Mathematical modeling of solidification paths in ternary alloys: Limiting cases of solute redistribution

Abstract

A simple mathematical framework is provided for calculating solidification paths of ternary alloys for equilibrium, paraequilibrium, and nonequilibrium conditions. The results are useful for estimating the possible range of primary solidification paths, the type of monovariant reaction expected to occur, and the relative amount of primary, monovariant eutectic and ternary eutectic constituents that form during solidification. Example calculations show that, for solidification of a ternary eutectic alloy under equilibrium conditions, the monovariant eutectic reaction will only occur when the nominal alloy concentration is above the maximum solid solubility. This result is similar to the binary case. For paraequilibrium conditions, a monovariant eutectic reaction is always expected to occur, but solidification can terminate before the invariant ternary eutectic reaction is reached. Finally, for nonequilibrium conditions, both the monovariant and invariant ternary eutectic reactions are always expected to occur, which is similar to the binary nonequilibrium case. The direction of liquid enrichment on the monovariant eutectic line can also be determined from the results.