Thermodynamic surface properties of single crystal faces of xenon calculated by employing the Einstein model of crystalline solids

By broadening the scope of the Einstein statistical-mechanical treatment of a crystalline solid to cover also low-index faces, and using the Lennard-Jones interaction potential and, in addition, adopting an approximate monolayer-nearest-neighbor model, we have calculated the thermodynamic properties of (100) and (111) single crystal faces of Xe(s) in the temperature range 20–80 K. The reversible cleavage work (that corresponds to the Gibbs σ -quantity of interfaces) was found to be on the order of 20–30 mJ m −2 and is largely due to reduction of the pair-wise dispersion interactions for monolayer atoms as compared with the atoms in the bulk of the crystal. For an unstrained crystal, σ diminishes slightly with temperature for both energetic as well as entropic reasons. On the other hand, the differential work of stretching a solid interface, γ , is a negative quantity (−5 to −30 mN m −1 ), corresponding to surface pressure, the main reason being that upon (elastic, homogeneous) stretching, the vibration energy levels of the top monolayer are shifted upward, at the same time becoming more closely spaced. It is shown that such a stretching operation causes the T × surface excess entropy term to increase at a faster rate than the corresponding surface energy term, which accounts for the negative sign found for γ . On the same basis, we can also verify that the general, though sometimes questioned, Shuttleworth relation, is necessarily fulfilled for an ideally terminated (metastable) Xe crystal face with a filled monolayer of immobile Xe atoms. As a matter of fact, this equation merely represents an alternative mathematical disguise of the basic energy differential expression for the monolayer.