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E NODULES NUCLEATION KINETICS AND RELATED SOLIDIFICATION DEFECTS IN SGI CASTINGS A. Heterogeneous Nucleation of Graphite Nodules

IN

the homogeneous single component melt, the liquid-solid transformation upon undercooling (DT) below the equilibrium solidification temperature (Ts) begins with randomly formed clusters. Clusters that are too small to survive are called embryos. This happens because of a positive increase of Gibbs surface energy (DGA) by the formed solid-liquid interface (A) is more than negative gain of Gibbs volume energy (DGV): DGA ¼ A sl

½1

DGV ¼ VqLDT=Ts

½2

where  sl is the surface energy of liquid-solid interface, V is volume, q is density, and L is latent heat per unit of mass.

SIMON N. LEKAKH is with the Missouri University of Science and Technology, 1400 N. Bishop, Rolla, MO, 65409. Contact e-mail: [email protected] Manuscript submitted September 27, 2017.

METALLURGICAL AND MATERIALS TRANSACTIONS B

When the embryos are sufficiently large to be stable (DG = DGV+ DGA< 0) they are termed nuclei. For spherical nuclei, a critical radius Rc at homogeneous nucleation barrier is: Rc ¼ 2 sl Ts =qLDT

½3

DT ¼ 2C=Rc

½4

where C =  slTs/qL is the Gibbs-Thomson coefficient. In the seminal article[1] Turnbull evaluated  sl and C for several homogeneously nucleated metals from experimentally measured maximum supercooling achieved in small droplets. Recently, Hashimoto et al.[2] confirmed these predictions using molecular dynamic simulation of solid-liquid interface. Homogeneous nucleation from stochastically formed nano-meter scale embryos requires a deep undercooling of the pure melt to pass the energy barrier. Therefore, a few degrees undercooling, which is typically observed in the technical alloys, indicates heterogeneous nucleation on existing micron-sized particles. Classical heterogeneous nucleation models assume that the melt above the liquidus temperature has ready potential nucleation sites with normal size distribution. In this case, heterogeneous nucleation will continue upon melt cooling below the liquidus temperature for a short initial period until a system reached a maximal undercooling (DTmax). The nucleation event will stop after that because all nucleation

sites are used up and the melt temperature in solidified casting will increase because latent heat liberation. In some cases, additional nucleation could be possible in the last portion of undercooled melt when DT > DTmax. Using the classical approach to simulate SGI solidification, Fras et al.[3] suggested that nuclei will grow on the flat substrates with size (l) during undercooling if: l>2Rc sinðhÞ

½5

where: h is a contact angle. This approach does not consider continuous nucleation after maximal undercooling. However, Chisamera et al.[4] found that the Fe-Si inoculation with Ce, Ca, S, O additions provided bi-modal nodule size distribution. Fewer large nodules formed at the start of solidification and a high number of much smaller nodules formed later toward the end of solidification were observed. Pederson et al.[5] a