It has become clear that, for a given undercooling DT_{0}, various combinations of
interlamellar spacing l and growth velocity V are possible. However, there is a particular
spacing which gives a maximum velocity. This can be found by evaluating dV/dl and setting it
equal to zero. 

When a spacing is adopted which gives this maximum velocity, growth is
said to be occurring under extremum conditions. It can be seen that the extremun spacing
is given by l_{e} = 2l_{min} 
This is also the spacing of which, for a fixed
velocity, growth would be taking place with the minimum interfacial undercooling. 


In practice, most eutectic systems tend to solidify at the extremum.
Substitution of the above expression for l into the equation
relating V to l
now gives 

which, using the relationship between l_{min} and DT_{0} can be written as 

or, expressed in terms of the expected spacing l
(=l_{e}) 

The RHS of this equation is a constant for a given system. It
typically has a value of about 10^{16} m^{3} s^{1}. Clearly
faster growth leads to finer lamellar spacings. 