A new concept for growth restriction during solidification

Abstract Growth restriction refers to the phenomenon of reduced growth velocity due to the solute enrichment/depletion at the solid/liquid interface during alloy solidification. Although significant progress has been made to understand this phenomenon, so far there has been no effective parameter to quantify growth restriction. In this paper, we have derived a new parameter, β, to quantify the growth restriction in multicomponent systems effectively, and which incorporates the nature of solutes, solute concentrations and solidification conditions holistically. Theoretical analysis and phase field simulations have confirmed that growth velocity is a unique function of β regardless of the nature of solutes, solute concentrations and solidification conditions, but it is not a unique function of the widely used growth restriction factor, Q. Our analysis suggests that the overall β for a multicomponent alloy system can be either calculated accurately by the ratio of the liquid fraction to the solid fraction (β = fL/fS) or approximated with great confidence by a linear addition of the β values of the constituent binary systems. In addition, we have shown theoretically that for a given alloy system solidifying under a given undercooling, there is a critical solute concentration, below which solidification becomes partitionless and therefore there is no growth restriction during solidification. Furthermore, our analysis has shown that the physical origin of growth restriction is the blockage of the supply of the critical elements for crystal growth, i.e., solvent atoms in the case of eutectic-forming.