*3.2. Local Equilibrium*

In LE [17], the chemical potential μ of carbon and substitutional element across the interface is constant, i.e.,

$$
\mu\_i^a = \mu\_i^\circ \tag{3}
$$

where μ is the chemical potential; the subscript i represents C or M. Due to the large difference in diffusivity between C and M, the LE is further classified into two types: negligible partition local equilibrium (NPLE) and partition local equilibrium (PLE). The Fe-C-Cr system, where Cr is a ferrite stabilizer, is used here for further elaboration.

In NPLE, as shown in Figure 3, the specific tie-line always connects the product phase with the Cr concentration of uCr0. Therefore, the product phase achieves the same Cr content as that in the bulk of the parent phase, and a positive or negative "spike" exists in front of the moving interface. When the interface is under NPLE, only local redistribution of Cr is required, and the transformation kinetics are controlled by carbon diffusion in the parent phase.

**Figure 3.** Schematic isotherm and concentration distributions depicting the (**a**) austenite-to-ferrite; (**b**) ferrite-to-austenite transformation under the negligible partition local equilibrium (NPLE) condition.

On the contrary, when partition of Cr takes place between the parent and product phase, as shown in Figure 4, long diffusion of Cr in the parent phase is necessary while a constant carbon activity is achieved from the interface to the bulk of the parent phase. In this case, the transformation is under PLE mode and the sluggish diffusion of Cr in the parent phase becomes the decisive step in controlling the kinetics.

**Figure 4.** Schematic isotherm and concentration distributions depicting the (**a**) austenite-to-ferrite; (**b**) ferrite-to-austenite transformation under the partition local equilibrium (PLE) condition.
