Absolute surface free energies of Pb

Three-dimensional (3D) equilibrium crystal shapes (ECS) of Pb are utilized for the first time to determine absolute surface free energies via a quantitative evaluation of the measured ECS and published values of step free energies of vicinal (1 1 1) surfaces. 3D images of Pb crystallites are obtained by scanning tunneling microscopy at 323–393 K. Line scans through high symmetry 〈1 1 0〉 azimuths are transformed into an anisotropic relative surface free energy, γ(θ,T). The absolute surface free energy of Pb(1 1 1) is obtained from the limiting slopes, df(θ,T)/d tanθ, of the orientation dependent f(θ,T)=γ(θ,T)/cosθ at the boundaries of the (1 1 1) facet, located at θ=0°. This value is 25.7±1.4 meV/Å2 or 440±22 mJ/m2. Absolute surface free energies of other low-index orientations, such as (1 0 0), (1 1 0) etc. are calculated from the relative anisotropy of γ(θ)/γ(1 1 1). It is found that surface free energies of orientation (h k l), expressed in meV/atom, scale with the number of bonds broken in forming such a surface. Free energies of steps bounding other facets, such as (1 0 0), (1 1 0), (1 1 2), (1 1 3) and (2 2 1), are evaluated in the [0 1 1̄] zone, using the corresponding facet radii and the absolute surface free energies of those facets.