Surface and Epitaxial Stresses on Supported Metal Clusters

Surface stress and energy are basic quantities in the Gibbsian formulation of the thermodynamic description of surfaces which is central in the formation and long-term behavior of materials at the nanoscale. However, their size dependence is a puzzling issue. It is even unclear whether they decrease or increase with decreasing particle size. In addition, for a given metal, estimates often span over an order of magnitude, far apart from bulk data, which, in the absence of any explicit size-dependence rule, escapes understanding. Here, we combine X-ray absorption and nanoplasmonics data with atomistic simulation to describe α-Al2O3(0001)-supported silver particles. By comparison to MgO(001)-supported and embedded silver, we distinguish epitaxial and surface stress. The latter is shown to dominate above 3 nm in size. Since the observation mostly relies on surface/bulk ratio, a metal-independent picture emerges that is expected to have far-reaching consequences for the understanding of the energetics of nanoparticles.