Trend for the multilayer relaxation sequence of stepped Cu surfaces

Abstract

We investigate suggested multilayer relaxation trends for the stepped metal surfaces by performing density-functional theory calculations, within the generalized gradient approximation and employing the all-electron full-potential linearized augmented plane wave (FLAPW) method, for stepped Cu surfaces. We found that the atom-rows trend, which correlates the multilayer relaxation sequence of stepped metal surfaces with the number of atom rows in the terrace, is not as general as has been assumed. While it holds true for closed stepped surfaces it does not apply for more open surfaces such as for Cu(320) and Cu(410). For example, we found relaxation sequences like \ensuremath{-}\ensuremath{-}\ensuremath{-}\ensuremath{-}+\ensuremath{-}\ensuremath{\cdots} for both surfaces, instead of the expected \ensuremath{-}\ensuremath{-}+\ensuremath{-}\ensuremath{\cdots} and \ensuremath{-}\ensuremath{-}\ensuremath{-}+\ensuremath{-}\ensuremath{\cdots}, respectively. The \ensuremath{-} and + signs indicate contraction and expansion, respectively, of the interlayer spacing. Our results show that the relaxation sequence of eleven stepped Cu surfaces, namely, (110), (311), (331), (211), (511), (210), (221), (711), (911), (410), and (320), follows the nearest-neighbor coordination trend, which correlates the relaxation sequence of the topmost interlayer spacings with the nearest-neighbor coordination number of the topmost surface atomic layers. Therefore, the reduction of the atomic coordination plays a stronger role in the relaxation sequences of stepped metal surfaces than the number of atoms exposed to the vacuum region.