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Eutectic Solidification

  Minimum Spacing     2 of 9
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
minspacing_eq1.gif (390 bytes)
minimum spacing
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. minspacing_eq2.gif (324 bytes)
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.


  Kinetics | Redistribution | Cell, dendrite and grain structure | Eutectic

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