E5 Binary Phase Diagram

Topic

The binary phase diagram for this alloy—which provides more detail than the lever rule used in another model within this set—also establishes the alloy's transformation temperatures and the maximum solute solubility for each phase at any given temperature. Between the solid and liquid solubility curves, this diagram defines the solute partition coefficient—the ratio of the solute concentration in the solid to that in the liquid when both are in equilibrium at the same temperature. Because this partition coefficient is less than one (meaning the solid accommodates less solute than the liquid at equilibrium), the solid rejects solute into the remaining liquid as the metal solidifies.

Furthermore, because the rejected solute does not have time to redistribute via diffusion within the solid itself—as solid-state diffusion is much slower than the solidification process—segregation occurs during solidification, as described by the Scheil equation. Solute rejected by each newly formed solid layer accumulates in the remaining liquid, which becomes increasingly enriched; consequently, the solid formed at the end of the process contains significantly more solute than the solid formed at the beginning. The further this partition coefficient deviates from one, the more severe this solidification segregation becomes, according to the Scheil equation. This same segregation—and, more generally, any deviation between the local composition of this alloy and its equilibrium composition as defined by this binary phase diagram—generates a relative supersaturation that drives any subsequent phase transformation: the further the alloy's local composition deviates from its equilibrium composition, the more free energy is available to propel that phase transformation back toward equilibrium. A higher degree of relative supersaturation results in a greater driving force for the phase transformation, causing it to proceed more rapidly.

For this reason, the present model—incorporating the binary phase diagram and partition coefficient introduced at the outset—serves as the foundation for another model in this set that describes the alloy's solidification from the liquid state in detail. That subsequent model utilizes the transformation temperatures and partition coefficient established here, as well as the resulting segregation (calculated via the Scheil equation) and the driving force generated by that segregation, to describe the step-by-step progression of the solidification process.

ID:4431