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Eutectic Solidification

  Lateral Diffusion     4 of 9

A further process must occur during eutectic growth, in addition to adsorption onto the solid end formation of the a/b interface.  This is redistribution of solute by diffusion in the liquid close to the advancing front.  Information about the rate at which this diffusion occurs can be used to relate the growth velocity to the undercooling and the lamellar spacing.

The driving force for diffusion must come from the overall free energy charge. Thus, part of the undercooling is used to generate a/b interface (i.e. l > lmin) and the remainder drives the necessary lateral diffusion of solute.

Fixing the spacing l and undercooling DT0 determines the location of the 3 free energy curves. Thus the concentration of liquid in equilibrium with the a phase is defined, as is the concentration of liquid in equilibrium with the b phase. Assuming these compositions to be maintained in the liquid ahead of the centre of each phase, the difference DC between them (together with l) controls the concentration gradient for lateral diffusion.  The relationship between DC and l can be mapped onto the phase diagram, where phase boundaries can be plotted taking into account the interfaced energy (l < ). A relationship is expected of the form lateral_eq1.gif (396 bytes)where DC0 is the concentration difference when l .

Note how, for fixed DT0, progressively increasing the spacing l from its minimum value lmin first increases and then decreases the lateral concentration gradients.


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

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