Consider now what happens during solidification of
a eutectic alloy.
When T falls below Te,
there is a driving force (decrease in free energy)
for liquid of composition Ce
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 (plate-like) eutectic morphology.
The a/b
interfacial area created per m3 is (2/l)
m2, where l
is the lamellar spacing. Therefore, for an interfacial
undercooling of DT0
(= Te - T*),
the net free energy charge is
 |
 |
|
|
| where gab is the interfacial energy
(J m-2) and DHf 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, DT0, there will be a minimum lamellar spacing, lmin, 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 Tc = Te (i.e. DT0
= 0), then lmin ® ¥ and
the free energy curves revert to those in the absence of the interfacial energy
contribution.
