Heat capacity and the commensurate-incommensurate transition ofHe4adsorbed on graphite

Abstract

The heat capacity of ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ adsorbed on graphite has been precisely measured over a fine grid of coverages for temperatures extending down to 100 mK and for coverages up to five atomic layers. This paper focuses mainly on the transitional region between the √3 × √3 commensurate structure and the incommensurate phase of the first adsorbed layer. At the commensurate coverage, ${\mathrm{\rho }}_{1/3}$, the low-temperature data have been used to extract a phonon energy gap of 10.5 K, in agreement with the neutron-scattering value obtained for adsorbed ${}_{}{}^3{}_{}{}^{}\mathrm{He}$. At coverages slightly greater than ${\mathrm{\rho }}_{1/3}$ the data are consistent with an incommensurate domain-wall solid. However, an abrupt change in behavior occurs at ρ=1.1 ${\mathrm{\rho }}_{1/3}$, which is interpreted as signalling the entrance into a coexistence region involving a commensurate structure in which 2/5 of the graphite adsorption sites are occupied by ${}_{}{}^4{}_{}{}^{}\mathrm{He}$ atoms. At ${\mathrm{\rho }}_{2/5}$ the system undergoes a sharp first-order transition near 1 K where the entropy per atom changes by 0.2${\mathit{k}}_{\mathit{B}}$. At somewhat higher coverages there is evidence for a 3/7 commensurate structure that transforms at 0.6 K into the floating incommensurate solid. Data for the second adsorbed layer indicate a solid registered relative to the compressed incommensurate first layer. Here the ratio of second- to first-layer densities is 4/7, in agreement with recent results for ${}_{}{}^3{}_{}{}^{}\mathrm{He}$ on graphite.