Modelling surface melting of macro-crystals and melting of nano-crystals for the case of perfectly wetting liquids in one-component systems using lead as an example

It is known that the majority of crystals melt without superheating. It is because liquids usually perfectly wet their own crystals, leading to surface melting at a lower temperature compared to the bulk melting point of the same crystal. In this paper first this phenomenon is modelled. The equilibrium thickness of the liquid nano-layer is found to approach asymptotically infinity as temperature approaches the bulk melting point of the macro-crystal. Further, the size of the solid crystal is gradually reduced below 100 nm and the size dependence of melting nano-crystals is modelled. Calculations are performed for pure lead (Pb), for which experimental results were published for both of the above mentioned phenomena. The validity of our models is confirmed by these literature experimental results. Co-existence of a core solid and a liquid shell is found in a finite temperature range below the macroscopic melting point in one-component nano-systems, explained by the extended phase rule of Gibbs. The lower temperature of this T-range is called here the solidus temperature, while the upper temperature of this T-range is called here the liquidus temperature of the one-component nano-crystal. Both the solidus and liquidus temperatures of the nano-crystal decrease with decreasing particle size and merge together at a critical particle size (found at 4.7 nm and at 493 K for pure lead with bulk melting point of 600.6 K). Below this critical size the nano-particle melts at a single temperature. A general rule is established claiming that when a one-component macro-crystal melts with surface melting, then the same nano-crystal melts with a solid-liquid co-existence within a finite temperature range and vice versa. Three principle types of binary nanophase diagrams are predicted for each type of macro-phase diagram, depending on whether the two components melt with or without surface melting.