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Ursula Kattner
Bill Boettinger
Dilip Banerjee
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Scheil Solidification
For the solidification of a solid phase, solution of the multicomponent
Scheil equation requires finding the composition of the liquid phase, CLi(T),
and fraction solid, fS(T).
The Scheil solidification path is usually approximated by
stepping through the temperature interval of interest and assuming
local equilibrium to exist at the liquid/solid interface for each
temperature
step. In the first step, the liquidus temperature of the initial
alloy
composition is determined and in subsequent small temperature steps,
the
fraction solid is obtained from a lever rule calculation using the
liquidus
composition from the previous step. The actual increment of
fraction
solid is the product of that obtained from the lever calculation with
the
fraction liquid remaining. Similarly, for two phase
solidification,
increments of solid fraction of the two phases are found from the three
phase
equilibrium condition. The calculation of the enthalpy vs. temperature
during Scheil solidification requires that the variations in the
compositions within the accumulated solid phases
be considered. Ideally the calculated compositions and increments of
solid
phase fraction are stored for each temperature step and the enthalpy is
then calculated for the current temperature from the summation of the
enthalpies
of all solidified "layers" and the remaining liquid phase. This
procedure
is very time consuming. This problem can be avoided by averaging the
composition for each individual solid at each temperature step. The
enthalpy is then calculated using the average composition and the total
fraction solid of each phase. Since no diffusion is allowed in
the solid phases,
stepping is usually stopped after a eutectic equilibrium has been
encountered
or a predetermined fraction of solid phases has formed. However,
calculation of the enthalpy may be continued if the results
are needed for other calculations such as process simulations.
Examples for the Scheil paths of Ni-Al-Ta and Sn-Bi-Pb alloys
are shown.
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