Phase Transformations in Nanosystems

As follows from the previous analysis, when dealing with the thermodynamics of nanoparticles it is necessary to specify the size range under discussion. Indeed, in the literature the term nanopaiticle is used for particles having sizes from 1 nm (a few atoms) up to 500 nm. The behavior of nanoparticles at the margins of the indicated size range is very different Here we treat cases where the thermodynamic description remains valid. This requirement implies the following  

The overall radius of the nanoparticle is relatively large (R 2 nm) so that the number of atoms is sufficient large allowing one to apply the thermodynamic approach. 

The radii of the core and the shell of a nanosystem are also relatively large. The surface of the core is characterized by a single value of the surface tension. This condition is met when the particle is either rounded or, conversely, presents the shape of a regular polyhedron with the same kind of facets [60]. The difference between the surface tension and specific surface free energy is neglected. 

In the present section, we introduce a thermodynamic model of phase separation in a nanoparticle and analyze how the depletion effects can be taken into account The last part is devoted to the analysis of the influence of size and depletion on phase diagrams of regular solutions. In the Appendix, we present the rule of parallel tangents construction (not to confuse with common tangent rule) for the extreme points of the phase transition. In the following, the starting single phase is called old or parent phase and the newly formed phase is called new one. 

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