Phase transition of two-dimensionalHe3from a dilute to a dense phase

Abstract

We have measured the heat capacity of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ as thin as 10 Å formed on a Nuclepore filter substrate. At low temperatures, where the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ is in the lowest state as far as motion perpendicular to the film surface, we find that the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ undergoes a transition from a dilute phase to a dense phase. We have observed this transition for films of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ of 12.3- and 10-Å thickness and for coverages of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ below about 0.2 atomic layers. For thicker ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films, and higher ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ coverages, the ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ remains homogeneously spread out over the surface of the ${}_{}{}^4{}_{}{}^{}\mathrm{He}$. The striking characteristic of the transition is the sudden onset of linear temperature dependence with a slope which is proportional to the amount of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ in the calorimeter. This is consistent with the formation of islands of a dense two-dimensional phase which grows in extent proportionately to the amount of ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. Two puzzling aspects of our results are the lack of a significant heat-capacity jump at the transition and, based on a linear extrapolation of the data to zero temperature, a substantial amount of missing entropy.