Lattice strain at c-Si surfaces: a density functional theory calculation
  The measurement of the Avogadro constant by counting Si atoms is based on the assumption that Si balls of about 94 mm diameter have a perfect crystal structure up to the outermost atom layers. This not the case because of the surface relaxation and reconstruction, the possible presence of an amorphous layer, and the oxidation process due to the interaction with the ambient. This paper gives the results of density functional calculations of the strain components orthogonal to crystal surface in a number of configurations likely found in real samples. 
Claudio Melis, Luciano Colombo, Giovanni Mana
cond-mat.mtrl-sci