| Popis: |
Thin liquid $^{4}\mathrm{He}$ films on graphite show evidence of layered growth with increasing number density via a succession of first-order phase transitions. These so-called "layering transitions" separate uniformly covering phases, such as monolayers and bilayers. The present work is a detailed theoretical study of such layering transitions using a Maxwell construction. We model the graphite surface by a strong substrate potential, and using a microscopic variational theory we obtain the uniform coverage solutions for liquid helium. For each layer, the theory yields the chemical potential $\ensuremath{\mu}$ and surface tension $\ensuremath{\alpha}$ as functions of coverage $n$, and from this we deduce $\ensuremath{\mu}(\ensuremath{\alpha})$. For each set of adjacent layers, we then obtain the crossing point in the curves of $\ensuremath{\mu}(\ensuremath{\alpha})$. In this way we obtain the values of $\ensuremath{\mu}$, $\ensuremath{\alpha}$, and surface coverages for the transition. Particular attention is paid to the monolayer-bilayer transition. |
