Calculation of finite-size effects and extraction of surface characteristics

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Abstract
We demonstrate a procedure for extracting surface characteristics of a substrate from thermodynamic information obtained from systems adsorbed upon that substrate. To do this we first employ renormalization-group approximations to calculate the specific heat of lattice-gas systems of various finite sizes. Results for the square lattice are in good agreement with exact results of Ferdinand and Fisher. Similar results for a honeycomb lattice are also presented. We then model the substrate as an assembly of platelets with a distribution of sizes. The specific heat from this model substrate is then compared to experimental data to obtain the parameters of the size distribution. Employing this procedure with data taken on the system of helium adsorbed on krypton-plated graphite, we determine that the mean platelet size is 140 Å with a root-mean-square deviation of 106 Å. We further conclude that about 50% of the adsorbed helium does not participate in the order-disorder transition.