Phase Relations Associated with One-Dimensional Shell Effects in Thin Metal Films

The physical and chemical properties of thin metal films show damped oscillations as a function of film thickness (one-dimensional shell effects). While the oscillation period, determined by subband crossings of the Fermi level, is the same for all properties, the phases can be different. Specifically, oscillations in the work function and surface energy are offset by 1/4 of a period. For Pb(111) films, this offset is similar to 0.18 monolayers, a seemingly very small effect. However, aliasing caused by the discrete atomic layer structure leads to striking out-of-phase beating patterns displayed by these two quantities.