A novel treatment of solute drag and solute trapping at a solid-liquid interface during rapid solidification of multicomponent alloys

Abstract

In response to the renewed interest in solute drag and solute trapping models fueled by their applications to additive manufacturing, a novel treatment is proposed to describe the diffusional behaviors of solute at a migrating solid-liquid interface during rapid solidification of multicomponent alloys. While the treatment is still built on irreversible thermodynamics and linear kinetic law, its novelty lies in breaking up the classical trans-interface diffusional flux into two separate fluxes one is the transferred-back flux with its ending point at the interface and the other is the bumping-back flux with its starting point at the interface. This novel treatment entails three significant improvements in reference to the existing models. Firstly, it reveals that the degree of solute drag is dependent on the ratio of liquid diffusive speed over interface diffusive speed. Secondly, a novel relation between the distribution coefficient and interface velocity is derived. It amends the confusing behavior seen in Aziz’s without-drag continuous growth model. Thirdly, the proposed treatment eliminates the need of prescribing the degree of solute drag parameter for the kinetic phase diagram calculation. The numerical solution to the proposed model is presented, and it is ready to be used for the kinetic phase diagram calculation.

Keywords

3D printing / CALPHAD / kinetic phase diagram / microstructure simulation / rapid solidification / solute drag and trapping

References

[1] Hillert M, Sundman B. A solute-drag treatment of the transition from diffusion-controlled to diffusionless solidification. Acta Metall. 1977; 25(1): 11-18.

[2] Aziz MJ, Kaplan T. Continuous growth model for interface motion during alloy solidification. Acta Metall. 1988; 36(8): 2335-2347.

[3] Aziz MJ, Boettinger WJ. On the transition from short-range diffusion-limited to collision-limited growth in alloy solidification. Acta Metall Mater. 1994; 42(2): 527-537.

[4] Hillert M, Rettenmayr M. Deviation from local equilibrium at migrating phase interfaces. Acta Mater. 2003; 51(10): 2803-2809.

[5] Hillert M, Odqvist J, Ågren J. Interface conditions during diffusion-controlled phase transformations. Scripta Mater. 2004; 50(4): 547-550.

[6] Hillert M, Sundman B. A treatment of the solute drag on moving grain boundaries and phase interfaces in binary alloys. Acta Metall. 1976; 24(8): 731-743.

[7] Liu Z-K, Ågren J. On the transition from local equilibrium to paraequilibrium during the growth of ferrite in Fe-Mn-C austenite. Acta Metall. 1989; 37(12): 3157-3163.

[8] Purdy GR, Brechet YJM. A solute drag treatment of the effects of alloying elements on the rate of the proeutectoid ferrite transformation in steels. Acta Metall Mater. 1995; 43(10): 3763-3774.

[9] Hareland CA, Guillemot G, Gandin C-A, Voorhees PW. The thermodynamics of non-equilibrium interfaces during phase transformations in concentrated multicomponent alloys. Acta Mater. 2022; 241:118407.

[10] Guillemot G, Senninger O, Hareland CA, Voorhees PW, Gandin C-A. Thermodynamic coupling in the computation of dendrite growth kinetics for multicomponent alloys. Calphad. 2022; 77:102429.

[11] Du Q, Azar AS, M’Hamdi M. Kinetic interface condition phase diagram for the rapid solidification of multi-component alloys with an application to additive manufacturing. Calphad. 2022; 76:102365.

[12] Du Q, M’Hamdi M, Reiersen M, Hovig EW, Zhang K. A fully kinetic phase diagram-coupled multicomponent columnar-to-equiaxed grain transition model with an application to additive manufacturing. Calphad. 2024; 84:102642.

[13] Antillon EA, Hareland CA, Voorhees PW. Solute trapping and solute drag during non-equilibrium solidification of Fe-Cr alloys. Acta Mater. 2023; 248:118769.

[14] Martin P, Guillemot G, Hareland CA, Voorhees PW, Gandin C-A. Kinetic effects during the plane-front and dendritic solidification of multicomponent alloys. Acta Mater. 2024; 263:119473.

[15] Ren N, Li J, Zhang R, et al. Solute trapping and non-equilibrium microstructure during rapid solidification of additive manufacturing. Nat Commun. 2023; 14(1):7990.

[16] Ghosh S, Zollinger J, Zaloznik M, Banerjee D, Newman CK, Arroyave R. Modeling of hierarchical solidification microstructures in metal additive manufacturing: challenges and opportunities. Addit Manuf. 2023; 78:103845.

[17] Hillert M. Solute drag, solute trapping and diffusional dissipation of Gibbs energy. Acta Mater. 1999; 47(18): 4481-4505.

[18] Gao S, Li Z, Van Petegem S, et al. Additive manufacturing of alloys with programmable microstructure and properties. Nat Commun. 2023; 14(1):6752.

[19] Baker JC, Cahn JW. The Thermodynamics of Solidification, the Selected Works of John W. Cahn; 1998: 253-288.

[20] Gurtin ME, Voorhees PW. The thermodynamics of evolving interfaces far from equilibrium. Acta Mater. 1996; 44(1): 235-247.

[21] Wang H, Liu F, Zhai H, Wang K. Application of the maximal entropy production principle to rapid solidification: a sharp interface model. Acta Mater. 2012; 60(4): 1444-1454.

[22] Kittl JA, Aziz MJ, Brunco DP, Thompson MO. Absence of solute drag in solidification. Appl Phys Lett. 1994; 64(18): 2359-2361.

[23] Kittl JA, Sanders PG, Aziz MJ, Brunco DP, Thompson MO. Complete experimental test of kinetic models for rapid alloy solidification. Acta Mater. 2000; 48(20): 4797-4811.

[24] Andersson J, Ågren J. Models for numerical treatment of multicomponent diffusion in simple phases. J Appl Phys. 1992; 72(4): 1350-1355.

[25] Du Q, Perez M, Poole WJ, Wells M. Numerical integration of the Gibbs-Thomson equation for multicomponent systems. Scripta Mater. 2012; 66(7): 419-422.

[26] Du Q, Wells MA. Tracking multi-phase boundaries using an integration-based approach. Comput Mater Sci. 2011; 50(11): 3153-3161.

RIGHTS & PERMISSIONS

2024 The Author(s). Materials Genome Engineering Advances published by Wiley-VCH GmbH on behalf of University of Science and Technology Beijing.