Lattice relaxation at a metal surface

It is shown that all interatomic potentials of the classical type---Morse, Lennard-Jones, etc.,---yield, by their very nature, an expansion of the interlayer separation between the topmost surface layers. No such prediction can be made a priori for the oscillatory-type potentials. Using a simple procedure to compute the relaxations, we also show that Friedel's tight-binding model for transition metals yields contraction for the (100), (110), and (111) surfaces of a face-centered-cubic transition metal, a result in agreement with experiment.