Temperature dependence of the atomic relaxations and vibrations on a stepped surface: a molecular dynamics study of Cu(1,1,19)

We have studied the relaxations and vibrations of atoms near the surface of a (1,1,19) copper crystal. For this purpose, we have performed molecular dynamics simulations using a semi-empirical many-body potential derived from tight binding models. The total displacement field can be described as the sum of a mean surface relaxation and a specific contribution of the steps, which is maximal for step edge atoms (0.08 Å) and corner atoms (0.06 Å). Whereas step edge atoms relax towards the inner terrace and towards the bulk, corner atoms relax in the opposite direction, leading to vortex-like structures in the displacement field. We demonstrate that, as predicted by continuous elasticity, the displacement field induced by steps is equivalent to the one created by a line of dipoles on a flat surface. In the particular case studied here, the equivalent dipole density is 3.3×10−10 N. The specific relaxations of kink atoms have been calculated. We have also studied the variation of the relaxations as a function of temperature (T). A strong effect is predicted for inner terrace atoms: when increasing T, the contraction of the first interplanar distance, with respect to the bulk value, progressively cancels and turns to an expansion at high T. This is not the case for the specific contraction of step edge atoms that is nearly temperature independent. This latter behaviour is related to very strong longitudinal correlation between vibrations of the step edge atom and of its nearest neighbour inside the terrace. In the same time, whereas the vibrations of inner terrace atoms are found to be isotropic, the ones of step edge atoms are anisotropic, with a larger component along the direction parallel to the terrace plane and perpendicular to the step edge, the other components being the same as for inner terrace atoms.