Contribution of d electrons to surface stresses and their changes by layer relaxation for a series of 4d transition metals

Abstract

Surface stresses and their changes by layer relaxation are crucial to understand the chemical and mechanical properties of transition-metal surfaces. Following our previous study (Shiihara et al., Phys. Rev. B 87 (2013) 125430) on unrelaxed surfaces of fcc late transition metals, both relaxed and unrelaxed surfaces of a series of 4d transition metals, including bcc and hcp structures, have been investigated by using the ab initio local-stress scheme and the Friedel stress model based on the second-moment tight-binding approximation. In ab initio results, an in-plane tensile stress is observed only at the surface top layer in an unrelaxed surface, while the layer relaxation reduces the tensile stress on the top layer and generates a small stress on the subsurface layer, except for the Pd(111) surface showing outward relaxation. All these results are properly reproduced by the Friedel stress model, especially for close-packed surfaces. Thus the surface stresses and their changes by layer relaxation are dominated by the d-band width changes, because of the coordination reduction and the d-orbital overlap change due to layer relaxation, generally for the series of 4d transition metals. The role of the d-electrons in the correlation among the surface relaxation, surface stress, and surface chemical reactivity is also discussed.