Step-step interactions and universal exponents studied via three-dimensional equilibrium crystal shapes

Equilibrated three-dimensional Pb crystallites, supported on Ru(001) and of about 1 µm diameter, were imaged by scanning tunnelling microscopy at 298-393 K. The top section of the crystallites exhibited large (111) facets and, depending on temperature, smaller (112) facets. The vicinal shapes close to (111) were analysed in detail to determine the critical shape exponent and the step-step interaction energy as well as the interaction constant of the potential. Analyzing the complete shape in sections of 1° or 3° azimuthal increments and averaging over all sections of one crystallite, we found a shape exponent of 1.490. The exponent is very close to the theoretically predicted universal value of 3/2 and as such clear evidence for the 1/ x 2 step interaction potential. Several crystallites had dislocations threading the (111) facet. For those crystallites the step interaction energy was determined as 16 meV Å -2 at about 350 K, equivalent to a dipole interaction energy of 8.1 meV Å -2 at 0 K. The interaction constant for the dipole-dipole part of step interaction was found to be 115 meV Å.