Reversed anisotropies and thermal contraction of fcc (110) surfaces

Abstract

The observed anisotropies of surface vibrations for unreconstructed fcc metal (110) surfaces are often reversed from the “common sense” expectation; for example, atoms in the top layer have larger amplitudes of vibration in the surface plane than normal to it, and the amplitudes normal to the surface are larger for atoms in the second layer than those in the first layer. The source of these reversals is investigated by performing ab initio density functional theory calculations to obtain the surface force constant tensors for Ag(110), Cu(110), and Al(110). The most striking result is a large enhancement in the coupling between the first and third layers of the relaxed surface, which strongly reduces the amplitude of out-of-plane vibrations of atoms in the first layer; the relaxation of interlayer spacings is found to be crucial in order to observe these effects. This enhancement also provides a partial explanation for the thermal contraction of interlayer distances. It is shown that the enhancement in the coupling between the first and third layers, and the consequent anomalous features, can be rationalized by simple geometric arguments.