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Eutectic Solidification

  Growth Velocity     5 of 9
 

A semi-quantitative analysis can now be applied relating the growth velocity to these compositional effects. Since the advance velocity of the font is dependent on the rate of solute partitioning in the liquid, and hence to the lateral flux of solute (= D C/y), we can write

growth velocity

 

velocity_eq1.gif (342 bytes)

where B1 is a constant and DL is taken as the interdiffusion coefficient for both solutes.
Using the relationship between DC and l given on the previous page, and noting that DC0 is proportional to DT0 (see phase diagram) this leads to

velocity_eq2.gif (454 bytes)

where B2 is another constant, which is found in practice to have a typical value of about 0.1 K-1. Since lmin is known (Click here to see), this allows V to be evaluated for given DT0 and l. The animation, on the next page, shows how V changes as l is increased from lmin

 

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

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