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
|
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 |
|
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
