Mean-square amplitudes of vibration and thermodynamic functions of the (0001) surface of graphite

Following our earlier work <article>[Phys. Rev. B 23, 4208 (1981)]</article> on the dynamics of the graphite (001) free surface, we present here the surface and bulk mean-square amplitudes (MSA's) of vibration and the surface thermodynamic functions of graphite. For crystals of finite size, the MSA's depend on the aspect ratio (lateral dimension divided by thickness) and for a given aspect ratio, on thickness. This is of importance for measurements on actual graphite crystals. In addition, this parametrization enables us to carry out an extrapolation to the thermodynamic limit (vanishing surface-to-volume ratio) in a single parameter, namely inverse thickness. For infinitely thick crystals the MSA's are independent of aspect ratio. The surface thermodynamic functions are similar to—but roughly a factor of 10 smaller than—those of more isotropic crystals. This is a result of the weak interplanar binding in graphite which makes the creation of a surface less of a perturbation on the bulk. We find no evidence of a significant contribution from the so-called "flexural mode" in the slab dynamics nor in the surface specific heat.