



The
formation of a second phase involves the interplay of two contributions
to the Gibbs function of the system. As the new phase forms, its radius,
r, increases, and its surface increases as r^{2}.
The surface energy of the nucleus increases as 4pr^{2}g,
where g
is the interphase surface energy. The new phase stable below the transformation
temperature, so that the volume energy of the nucleus is less than that
of the same volume of the initial phase. The volume energy term therefore
decreases the Gibbs function of the system as r^{3}.
For the nucleus of radius r, the volume energy is  (4/3)pr^{3}(DG_{V}),
where DG_{V}
is the volume energy decrease upon creating the new phase.
As
shown, initially the surface energy dominates the process of nucleation
and a nucleus of radius


From:
Ashby and Jones,
"Engineering Materials 2," Pergamon (1986) 