We report heat-capacity measurements on ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ films adsorbed on graphite for surface densities at and smaller than that required to form a commensurate (√3 × √3 )R30° monolayer in the temperature range 0.4 K<T<4.2 K. At densities below 0.039 A${\mathrm{̊}}^{\mathrm{-}2}$, a single transition is observed at T<1.3 K. For densities larger than 0.039 A${\mathrm{̊}}^{\mathrm{-}2}$, two transitions are observed, the higher-T one developing into the order-disorder transition previously studied by several authors. Our measurements are consistent with a phase diagram showing a large region of existence of a single-phase commensurate (with vacancies) film, and a two-phase region of coexisting commensurate and vapor phases. For this phase diagram a tricritical point exists at $T_{\mathrm{TCP}\mathrm{\simeq }1.3}$ K and a density $n_{\mathrm{TCP}\mathrm{\simeq }0.039}$ A${\mathrm{̊}}^{\mathrm{-}2}$. We observe strong evidence for Fisher renormalization of the constant-density specific heat along the critical line. The effects of inhomogeneities on all transitions are discussed.

• Received 9 July 1984

DOI:https://doi.org/10.1103/PhysRevB.31.448