Effect of Curvature on Melting Point

Hoop stress in a sphere with a pressure difference. 

A small solid sphere in its melt also feels a similar pressure difference except y now refers to the interfacial energy between the solid and melt. Just as in the case of surface fension, this interfacial energy comes about because of unsatisfied or partially satisfied bonds at the interface which give rise fo a nef radial inward force on the surface atoms. 

From Equations 11.3 and 11.4, the differential Gibbs energies can be written 

Note that the pressure term is absent in the liquid because the pressure is only felt in the solid. Again equating the AG terms to obtain phase equilibrium, we find 

It is also important to imderstand the difference between the lowering of the melting temperature predicted by Equation 11.9 and that predicted by the Clapeyron equation (Equation 11.6). The Clapeyron equation applies when both the solid and the liquid phase are under the same pressure. It predicts a raising of the freezing temperature with pressure of a substance such as a metal that contracts when it freezes. Equation 11.9 applies when only the solid is subjected to pressure such as occurs at the point of contact between 

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