Two-phase planar and regular lamellar coupled growth along the univariant eutectic reaction in ternary alloys: An analytical approach and application to the Al–Cu–Ag system

Abstract

Unidirectional solidification of ternary eutectic alloys with a composition close to the univariant eutectic reaction under certain conditions leads to two-phase planar growth, showing a lamellar morphology similar to what is known from binary (invariant) eutectic growth. In the latter case, the most applied analytical description is the Jackson–Hunt model. The present paper extends this model to steady-state two-phase planar and regular lamellar coupled growth in the case of the univariant eutectic reaction in ternary alloys as obtained during unidirectional solidification. It is shown that during steady state, a similar expression between the lamellar spacing λ and the growth velocity v, i.e., λ2v= constant, describes the spacing selection whenever minimum undercooling is assumed. The constant is only dependent on the material properties of the selected alloy. The theory is applied to growth along the univariant reaction L→α(Al)+θ-Al2Cu in Al–Cu–Ag alloys resulting in a good agreement between the calculations and the experimental results. However, some uncertainties concerning the variation of the material properties, in particular, the interfacial properties, remain when going from the binary system towards ternary univariant growth. So, finally a sensitivity analysis is made, being a good solution to show the effect of a change in alloy and material properties on the eutectic growth morphology, e.g., by a change in the amount of the alloying elements.