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The local curvature of the Gibbs free energy of solution with respect to composition
determines whether an unstable composition will achieve stability by small widely-spaced
composition fluctuations or large isolated fluctuations in composition. The later
is an important process called nucleation.
For the case of nucleation of very small nucleating particles, one needs to consider the
extra energy associated with a surface of the particles.
This extra energy has to be overcome by a decrease in the Gibbs free energy of the
This leads to the possibility of under-cooling and the prediction of minimum size
of a particle (a nucleus) that can grow.
W. Craig Carter