Abstract
Numerical simulations based on a new regularized phase-field model were presented, to simulate the solidification of hexagonal close-packed materials with strong interfacial energy anisotropies. Results show that the crystal grows into facet dendrites, displaying six-fold symmetry. The size of initial crystals has an effect on the branching-off of the principal branch tip along the 〈100〉 direction, which is eliminated by setting the b/a (a and b are the semi-major and semi-minor sizes in the initial elliptical crystals, respectively) value to be less than or equal to 1. With an increase in the undercooling value, the equilibrium morphology of the crystal changes from a star-like shape to facet dendrites without side branches. The steady-state tip velocity increases exponentially when the dimensionless undercooling is below the critical value. With a further increase in the undercooling value, the equilibrium morphology of the crystal grows into a developed side-branch structure, and the steady-state tip velocity of the facet dendrites increases linearly. The facet dendrite growth has controlled diffusion and kinetics.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
XIAO R Z, WANG Z P, ZHU C S, LI W S, FENG L. Influence of anisotropy on dendritic growth in binary alloy with phase-field simulation [J]. ISIJ International, 2009, 49(8): 1156–1160.
KARMA A, RAPPEL W J. Phase-field method for computationally efficient modeling of solidification with arbitrary interface kinetics [J]. Physical Review E, 1996, 53(4): 3017–3020.
ZHANG Y T, WANG C Z, LI D Z, LI Y Y. Phase field modeling of dendrite growth [J]. Acta Metall Sin (Engl Lett), 2009, 22(3): 197–201.
WANG J W, WANG Z P, LU Y, ZHU C S, FENG L, XIAO R Z. Effect of forced lamina flow on micro-segregation simulated by phase field method quantitatively [J]. Transactions of Nonferrous Metals Society of China, 2012, 22(2): 391–397.
LIU X Y, DU L F, ZHANG R, ZHANG L M. Phase-field simulation of effect of lateral constrains on dendritic spacing change [J]. The Chinese Journal of Nonferrous Metals, 2014, 24(2): 409–415. (in Chinese)
CHEN Mei-ying, FENG Li, OU Zhong-hui, CHEN Jin-quan, ZHUO Yan-yun. Phase-field modeling of isothermal crystallization process in juice crystal growth [J]. Journal of China Agricultural University, 2013, 18(6): 192–197. (in Chinese)
QIN R S, BHADESHIA H K D H. Phase-field model study of the crystal morphological evolution of hcp metals [J]. Acta Mater, 2009, 57(11): 3382–3390.
MIAO Jia-ming, JING Tao, LIU Bai-cheng. Numerical simulation of dendritic morphology of magnesium alloys using phase field method [J]. Acta Metall Sin, 2008, 44(4): 483–488. (in Chinese)
YUAN Xun-feng, DING Yu-tian, GUO Ting-biao, HU Yong. Numerical simulation of dendritic growth of magnesium alloys using phase-field method under forced flow [J]. The Chinese Journal of Nonferrous Metals, 2010, 20(8): 1474–1480. (in Chinese)
YAO Jun-ping, LI Xiang-guang, LONG Wen-yuan, ZHANG Lei. Numerical simulation of multiple grains with different preferred growth orientation of magnesium alloys using phase-field method [J]. The Chinese Journal of Nonferrous Metals, 2014, 24(2): 302–309. (in Chinese)
EGGLESTON J J, MCFADDEN G B, VOORHEES P W. A phase-field model for highly anisotropic interfacial energy [J]. Physica D, 2001, 150(1/2): 91–103.
KASAJIMA H, NAGANO E, SUZUKI T, KIM S G, KIM W T. Phase-field modeling for facet dendrite growth of silicon [J]. Sci Technol Adv Mater, 2003, 4(6): 553–557.
ZHANG G W, HOU H, CHENG J. Phase field model for strong anisotropys of kinetic and highly anisotropic interfacial energy [J]. Transactions of Nonferrous Metals Society of China, 2006, 16(s2): s307–s313.
SUZUKI T, KIM S G, KIM W T. Two-dimensional facet crystal growth of silicon from undercooled melt of Si-Ni alloy [J]. Mater Sci Eng A, 2007, 449: 99–104.
YUAN Xun-feng, DING Yu-tian. Phase-field simulation of dendrite growth process for binary Ni-Cu alloy with anisotropy of strong interface energy [J]. The Chinese Journal of Nonferrous Metals, 2011, 21(7): 1656–1663. (in Chinese)
YUAN X F, DING Yu-tian. Phasefield simulation of dendrite growth for binary alloy with strong anisotropy [J]. The Chinese Journal of Nonferrous Metals, 2011, 21(9): 2216–2222. (in Chinese)
CHEN Z, CHEN C L, HAO L M. Numerical simulation of facet dendritic growth in a forced flow [J]. Can J Phys, 2009, 87(2): 117–123.
CHEN Z, HAO L M, CHEN C L. Simulation of faceted dendrite growth of non-isothermal alloy in forced flow by phase field method [J]. Journal of Central South University of Technology, 2011, 18(6): 1780–1788.
BURTON W K, CABRERA N, FRANK F C. The growth of crystals and the equilibrium structure of their surfaces [J]. Phil Trans R Soc, 1951, 243(866): 299–358.
TONHARDT R, AMBERG G. Phase-field simulation of dendritic growth in a shear flow [J]. J Cryst Growth, 1998, 194(3/4): 406–425.
LANGER J S, MULLER-KRUMBHAAR H. Theory of dendritic growth-I, elements of a stability analysis [J]. Acta Metall, 1978, 26(11): 1681–1687.
Author information
Authors and Affiliations
Corresponding author
Additional information
Foundation item: Project(10834015) supported by the National Natural Science Foundation of China; Project(12SKY01-1) supported by the Doctoral Fund of Shangluo University, China; Project(14JK1223) supported by the Scientific Research Program of Shaanxi Provincial Education Department, China
Rights and permissions
About this article
Cite this article
Yuan, Xf., Liu, By., Li, C. et al. Simulation of facet dendrite growth with strong interfacial energy anisotropy by phase field method. J. Cent. South Univ. 22, 855–861 (2015). https://doi.org/10.1007/s11771-015-2593-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11771-015-2593-8