Theory of first-order layering transitions in thin helium films
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Thin liquid He-4 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 mu and surface tension alpha as functions of coverage n, and from this we deduce mu(a). For each set of adjacent layers, we then obtain the crossing point in the curves of mu(alpha). In this way we obtain the values of mu, alpha, and surface coverages for the transition. Particular attention is paid to the monolayer-bilayer transition.
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