Phase transition of two-dimensional He3 from a dilute to a dense phase

We have measured the heat capacity of He3 in films of He4 as thin as 10 A formed on a Nuclepore filter substrate. At low temperatures, where the He3 is in the lowest state as far as motion perpendicular to the film surface, we find that the He3 undergoes a transition from a dilute phase to a dense phase. We have observed this transition for films of He4 of 12.3- and 10-Athickness and for coverages of He3 below about 0.2 atomic layers. For thicker He4 films, and higher He3 coverages, the He3 remains homogeneously spread out over the surface of the He4. The striking characteristic of the transition is the sudden onset of linear temperature dependence with a slope which is proportional to the amount of He3 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 He3. 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.