Role of sp–d hybridization in the formation of stacking defects at metal surfaces

Stacking fault formation is at the origin of nanostructuration phenomena at close-packed surfaces like in the case of the well-known Au(1 1 1) herringbone reconstruction. The structural homogeneity of an epitaxial growing deposit on (1 1 1) metal surfaces is dependent on the energy balance between FCC stacking and HCP stacking. In this context we apply a sp–d tight-binding model to study the evolution of the stacking fault energy at the (1 1 1) surfaces of metals. We show in this way the relative importance of sp–d hybridization both in the formation of defects at the surface of metals and in reconstruction phenomena as a function of band filling especially at the end of transition metal series. Comparing our results with atomistic simulations it is concluded that although atomistic calculations are powerful tools to investigate relaxation mechanisms at surfaces, a higher degree of accuracy on electronic structure is necessary to quantify the energy of some defects at surfaces like FCC stacking and HCP stacking. In particular long range interactions associated to less localized sp electrons are playing a rather important role in reconstruction phenomena for metals like platinum and gold.