3D equilibrium crystal shapes of Pb: the significance of step-resolved images

Abstract

Scanning tunnelling microscopy has proven to be an extremely useful technique for imaging small crystallites equilibrated at elevated temperature. As an example, we review recent work on three-dimensional Pb crystallites of 1–2 μm diameter, supported on Ru(0 0 1). Large (1 1 1) facets and, depending on temperature, small (1 1 2) facets were observed in the top section of the crystallites. The temperature dependent facet anisotropy was analyzed to yield the absolute step free energies of Pb(1 1 1) vicinal steps. The vicinal region close to the (1 1 1) facet was studied in detail to determine the shape exponent, the step–step interaction energy and the constant of the dipole interaction potential. Boundary conditions of the evaluated vicinal region have been specified for proving the universality of shapes, characterized by the exponent of 3/2, which is clear evidence for the 1/ x 2 step interaction potential. The role of the activation barrier for facet growth or shrinkage is discussed in the context of attaining 3D equilibrium of crystallites. A comparative study of crystallites with defect-free and dislocated facets shows significant differences, providing direct evidence of the activation barrier. Reliable step–step interaction energies were obtained for dislocated crystallites. Extrapolating the temperature dependent total step interaction energy to 0 K yields for the first time values of the structure dependent dipole–dipole step interaction energies of A- and B-steps.