...-phase.¹

It may be supposed that such a metastable composition comes about by cooling a stable composition into a two phase field. Such supercooling can occur because phase transformations are retarded by the time required to form a critical nucleus.

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....²

The volumetric term $\Delta g$ can be determined from the construction in Fig. 24-1 and is necessarily negative for nucleation ( $\Delta g < 0$). Other contributions to free energy, such as stress or composition gradients may exist, and are not included in this simple theory. The surface tension may also vary from absorption of solutes or the existence of interface dislocations--these effects are also ignored here.

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... $\Delta G(R)$³

Further reflection shows that the critical nucleus is not the one that maximizes $\Delta G(R)$. In the spherical example, it was assumed that the particle is always in its most energetically favorable state. In other words, other nuclei shapes would give larger critical nucleus volumes for the same driving forces. Because the shape is energy-minimizing, the critical nucleus size corresponds to the lowest saddle point of $\Delta G$ that separates subcritical nuclei from supercritical nuclei.

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... so⁴

This is the assumption of ``microscopic reversibility.'' It is a bit suspicious to find it in a theory of non-equilibrium processes...

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