  Molecular dynamic simulations were performed for ice Ih with a free surface
by using four water models, SPC/E, TIP4P, TIP4P/Ice and TIP4P/2005. The
behavior of the basal plane, the primary prismatic plane and of the secondary
prismatic plane when exposed to vacuum was analyzed. We observe the formation
of a thin liquid layer at the ice surface at temperatures below the melting
point for all models and the three planes considered. For a given plane it was
found that the thickness of a liquid layer was similar for different water
models, when the comparison is made at the same undercooling with respect to
the melting point of the model. The liquid layer thickness is found to increase
with temperature. For a fixed temperature it was found that the thickness of
the liquid layer decreases in the following order: the basal plane, the primary
prismatic plane, and the secondary prismatic plane. For the TIP4P/Ice model, a
model reproducing the experimental value of the melting temperature of ice, the
first clear indication of the formation of a liquid layer appears at about -100
Celsius for the basal plane, at about -80 Celsius for the primary prismatic
plane and at about -70 Celsius for the secondary prismatic plane.
