A Novel Approach to Determine Variable Solute Partition Coefficients
- PDF / 1,884,751 Bytes
- 10 Pages / 593.972 x 792 pts Page_size
- 74 Downloads / 205 Views
THE partitioning of solute elements during the solidification of alloys has a significant effect on microstructural evolution and can result in an array of detriments including the formation of undesirable phases,[1,2] increased susceptibility to solidification cracking,[3,4] and heterogeneous resistance to corrosion.[5,6] Proper characterization of this segregation is vital to understand and predict the microstructure and properties of cast and welded alloys. Previous studies have shown that many alloys solidify under non-equilibrium conditions due to the slow diffusion of substitutional solute elements in these processes.[7] This is especially true for austenitic alloys and for processes that involve moderate to high cooling rates.[8,9] Non-equilibrium solidification conditions assume complete diffusion in the liquid, negligible diffusion in the solid, local equilibrium at the solid-liquid interface, and no dendrite tip undercooling during solidification.[10] The lack of solid-state diffusion in this model corresponds to the most severe representation of
C.J. FARNIN, S. ORZOLEK, and J.N. Dupont are with the Lehigh University, Bethlehem, PA 18015. Contact e-mail: [email protected] Manuscript submitted June 9, 2020.
METALLURGICAL AND MATERIALS TRANSACTIONS A
solute partitioning and is described by the Scheil equation shown in Eq. [1]: CL ¼ C0 fLk1 ;
½1
where CL is the concentration of solute in the liquid, C0 is the nominal composition, fL is the fraction of liquid, and k is the partition coefficient. Due to its exponential relationship with the liquid concentration, the partition coefficient is a vital parameter in solidification modeling to quantify the extent of segregation for each element in a system. Described by the ratio between the solid and liquid concentrations, k is defined by Eq. [2]: k¼
Cs ; CL
½2
where Cs is the concentration of solute in the solid. Elements for which k < 1 partition to the liquid during solidification leaving the dendrite cores depleted of solute. Elements for which k > 1 partition to the solid, leading to solute enrichment of the dendrite cores. In addition to the Scheil equation, many other models have been developed to account for a variety of phenomenon which occur during solute redistribution. For example, Clyne and Kurz[11] built upon the model developed by Brody and Flemings[12] to incorporate solid-state diffusion into a solidification model. Kurz and Fisher,[13] and Smith et al.[14] developed equations
to account for the effects of incomplete mixing in the liquid phase during solidification. Despite their differences, each model is dependent on the partition coefficient to describe the segregation of solute between the solid and liquid phases. Proper characterization of k is thus essential for the use of these models to describe the solute segregation during solidification. Due to the difficulty associated with measuring the concentration of the liquid, the partition coefficient at the start of solidification (kinit) is often estimated by assuming CL is equal to the nominal composition (C0).
Data Loading...
