Continuous and discontinuous transitions on 3D equilibrium crystal shapes: a new look at Pb and Au

Equilibrium crystal shapes exhibit flat facets and rough vicinal surfaces, with transitions between them being either continuous or discontinuous, the latter recognizable by a sharp edge. In general, mixed repulsive/attractive step–step interactions may lead to continuous or discontinuous facet-to-vicinal transitions. In can be shown that the contact angle at the facet for a discontinuous transition is directly related to the ratio of the step interaction strengths. Alternatively, surface reconstruction of facets can also be responsible for sharp edges at the facet boundary. In this case the contact angle is related to the difference between surface free energies of the reconstructed and unreconstructed facet as well as the corresponding difference of step interaction energies. Fitting the experimental shapes by theoretical expressions can be used to extract the relevant surface and step free energies and also step interaction energies. Experimental examples of Pb and Au equilibrium shapes are evaluated and discussed. Step free energies of vicinal Au(1 1 1) and Au(1 0 0) surfaces, evaluated by both models, are 30 and 10 meV/Å2, respectively.