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Solidification Kinetics

  Growth Velocity (ii)     7 of 7

The net velocity is given by the difference between these two. image44.gif (1719 bytes)

Elementary diffusion theory relates the jump frequency to the diffusion coefficient and the jump distance image16.gif (1013 bytes) so that, assuming l* @ lL @ d (molecular diameter), the velocity can be written as image45.gif (1244 bytes)  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: image46.gif (1266 bytes)

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.



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

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