the transformation are located at temperatures near the melting points of hcp ${\mathrm{He}}^{4}$ having the same interatomic spacing. At very low coverage the $2D$ gas character gives way to a regime resembling a low-density $2D$ solid.