The net velocity is given by the
difference between these two. 
Elementary diffusion theory relates the jump frequency to the diffusion coefficient and
the jump distance 
so that, assuming l* @ lL @ d (molecular
diameter), the velocity can be written as 
which is
often termed the Wilson-Frenkel equation.
Since DGf
is given by DHf DT / Tf
(page 1.2) and assuming DT is small, so that the approximation
1 - exp(-x) @ x for small x
can be used, this equation reduces to: 
Typical data: |
 |
Even a relatively high velocity of @ 1 mm/s thus requires a (kinetic) undercooling of only about
0.1K. Conversely, if a melt is significantly undercooled before a crystal forms, the
initial growth rate will be very fast. |
