Properties of the Surface Region of a Metal Crystal

Total-energy calculations from first principles have been made on a seven-atomic-
layer slab of Mo(001) as a function of the in-plane lattice parameter with full relaxation
of the layer spacings. The energy minimum gives the equilibrium state of the
slab, which contracts both in-plane and out-of-plane between one and two percent with
respect to bulk. The energy changes under deformation from equilibrium are treated
as strain energies and are fitted to a composite elastic model consisting of two surface
regions and a bulk region, each with its structural and elastic parameters. These parameters
are evaluated in a separate calculation for the bulk region, so that subtracting
the known bulk strain energies from the total strain energy permits evaluation of the
parameters of the surface region. Six deformations of the slab around equilibrium give
the six elastic constants of the tetragonal surface regions. The surface region material
is about two atomic layers deep, slightly prolate in its own equilibrium state, substantially
elastically anisotropic compared to cubic symmetry, stable, but considerably weaker
elastically and closer to instability than bulk.