  We computed a Lennard Jones frozen liquid with a free surface using classical
molecular dynamics. The structure factor curves on the free surface of this
sample was calculated for different depths knowing that we have periodic
boundary conditions on the other parts of the sample. The resulting structure
factor curves show an horizontal shift of their first peak depending on how
deep in the sample the curves are computed. We analyze our resulting curves in
the light of spatial correlation functions during melting and at when the
liquid is frozen. The conclusion is that near the free surface the sample is
less dense than in the bulk and that the frozen liquid surface has a spatial
correlation which does not differ very much from that of the bulk. This result
is intrinsic to the melting of the Lennard Jones liquid and does not depend on
any other parameter.
