Absolute surface free energies of Pb

• Published in: Surface science 2002-06, Vol.511 (1-3), p.83-96
• Main Authors: BOMBIS, C, EMUNDTS, A, NOWICKI, M, BONZEL, H. P
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Exact sciences and technology; Physics; Solid surfaces and solid-solid interfaces; Surface energy; thermodynamic properties; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties)
• ISSN: 0039-6028; 1879-2758
• DOI: 10.1016/S0039-6028(02)01554-6

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 (111) surfaces. 3D images of Pb crystallites are obtained by scanning tunneling microscopy at 323-393 K. Line scans through high symmetry < 110 > azimuths are transformed into an anisotropic relative surface free energy, gamma ( theta , T). The absolute surface free energy of Pb(111) is obtained from the limiting slopes, df( theta , T)/d tan theta , of the orientation dependent f( theta , T) = gamma ( theta , T)/cos theta at the boundaries of the (111) facet, located at theta = 0 deg . This value is 25.7 plus/minus 1.4 meV/A exp 2 or 440 plus/minus 22 mJ/m exp 2 . Absolute surface free energies of other low-index orientations, such as (100), (110) etc. are calculated from the relative anisotropy of gamma ( theta )/ gamma (111). It is found that surface free energies of orientation (hkl), 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 (100), (110), (112), (113) and (221), are evaluated in the [011] zone, using the corresponding facet radii and the absolute surface free energies of those facets.