Short-Range Order and Melting Anomalies in Thin Films

Recent experiments show that high-coverage He-4 monolayers adsorbed on graphite have low-temperature heat capacities corresponding to two-dimensional solids. At higher temperatures the solid phase appears to "melt" by a continuous process, suggesting a connection with the theoretical prediction that there can be no long-range crystalline order at finite T in two-dimensional systems governed by typical interatomic forces. This paper explores the theory in greater detail, with attention to long-range and short-range order and their experimental implications. Several models are studied: two-dimensional harmonic solids with "Debye" phonon spectra, lattices with Van Hove singularities, two-dimensional quantum solids, and effects of periodic potentials due to substrate structure. The theory is discussed in the light of current understanding of melting, and the following new melting hypothesis is proposed. The solid-liquid transition occurs on a mode-by-mode basis, beginning with the lowest wave vectors. Solid instability is primarily associated with transverse modes. A mode becomes unstable when the range of crystalline order becomes comparable with its wavelength. Applied to two-dimensional systems, the hypothesis predicts a continuous transition with a heat-capacity contribution similar in its temperature dependence to the anomalies seen in He-4 monolayers and N-2 multilayei's. Applied to three-dimensional Debye solids, the same hypothesis predicts an abrupt first-order process, with a melting temperature obeying the Lindemann law.