Abstract
To study the dynamical formation and evolution of cellular and dendritic arrays under diffusive growth conditions, three-dimensional (3D) directional solidification experiments were conducted in microgravity on a model transparent alloy onboard the International Space Station using the Directional Solidification Insert in the DEvice for the study of Critical LIquids and Crystallization. Selected experiments were repeated on Earth under gravity-driven fluid flow to evidence convection effects. Both radial and axial macrosegregation resulting from convection are observed in ground experiments, and primary spacings measured on Earth and microgravity experiments are noticeably different. The microgravity experiments provide unique benchmark data for numerical simulations of spatially extended pattern formation under diffusive growth conditions. The results of 3D phase-field simulations highlight the importance of accurately modeling thermal conditions that strongly influence the front recoil of the interface and the selection of the primary spacing. The modeling predictions are in good quantitative agreements with the microgravity experiments.
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References
B. Billia and R. Trivedi, Handbook of Crystal Growth, vol. 1 (Bristol: Elsevier, 1993), pp. 899–1074.
R. Trivedi, Y. Shen, and S. Liu, Advances in Materials and Materials Processing (New Delhi: Tata McGraw-Hill Publ. Ltd., 2001), pp. 42–49.
M.E. Glicksman, S.R. Coriell, and G.B. Mcfadden, Annu. Rev. Fluid Mech. 18, 307 (1986).
S.H. Davis, J. Fluid Mech. 212, 241 (1990).
G. Muller and A. Ostrogorsky, Handbook of Crystal Growth, vol. 2B (Amsterdam: Elsevier, 1994), p. 709.
M.D. Dupouy, D. Camel, and J.J. Favier, Acta Metall. 37, 1143 (1989).
H. Nguyen-Thi, G. Reinhart, and B. Billia, C. R. Mec. 345, 66 (2017).
N. Bergeon, D. Tourret, L. Chen, J.M. Debierre, R. Guerin, A. Ramirez, B. Billia, A. Karma, and R. Trivedi, Phys. Rev. Lett. 110, 6102 (2013).
J. Pereda, F.L. Mota, L. Chen, B. Billia, D. Tourret, Y. Song, J.M. Debierre, R. Guérin, A. Karma, R. Trivedi, and N. Bergeon, Phys. Rev. E 95, 2803 (2017).
D. Tourret, J.-M. Debierre, Y. Song, F.L. Mota, N. Bergeon, R. Guérin, R. Trivedi, B. Billia, and A. Karma, Phys. Rev. E 92, 2401 (2015).
M. Georgelin and A. Pocheau, Phys. Rev. Lett. 79, 2698 (1997).
A.J. Clarke, D. Tourret, Y. Song, S.D. Imhoff, P.J. Gibbs, J.W. Gibbs, K. Fezzaa, and A. Karma, Acta Mater. 129, 203 (2017).
G. Grange, J. Gastaldi, C. Jourdan, and B. Billia, J. Cryst. Growth 151, 192 (1995).
R. Trivedi, S. Liu, P. Mazumder, and E. Simsek, Sci. Technol. Adv. Mater. 2, 309 (2001).
B. Drevet, H. Nguyen-Thi, D. Camel, B. Billia, and M.D. Dupouy, J. Cryst. Growth 218, 419 (2000).
H. Nguyen-Thi, Y. Dabo, B. Drevet, M.D. Dupouy, D. Camel, B. Billia, J.D. Hunt, and A. Chilton, J. Cryst. Growth 281, 654 (2005).
G. Pont, S. Barde, B. Zappoli, F. Duclos, Y. Garrabos, C. Lecoutre, D. Beysens, B. Billia, N. Bergeon, N. Mangelinck, R. Marcout, and D. Blonde, 60th International Astronautical Congress (Daejeon: IAC, 2009).
N. Bergeon, C. Weiss, N. Mangelinck-Noel, and B. Billia, Trans. Ind. Inst. Met. 62, 455 (2009).
N. Bergeon, A. Ramirez, L. Chen, B. Billia, J.H. Gu, and R. Trivedi, J. Mater. Sci. 46, 6191 (2011).
F.L. Mota, N. Bergeon, D. Tourret, A. Karma, R. Trivedi, and B. Billia, Acta Mater. 85, 362 (2015).
