Hello Malathe,
The surface energy, sigma, for a slab with a thickness of K unit cells
(or supercells) is given by E(K) = (2A)*sigma + K*E(b) where A is the surface
area of the unit cell (or supercell) and E(b) is the energy of the bulk unit
cell (or supercell). Here E(K) is the total energy per slab unit cell (or
supercell). This assumes that the slab is symmetric so that both surfaces are
the same. Also, it has been noted (V. Fiorentini, M. Methfessel, J. Phys.:
Condens. Matter 8 (1996) 6525) that one can't simply use E(b) from a
calculation for a bulk (three-dimensional) material. The correct thing to do is
to compute E(K) vs. K for increasing values of K until linear behavior is
observed and then to extrapolate to K=0 to get (2A)*sigma.
Hope this helps.
Vic Bermudez
U.S. Naval Research Lab. (retired)
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