|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
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