Surface energy and stress release by layer relaxation

S. K. Kwon, Z. Nabi, K. Kádas, L. Vitos, J. Kollár, B. Johansson, R. Ahuja

Research output: Article

44 Citations (Scopus)


The surface energy (γ) and surface stress (τ) for semi-infinite close-packed surfaces of 4d transition metals have been calculated using ab initio total-energy methods. The moderate agreement between the present and former theoretical data for τ indicates the high level of numerical difficulty associated with such calculations. For the most close-packed surfaces, the present unrelaxed τ values follow the typical trend characteristic for the cohesive energy in nonmagnetic transition-metal series, whereas the relaxed τ values group around ∼1mJ/m2, obtained for Y, Zr, and Ag, and ∼3mJ/m2, calculated for Nb, Mo, Tc, Ru, Rh, and Pd. We have found that the average surface energy reduction upon layer relaxation is around 4%. At the same time, a large part of the surface stress is released during the surface relaxation process. To explain the observed behaviors, we have established a simple relationship, which connects the variations of γ and τ to the layer relaxation. This relation reveals the principal factors determining the difference between the surface energy and stress release rates at 4d transition-metal surfaces.

Original languageEnglish
Article number235423
JournalPhysical Review B - Condensed Matter and Materials Physics
Issue number23
Publication statusPublished - dec. 15 2005


ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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