Analytical multicomponent microsegregation model for equiaxed globular growth with diffusion interaction between species

Abstract : In casting processes, the development of one solid phase from the liquid gives rise to microsegregation. The liquid is enriched in solute species that diffuse to/from the solid/liquid interface. In multicomponent alloys, this enrichment mainly controls the solidification path and plays a major role for the estimation of the nature and amount of secondary phases. While numerical models usually rely on few approximations [1], analytical models also remain of interest for coupling with large scale simulations of casting processes [2]. Several models have been proposed to predict microsegregation [3]. However, very few models have been applied to multicomponent alloys and coupled with thermodynamic equilibrium calculations [4]. Moreover, interaction between species (or cross diffusion phenomena) is always neglected. We propose an analytical solution for a multicomponent microsegregation model with interaction between species. This paper relies on the approximation developed by Martorano et al. [3] initially proposed for binary alloys. The model is coupled with an energy balance and applied to simulate globulitic grain solidification in a ternary alloy during a cooling process. The influence of the cross-diffusion terms in the liquid diffusion matrix is demonstrated. A comparison is also provided with an exact solution using a front tracking method. References [1]Q. Chen, B. Sundman, Materials Transactions 43 (2002) 551-559 [2]H. Combeau, M. Zaloznik, S. Hans, P.-E. Richy, Metall. Mater. Trans. B 40 (2009) 289-304 [3]M.A. Martorano, C. Beckermann, Ch.-A. Gandin, Metall. and Mater. Trans. A 34 (2003), 1657-1673, 35A (2004) 1915 [4]H. Zhang, Ch. A. Gandin, H. Ben Hamouda, D. Tourret, K. Nakajima, J. He, ISIJ International 50 (2010) 1859-1866