Mechanism of Nanoshell Shrinkage

It is energetically favorable for a nanoshell to shrink into a compact nanosphere as the interface area is reduced, i.e., if the inequality 

Here y is the surface tension, qo and r o are the initial internal and external radii of a nanosheU, and rf is the final radius of the collapsed particle. 

The proposed atomistic mechanism of shrinkage is the vacancy flux from the internal surface (with radius q) to the external surface (with radius Tg). The driving force of the vacancy flux is the difference in vacancy/atoms chemical potentials and the corresponding difference in equilibrium vacancy concentrations at the curved interfaces Cv(ri) cy(re). This Gibbs-Thomson effect can be expressed, in a linear approximation so far, as 

for the case of nanosheUs of a single element, the physical picture of shrinkage seems to be very clear. It is analogous to the LSW theory of caking [14], 

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