Plane Front Solidification Scheil Equation

We now consider the details of the solid-liquid growth front in more depth. As a solidification process proceeds, the boundary between the solid and liquid phases progressively advances through the volume of the material until the whole material 

LIQUID-SOLID AND SOLID-SOLID PHASE TRANSFORMATIONS 

FIGURE 6.32 Plane front solidification of an isomorphous binary alloy system, (a) As the 

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During a plane front solidification process, partitioning of species between the solid and liquid phases can take place, which results in a nonuniform compositional profile at the end of the solidification process. The severity of the compositional nonuniformity depends on the degree of solute partitioning between the solid and the liquid as well as the rate of solidification relative to the rate of solid-state diffusion. If solid-state diffusion is fast, then the composition gradient in the solid can be quickly erased, leading to a more uniform composition profile. However, in most cases, solid-state diffusion is slow compared to solidification, and thus these nonuniform composition gradients tend to be frozen in. The Scheil equation provides a way to model the nonuniform concentration profile that arises in such a plane front solidification process ... 

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