Consider now what happens during solidification of
a eutectic alloy.
When T falls below T_{e},
there is a driving force (decrease in free energy)
for liquid of composition C_{e}
to transform to a mixture of a
and b phases. These commonly
form as alternate plates (lamellae) of a
and b (or sometimes,
if the proportion of B is low, as rods of B in an
a matrix) with the plates
or rods oriented parallel to the growth direction.
However, there is energy associated with the a/b
interface created as the eutectic mixture forms
assume a lamellar (platelike) eutectic morphology.
The a/b
interfacial area created per m^{3} is (2/l)
m^{2}, where l
is the lamellar spacing. Therefore, for an interfacial
undercooling of DT_{0}
(= T_{e}  T_{*}),
the net free energy charge is




where g_{ab} is the interfacial energy
(J m^{2}) and DH_{f} is the latent
heat of fusion (J m^{3})  see page
1.2. 

This can be represented on the free energy plot by raising the a
and b curves to account for the energy associated with the a/b interface for a given undercooling, DT_{0}, there will be a minimum lamellar spacing, l_{min}, obtained by setting DG = 0. 

Note that, in writing the above equation, the
kinetic undercooling, needed to drive the atomic absorption process as the interface
advances, is assumed to be negligible  see page
1.6 
The three free energy curves will, for the l = l_{ min} case, have a common tangent (DG
= 0). When T_{c} = T_{e} (i.e. DT_{0}
= 0), then l_{min} ® ¥ and
the free energy curves revert to those in the absence of the interfacial energy
contribution.