L.Q. Chen, Annu. Rev. Mater. Res. 32, 113 (2002).
W.J. Boettinger, J.A. Warren, C. Beckermann, and A. Karma, Annu. Rev. Mater. Res. 32, 163 (2002).
J.J. Hoyt, M. Asta, and A. Karma, Mater. Sci. Eng. R 41, 121 (2003).
I. Steinbach, JOM 65, 1096 (2013).
A. Karma and W.J. Rappel, Phys. Rev. E 53, 3017 (1996).
A. Karma and W.J. Rappel, Phys. Rev. E 57, 4323 (1998).
A. Karma, Phys. Rev. Lett. 87, 5701 (2001).
B. Echebarria, R. Folch, A. Karma, and M. Plapp, Phys. Rev. E 70, 1604 (2004).
N. Bergeon, F.L. Mota, L. Chen, D. Tourret, J.M. Debierre, R. Guerin, A. Karma, B. Billia, and R. Trivedi, IOP Conf. Ser. Mater. Sci. Eng. 84, 012077 (2015).
C. Weiss, N. Bergeon, N. Mangelinck-Noel, and B. Billia, Mater. Sci. Eng. A 413, 296 (2005).
W.A. Tiller, K.A. Jackson, J.W. Rutter, and B. Chalmers, Acta Metall. 1, 428 (1953).
W. Mullins and R. Sekerka, J. Appl. Phys. 35, 444 (1964).
J.A. Warren and J.S. Langer, Phys. Rev. E 47, 2702 (1993).
J.J. Favier, Acta Metall. 29, 205 (1981).
D. Camel and J.J. Favier, J. Cryst. Growth 67, 42 (1984).
D. Camel and J.J. Favier, J. Cryst. Growth 67, 57 (1984).
S.R. Coriell, D.T.J. Hurle, and R.F. Sekerka, J. Cryst. Growth 32, 1 (1976).
J.A. Burton, R.C. Prim, and W.P. Slichter, J. Chem. Phys. 21, 1987 (1953).
H. Jamgotchian, N. Bergeon, D. Benielli, P. Voge, B. Billia, and R. Guerin, Phys. Rev. Lett. 87, 6105 (2001).
J.P. Garandet, J.J. Favier, and D. Camel, Handbook of Crystal Growth, vol. 2 (Bristol: Elsevier, 1994), pp. 659–707.
P. Lehmann, R. Moreau, D. Camel, and R. Bolcato, J. Cryst. Growth 183, 690 (1998).
S. Kaddeche, J.P. Garandet, C. Barat, H. BenHadid, and D. Henry, J. Cryst. Growth 158, 144 (1996).
F.L. Mota, L.M. Fabietti, N. Bergeon, L.L. Strutzenberg, A. Karma, B. Billia, and R. Trivedi, J. Cryst. Growth 447, 31 (2016).
R.N. Grugel and Y. Zhou, Metall. Trans. A 20, 969 (1989).
K. Somboonsuk, J.T. Mason, and R. Trivedi, Metall. Trans. A 15, 967 (1984).
R. Trivedi and K. Somboonsuk, Mater. Sci. Eng. 65, 65 (1984).
K. Somboonsuk and R. Trivedi, Acta Metall. 33, 1051 (1985).
R. Trivedi and K. Somboonsuk, Acta Metall. 33, 1061 (1985).
B. Echebarria, A. Karma, and S. Gurevich, Phys. Rev. E 81, 1608 (2010).
Acknowledgements
The authors express their gratitude to CNES (Centre National d’Etudes Spatiales) and NASA (National Aeronautics and Space Administration) for the support received in the scientific projects MISOL3D (MIcrostructures de SOLidification 3D) and DSIP (Dynamical Selection of Interface Patterns). A.K. and R.T. were supported by NASA Grants NNX12AK54G and NNX16AB54G. D.T. gratefully acknowledges support of the U.S. Department of Energy through a Director’s Postdoctoral Fellowship from the LANL/LDRD Program.
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Mota, F.L., Song, Y., Pereda, J. et al. Convection Effects During Bulk Transparent Alloy Solidification in DECLIC-DSI and Phase-Field Simulations in Diffusive Conditions. JOM 69, 1280–1288 (2017). https://doi.org/10.1007/s11837-017-2395-6
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DOI: https://doi.org/10.1007/s11837-017-2395-6