Dynamics of a krypton-covered graphite slab, and mean-square amplitudes of vibration and thermodynamic functions of krypton and xenon layers adsorbed on the (0001) surface of graphite

Following earlier work on the dynamics of the graphite (0001) free surface [paper I, Phys. Rev. B 23, 4208 (1981)], and of that surface with a registered adsorbed monolayer of xenon [paper II, Phys. Rev. B 24, 6050 (1981)], we present here a full dynamical calculation of a (0001) graphite slab with registered monolayers of krypton adsorbed on its two surfaces. As in II, the krypton-krypton and krypton-carbon interactions are modeled with Lennard-Jones potentials, whereas the carbon-carbon interactions are described by the extended axially symmetric force-constant model of I. The surface-mode spectrum of the krypton-covered graphite slab displays obvious qualitative similarities with that of the xenon-covered graphite slab described in II, but there are also significant quantitative differences. We calculate for both the krypton- and xenon-covered slabs the mean-square amplitudes of vibration (MSA's) and the thermodynamic functions as functions of temperature. For the sizes of crystal that we could handle computationally, the MSA's of the in-plane vibrations $〈u_{\parallel }^2〉$ show the beginnings of the logarithmic dependence on crystal size expected for two-dimensional systems, but this is not yet the case for the MSA's of the out-of-plane vibrations $〈u_{\perp }^2〉$. The most striking difference between krypton and xenon is the large difference in $〈u_{\parallel }^2〉$ between the two cases, resulting from density differences between the registered adsorbed layers and their respective bulk crystals. No absolute measurements of MSA's are presently available for comparison. The adsorbate thermodynamic functions show the behavior expected for a simple two-dimensional crystal. Comparison with experimental quantities for adsorbed systems is made difficult by the fact that the calculations could only be carried out for one density, namely that of the registered monolayer.