Effects of local non-equilibrium solute diffusion on rapid solidification of alloys

Abstract

A conceptual foundation for the study of local non‐equilibrium solute diffusion under rapid solidification conditions is proposed. The model takes into account the relaxation to local equilibrium of the solute flux and incorporates two diffusion speeds, VDb, the bulk liquid diffusion speed, and VDi, the interface diffusive speed, as the most important parameters governing the solute concentration in the liquid phase and solute partitioning. The analysis of the model predicts complete solute trapping and the transition to a purely thermally controlled solidification, which occur abruptly when the interface velocity V equals the bulk liquid diffusion speed VDb. The abrupt change in the solidification mechanism is described by the velocity dependent effective diffusion coefficient D* = D(1 ‐ V2/V2Db) and the generalized partition coefficient K*. If V > VDb, then D* = 0 and K* = 1. This implies an undisturbed diffusion field in the liquid (diffusionless solidification) and complete solute trapping at V > VDb. The interface diffusion speed VDi governs solute redistribution at a relatively low interface velocity V ∼ VDi < VDb. The influence of the local non‐equilibrium solute transport on the temperature field and interface stability under rapid solidification conditions is also discussed.

Extended thermodynamical analysis of a motion of the solid-liquid interface in a rapidly solidifying alloy

“…26,27 In the local equilibrium limit, i.e., when the bulk diffusive speed is infinite, V D →ϱ, expression ͑40͒ reduces to the function k(V), which takes into account the deviation from local equilibrium at the interface only, Eq. ͑39͒.…”

Boron Partitioning Coefficient above Unity in Laser Crystallized Silicon

“…Local bonding fluctuation in liquid Si was identified as the underlying physical mechanism [21,22,27]. However, while the models in these works indeed reproduce the reported respective experimental results, they cannot give a particular value of the partitioning coefficient for a specific solidification velocity, as is possible with the solute trapping models [10,14,15,16,17,18]. …”

Kinetic Phase Diagrams of Ternary Al-Cu-Li System during Rapid Solidification: A Phase-Field Study

“…Experimental results for alloys during rapid solidification show that under this non-equilibrium condition, solute concentration could differ significantly from that given by the equilibrium phase diagram. This effect in rapid solidification, known as “solute trapping” [ 3 , 5 ], has been studied extensively by experimental [ 6 , 7 ], theoretical [ 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 ] and numerical methods [ 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 ].…”

“…Aziz et al [ 8 ] formulated a continuous growth model (CGM) by considering the flux balance across the moving solid-liquid interface, and predicted the velocity-dependent solute segregation coefficient k ( V ) at different interface moving velocities V s. By combining chemical rate theory, the CGM was employed to predict the kinetic interface condition diagram for ideal solution systems and binary Ag-Cu systems without/with solute drag effects [ 9 ]. Later on, Sobolev proposed a local-non-equilibrium model (LNM) [ 10 , 11 , 14 , 15 , 16 ], which took into account the relaxation to local equilibrium of the solute flux under rapid solidification conditions. The model predicted the abrupt transition to diffusionless and partitionless solidification with complete solute trapping when the interface velocity V reached the bulk liquid diffusion velocity V D [ 10 , 11 , 14 , 15 , 16 ].…”