Solute trapping in rapid solidification
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Introduction For rapid solidification of alloys, one of the key kinetic effects is solute trapping, where solute partitioning decreases across the solid–liquid interfaces. This is described by a velocitydependent partition coefficient k(V), which tends toward unity as velocity V increases.1,2 In addition, solute trapping kinetics alters the kinetic undercooling relationship T(V),3 which in part depends on a phenomenon called solute drag. Solute trapping influences the solidification morphology (dendritic versus cellular versus banded versus planar) and the dendrite or cell size.4 The different approximate solute trapping regimes with illustrations of the solute profiles across the solid–liquid interface, and the solidification growth morphologies, are shown in Figure 1 for a Al-4.5at.%Cu alloy. It becomes crucial to understand solute trapping kinetics in order to control and design rapid solidification microstructures in industrial processes such as thermal spray-coating deposition,5 high cooling rate welding techniques,6 and metal additive manufacturing.7 Metal additive manufacturing is discussed in greater detail in another article in this issue,8 titled “In situ/operando synchrotron x-ray studies of metal additive manufacturing.” This article is organized as follows. First, an overview of the prominent phenomenological solute trapping models is given, focusing on the continuous growth model and the local nonequilibrium model. Next, we present different approaches to parametrize solute trapping kinetics, including molecular
dynamics simulations and pulsed laser melting experiments. Finally, we review methods to better understand rapid solidification microstructures; first through phase-field simulations, and second, with a novel transient imaging technique called dynamic transmission electron microscopy (DTEM).
Theories of solute trapping kinetics Continuous growth model Solute trapping kinetics is best understood in terms of phenomenological solute trapping models, such as the one by Jackson and co-workers,9 and the diffuse interface model by Hillert and Sundman.10 The most popular solute trapping model, however, is the continuous growth model,11 which is amenable to a compact closed-form analytical description when specialized to ideal dilute binary alloys.3 This model makes two predictions: a functional form for the velocitydependent partition coefficient kCGM(V) and a kinetic undercooling relationship TCGM(V). Solidification that follows equilibrium partitioning satisfies ke = CS/CL, where ke is the equilibrium partition coefficient, and CS (CL) is the equilibrium solidus (liquidus) concentration. Under more rapid solidification conditions, the continuous growth model11 uses simple kinetic arguments to predict a velocity-dependent partition coefficient of the form:
(
)(
)
k CGM (V ) = k e + V / V DCGM / 1 + V /V DCGM ,
(1)
Tatu Pinomaa, VTT Technical Research Centre of Finland Ltd., Finland; [email protected] Anssi Laukkanen, VTT Technical Research Centre of Finland Ltd., Finland; anssi.laukkane
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