Abstract
Rapid solidification gives rise to solute trapping, which decreases solute partitioning and alters equilibrium solidification velocity-undercooling relationships. These effects influence microsegregation, solidification morphology, and the emergent microstructure length scales. Here, we review solute trapping and solute drag in rapid solidification in terms of theory, simulation methods, and experimental techniques. The basic theory to describe solute trapping is contained in the continuous growth model. This model breaks down at high solidification velocities, where solidification transitions abruptly to complete trapping, a limit that can be captured with the local nonequilibrium model. Solute trapping theories contain unknown parameters. Their determination from atomistic simulations or pulsed laser melting experiments is discussed. Microstructural evolution in rapid solidification can be readily investigated with the phase-field method, various alternatives of which are presented here. Uncertainties related to kinetic parameters and heat transfer during rapid solidification can be studied by comparing phase-field simulations to dynamic transmission electron microscopy observations.
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References
J.W. Cahn, The Selected Works of John W. Cahn (Wiley, New York, 1998).
M.J. Aziz, Metall. Mater. Trans. A 27A, 67 (1996).
M.J. Aziz, W. Boettinger, Acta Metall. Mater. 42, 527 (1994).
R. Trivedi, W. Kurz, Acta Metall. Mater. 42, 15 (1994).
E.J. Lavernia, T.S. Srivatsan, J. Mater. Sci. 45, 287 (2010).
S.A. David, S.S. Babu, J.M. Vitek, JOM 55, 14 (2003).
T. DebRoy, H.L. Wei, J. Zuback, T. Mukherjee, J. Elmer, J. Milewski, A. Beese, A. Wilson-Heid, A. De, W. Zhang, Prog. Mater Sci. 92, 112 (2018).
J.T. McKeown, J.M. Wiezorek, A.J. Clarke, MRS Bull. 45 (11), 916 (2020).
K.A. Jackson, K.M. Beatty, K.A. Gudgel, J. Cryst. Growth 271, 481 (2004).
M. Hillert, B. Sundman, Acta Metall. 25, 11 (1977).
M.J. Aziz, T. Kaplan, Acta Metall. 36, 2335 (1988).
Y. Yang, H. Humadi, D. Buta, B.B. Laird, D. Sun, J.J. Hoyt, M. Asta, Phys. Rev. Lett. 107, 025505 (2011).
S. Raman, J.J. Hoyt, P. Saidi, M. Asta, Comput. Mater. Sci. 182, 109773 (2020).
J. Kittl, P.G. Sanders, M.J. Aziz, D.P. Brunco, M.O. Thompson, Acta Mater. 48, 4797 (2000).
H. Humadi, J.J. Hoyt, N. Provatas, Phys. Rev. E 87, 022404 (2013).
M. Hillert, Acta Mater. 47, 4481 (1999).
N.A. Ahmad, A.A. Wheeler, W.J. Boettinger, G.B. McFadden, Phys. Rev. E 58, 3436 (1998).
P.K. Galenko, S. Sobolev, Phys. Rev. E 55, 343 (1997).
P.K. Galenko, D. Jou, Phys. Rep. 818, 1 (2019).
P.K. Galenko, Phys. Rev. E 76, 031606 (2007).
I. Steinbach, Model. Simul. Mater. Sci. Eng. 17, 073001 (2009).
N. Provatas, K. Elder, Phase-Field Methods in Materials Science and Engineering (Wiley, Weinheim, Germany, 2011).
R. Almgren, SIAM J. Appl. Math. 59, 2086 (1999).
B. Echebarria, R. Folch, A. Karma, M. Plapp, Phys. Rev. E 70, 061604 (2004).
T. Pinomaa, N. Provatas, Acta Mater. 168, 167 (2019).
I. Steinbach, L. Zhang, M. Plapp, Acta Mater. 60, 2689 (2012).
W. Kurz, R. Trivedi, Metall. Mater. Trans. A 27, 625 (1996).
M. Asta, C. Beckermann, A. Karma, W. Kurz, R. Napolitano, M. Plapp, G. Purdy, M. Rappaz, R. Trivedi, Acta Mater. 57, 941 (2009).
W. Kurz, R. Trivedi, Metall. Mater. Trans. A 27, 625 (1996).
J. McKeown, A. Kulovits, C. Liu, K. Zweiacker, B. Reed, T. LaGrange, J.M. Wiezorek, G. Campbell, Acta Mater. 65, 56 (2014).
V. Bathula, C. Liu, K. Zweiacker, J. McKeown, J. Wiezorek, Acta Mater. 195, 341 (2020).
M. Conti, Phys. Rev. E 58, 2071 (1998).
T. Pinomaa, J.T. McKeown, J.M. Wiezorek, N. Provatas, A. Laukkanen, T. Suhonen, J. Cryst. Growth 532, 125418 (2020).
Acknowledgments
T.P. and A.L. wish to acknowledge the support of the Academy of Finland through the HEADFORE project, Grant No. 333226. N.P. wishes to acknowledge the National Sciences and Engineering Research Council of Canada, the Canada Research Chairs Program for funding, and Compute Canada for computing resources.
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Tatu Pinomaa is a research scientist at the VTT Technical Research Centre of Finland Ltd. He received his doctor of science (tech) degree in 2020 from Aalto University, Finland. His research includes developing computational approaches for understanding process–structure–property relationships for materials design. His current research focuses on microstructure formation and evolution using phase-field methods, computational thermodynamics, molecular dynamics, computational fluid dynamics, and micromechanical modeling. Pinomaa can be reached by email at tatu.pinomaa@vtt.fi.
Anssi Laukkanen is a research professor for computational materials and data science at the VTT Technical Research Centre of Finland Ltd. He received his doctor of science (tech) degree from Tampere University of Technology, Finland, in 2017. His research interests include multiscale and multiphysical modeling in the development of hierarchically coupled and concurrent across-scales modeling solutions. His current research focuses on the study of deformation and strengthening mechanisms by way of micromechanics and crystal plasticity. Laukkanen can be reached by email at anssi.laukkanen@vtt.fi.
Nikolas Provatas is a professor in physics at McGill University, Canada. He received his doctor of science degree from McGill University in 1995. He was a professor in materials science and engineering at McMaster University, Canada, between 2002 and 2012. His research interests lie at the interface of condensed-matter physics and materials science. His current research combines high-performance computing with nonequilibrium thermodynamics, statistical mechanics, and experiments to understand the fundamental origins of microstructure evolution in materials processes. Provatas can be reached by email at provatas@physics.mcgill.ca.
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Pinomaa, T., Laukkanen, A. & Provatas, N. Solute trapping in rapid solidification. MRS Bulletin 45, 910–915 (2020). https://doi.org/10.1557/mrs.2020.274
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DOI: https://doi.org/10.1557/mrs.2020.274