Geometry of a Nanoparticle and Nucleation Modes

The phase separation might lead to either the formation of a core-sheU stmcture (as studied here) or to the disintegration into two new nanopartides. The condition to obtain the core-shell structure is that the two phases wet each other. Let us look at the evolution of the surface energy when the core-shell structure appears. The initial surface energy of the particle is equal to  

a is the surface tension of the new free phase, and r is the radius of the parent phase. 

S p is the surface area between the nucleus and the parent phase, and S and Sp are the free surface areas of the new and parent phases, respectively. 

If the atomic densities are practically the same (so that R = R) and (t a, the differences in surface energies between the initial single-phase state and the separated two-phase states are given by  

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