Rule for Structures of Open Metal Surfaces

We present a clear and simple rule for determining the relaxation sequences on open (stepped, vicinal, or high-Miller-index) metal surfaces. At the bulk-truncated configuration of a surface, a surface slab is defined where the coordination of atoms is reduced from the bulk. The rule predicts that the interlayer spacings within this slab contract, while the interlayer spacing between this slab and the substrate expands. By first-principles calculations, we show that this rule is obeyed on all open Cu surfaces with interlayer spacings down to about 0.5 Å. We also illustrate a direct relation of the relaxation sequences to the charge redistribution on these surfaces, which is demonstrated to be driving the multilayer relaxations. The applicability of the rule can be extended to other fcc and bcc metals, including unreconstructed and missing-row surfaces.