Layering transitions, disordered flat phases, reconstruction, and roughening

We study in light of recent ellipsometry, vapor pressure isotherm and specific-heat measurements on the thermodynamics of adsorbed thin films on graphite, the connection between the layering phase diagrams of thin films on periodic substrates and the thermodynamics of the solid-vapor interface of a semi-infinite crystal. The latter is the limit of the former when the film becomes infinitely thick, and we are interested in connecting this limiting behavior to the thermodynamics of films of finite thickness. We argue that the concepts of surface roughening, preroughening, and reconstruction provide a quantitatively useful framework within which to discuss this connection. Through general renormalization-group arguments and, in more detail, through a self-consistent mean-field treatment that explicitly accounts for all relevant phases, we show that the same types of interactions that lead to these different surface phases lead also to the reentrant layering transitions seen in the recent experiments. By appropriate tuning of the mean-field parameters we can semiquantitatively reconstruct all the observed experimental phase diagrams. It turns out that certain experimental phase diagrams with “zippers” require that the preroughening transition become first order. Our renormalization-group arguments predict such behavior in certain parameter ranges. In addition, for different parameters we predict the existence of an, as yet unobserved, $\theta$ disordered flat phase with spontaneously broken particle-hole symmetry and continuously varying surface height with an accompanying intermeshing layering phase diagram. The underlying lattice in the experiments is triangular, and this actually enhances the stability of the disordered flat phase and the corresponding reentrant layering transitions in the films.