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Cell dendrite & grain structure

  Constitutional Undercooling     1 of 5
 
An important consequence of this accumulation of solute is that it can cause the front to break down into cells or dendrites. This occurs because there is a liquid ahead of the front with lower solute content, and hence a higher freezing temperatures than liquid at the front.

As a solidification front advances, solute is redistributed at the interface. Commonly, solute is rejected into the liquid, where it accumulates into solute boundary layer.

Depending on the temperature gradient, such liquid may be undercooled below its freezing temperature, even though it is hotter than liquid at the front. This is termed constitutional undercooling, to emphasize that it arises from variations in liquid composition.

Once constitutional undercooling occurs, the plane front becomes unstable, since a bump on the interface penetrates into undercooled liquid, where it grows more quickly.

The condition for constitutional undercooling to occur may be written in terms of the thermal gradient across the interface, G -------------
where mL is the gradient of the liquidus line on the phase diagram (usually negative). The gradient of the liquidus temperature thus depends on the solute profile which has been set up. For example, if the steady state profile derived in page 2.2 has been established --------------
then the constitutional undercooling criterion can be written as ------------
or, expressed as a critical (maximum) velocity for the avoidance of constitutional undercooling ------------------
 

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

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