Microsegregation Measurement: Methods and Applications
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OSEGREGATION is chemical variation at the microstructural level in a solidified ingot driven by the difference in solubility for solute elements between the solid phase forming during solidification and the liquid phase. Under most solidification conditions, equilibrium can be assumed to exist at the solid/liquid interface, and the concentrations of solid, CS and liquid, Cl ; for any given element at the interface, can be used to define a partition ratio, k[1]: k¼
CS ; Cl
½1
where C is composition; subscripts S and l indicate solid and liquid, respectively; and superscript * indicates a quantity at the solid/liquid interface. Solute–elements can preferentially segregate either to liquid or solid phases with the direction of segregation defined as
RICHARD SMITH is with Carpenter Technology, P.O. Box 14662, Reading, PA 19612. Contact e-mail: [email protected] Manuscript submitted May 21, 2018.
METALLURGICAL AND MATERIALS TRANSACTIONS B
Positive segregation solute goes to liquid: k < 1, Negative segregation solute goes to solid (depletes in liquid): k > 1. The left-hand side of a generic binary phase diagram of components A and B is shown in Figure 1. Liquidus, solidus, and eutectic lines are indicated. The freezing point of pure solid A is indicated by Tf. Following the vertical solidification path indicated by line a–a, for an alloy with composition Ca, when the liquidus line is reached, solid (labeled a) with a composition of kCa starts to form. Again, if local equilibrium exists at the solid/liquid interface, the concentrations of the solid and liquid at the interface can be determined off the liquidus and solidus lines at a given temperature. For example, at temperature T1 in Figure 1, the compositions of the solid at the interface, CS ¼ Csol;T1 and liquid at the interface, CS ¼ Cliq;T1 are indicated, with k at that temperature being equal to Csol,T1/Cliq,T1. In addition, if equilibrium solidification is occurring for the system, with complete diffusions in solid and liquid phases at that temperature, Csol,T1 and Cliq,T1 represent the overall compositions of the solid, a, and liquid phases, respectively, at that temperature. Similar behavior is initially exhibited for solidification of the alloy with composition Cb, following the line indicated by b–b, forming proeutectic a phase until the eutectic temperature is
Fig. 1—Diagram of left-hand side of a binary phase diagram for hypothetical elements A and B. Tf is the freezing point of pure alloy A. Line a–a (composition Ca) denotes solidification from liquid to solid phase a, and line b–b (composition Cb) denotes solidification to proeutectic phase a, and eventually to eutectic a and b.
reached. Again, if equilibrium solidification is occurring, the increase in solute level in the solid and liquid phases can be determined by the phase diagram along with the amount of eutectic phase that forms. If a nonequilibrium condition exists, for example, due to a lack of diffusion of the solute element in the solid away from the interface, composition variations ca
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