Surface energy and stress release by layer relaxation

• The surface energy (gamma) and surface stress (tau) 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 tau indicates the high level of numerical difficulty associated with such calculations. For the most close-packed surfaces, the present unrelaxed tau values follow the typical trend characteristic for the cohesive energy in nonmagnetic transition-metal series, whereas the relaxed tau values group around similar to 1 mJ/m(2), obtained for Y, Zr, and Ag, and similar to 3 mJ/m(2), 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 gamma and tau 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.

Nyckelord

initio molecular-dynamics

augmented-wave method

transition-metals

force microscopy

electron-gas

representation

simulation

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