How is the density of the first few atomic layers of a metal compared to the bulk material?
Well, it seems this can not be answered in general since there are a bunch of different things which can happen, these are just some of them:
a) deformation, b) and c)superstructure formation, d)facette layers e)incomplete layer It seems to be not that easy at all (source=enter link description here:
"The physical basis of the model is the Smoluchowski smoothing of the electron charge density at the surface. When a crystal is cut to form a surface, the electrons rearrange in order to reduce the charge-density corrugations and by this way their kinetic energy. This leads to a motion of the electrons left on top of the surface atoms downward to the crystal resulting in an electrostatic attraction of the top layer ions toward the rest of the crystal ....
he model as outlined above, however, is not as general as one might be lead to expect,and not as widely applicable as it is often said to be. In particular the closest packed hexagonal surfaces of the fcc and hcp metals often undergo an “anomalous” expansion of the first to second layer distance relative to the bulk interlayer spacing"