Thermodynamic study of theHe4monolayer adsorbed on Grafoil

Abstract

A calorimetric and vapor-pressure study of the behavior of $^{4}\mathrm{He}$ adsorbed on Grafoil in the temperature range 4 to 15 K is reported. These results have been combined with preexisting low-temperature heat-capacity data to form a complete thermodynamic description of the film. The Grafoil substrate evidently consists almost entirely of basal-plane graphite, with only a small fraction of energetically distinct adsorption sites. Techniques of semiempirical modelling are introduced which make it possible to eliminate the effects both of these inhomogeneities and of the formation of second and higher layers, so that a detailed picture may be formed of the behavior of the $^{4}\mathrm{He}$ first layer on an ideal graphite substrate. The binding energy of a $^{4}\mathrm{He}$ atom on the graphite substrate is reported to be 143 \ifmmode\pm\else\textpm\fi{} 2 K, with a first excited state at 89 \ifmmode\pm\else\textpm\fi{} 3 K. A lattice-gas ordering transition occurs near 3 K at a coverage corresponding to one $^{4}\mathrm{He}$ atom for every three carbon hexagons in the graphite surface, and is used as a fiducial for calibrating our system relative to those of previous investigators. At both higher and lower densities the film seems little influenced by the crystal structure of the substrate. Particular attention is given to the high-coverage low-temperature region, which has been identified as a two-dimensional (2D) solid bounded by a melting-phase transition. The available data are combined with two-dimensional elastic theory to establish the presence of low-lying transverse sound modes, thus confirming the solidlike character of this medium. The behavior of the thermodynamic variables of state through the observed transition is also presented. The theoretical implications of the existence of a 2D solid are discussed, together with a dislocation theory of melting which gives rise to the well-known three-dimensional Lindemann empirical melting formula without an adjustable parameter. It is shown that at very low coverage the film does not form a low-density solid as previously suggested, but is rather dominated by substrate inhomogeneities. At intermediate temperatures and coverages the film is a fluid which is accurately described if a leading-order quantum virial correction is made to the 2D ideal-gas equation of state.