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In this paper, the process of the free dendritic growth of Mg-0.5 wt.%Al alloy in the basal plane (0001) is simulated in two-dimensional system by using a quantitative phase-field model. A convergence study is carried out to choose the optimal coupling parameter λ and grid width Δx/W0 in simulation. Then we systematically discuss the effects of the anisotropic strength ε and the supersaturation Ω on dendritical tip growth velocity, radius, Péclet number, and stability parameter σ *. Results show that the stability parameter σ * defined by the theory of microscopic solvability is a function of the anisotropy strength ε, i.e., σ* ≅ ε1.81905, which is obviously closest to σ * (ε) ≅ ε 1.75 obtained from the analytical solution. Moreover, for Ω σ * is approximately a constant while it sharply and monotonically decreases with the augment of the value of ε for Ω > 0.6. This indicates that there is a transition from solute-controlled dendrite to kinetic dendrite as Ω increases. Furthermore, the transition of the growth pattern from the snow-like to the circle-like patterns occurs as Ω increases.
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Keywords:
- phase-field simulations /
- magnesium alloys /
- free dendritic growth
[1] Gurevich S, Amoorezaei M, Montiel D, Provatas N 2012 Acta Mater. 60 3287
[2] Shi C X, Li H D, Wang D Z, Li Y Y, Zuo T Y 2001 Mater. Rev. 15 5 (in Chinese) [师昌绪, 李恒德, 王淀佐, 李依依, 左铁镛 2001 材料导报 15 5]
[3] Cao R C, Ke W, Xu Y B 2001 Acta Metal. Sin. 51 2 (in Chinese) [曹荣昌, 柯伟, 徐永波 2001 金属学报 51 2]
[4] Asta M, Beckermann C, Karma A, Kurz W, Napolitano R, Plapp M 2009 Acta Mater. 57 941
[5] Amoorezaei M, Gurevich S, Provatas N 2012 Acta Mater. 60 657
[6] Ivantsov G R, Nauk D A 1947 SSSR 58 567
[7] Kessler D A, Koplik J, Levine H 1988 Adv. Phys. 37 255
[8] Pomeau Y, Ben-Amar M 1992 Solids far from Equilibrium (Cambridge: Cambridge University Press) pp365-378
[9] Lipton J, Glicksman M E, Kurz W 1984 Mater. Sci. Eng. 65 57
[10] Lipton J, Glicksman M E, Kurz W 1987 Metall Trans. A 18 341
[11] Lipton J, Kurz W, Trivedi R 1987 Acta Metall 35 957
[12] Plapp M 2011 Philos. Mag. 91 25
[13] Yamanaka A, Aoki T, Ogawa S, Takaki T 2011 J. Cryst. Growth 318 40
[14] Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘琳 2013 62 106401]
[15] Boussinot G, Brener E A, Temkin D E 2010 Acta Mater. 58 1750
[16] Zhang X G, Zong Y P, Wu Y 2012 Acta Phys. Sin. 61 088104 (in Chinese) [张宪刚, 宗亚平, 吴艳 2012 61 088104]
[17] Wang X D, Ouyang J, Su J, Zhou W 2013 Chin. Phys. B 22 106103
[18] Wang Z J, Wang J C, Yang G C 2010 Chin. Phys. B 19 078101
[19] Li J J, Wang J C, Yang G C 2008 Chin. Phys. B 17 3516
[20] Karma A, Rappel W J 1998 Phys. Rev. E 57 4323
[21] Echebarria B, Folch R, Karma A, Plapp M 2004 Phys. Rev. E 70 061604
[22] Bergeon N, Tourret D, Chen L, Debierre J M, Guérin R, Ramirez A, Billia B, Karma A, Trivedi R 2013 Phys. Rev. Lett. 110 226102
[23] Amoorezaei M, Gurevich S, Provatas N 2010 Acta Mater. 58 6115
[24] Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478
[25] Wang M, Jing T, Liu B 2009 Script. Mater. 61 777
[26] Eiken J 2009 Int. J. Cast. Met. Res. 22 1
[27] Karma A 2001 Phys. Rev. Lett. 87 115701
[28] Kara M, Kurki-Suonio K 1981 Acta Crystallogr. A: Cryst. Phys. Diffr. Theor. Gen. Crystallogr. 37 201
[29] Sun D Y, Mendelev M I, Becker C A, Kudin K, Haxhimali T, Asta M, Hoyt J J, Karma A, Srolovitz D J 2006 Phys. Rev. B 73 024116
[30] Fu Z, Xu Q, Xiong S 2007 Mater. Sci. Forum. 546-549 133
[31] Ohno M 2012 Phys. Rev. E 86 051603
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[1] Gurevich S, Amoorezaei M, Montiel D, Provatas N 2012 Acta Mater. 60 3287
[2] Shi C X, Li H D, Wang D Z, Li Y Y, Zuo T Y 2001 Mater. Rev. 15 5 (in Chinese) [师昌绪, 李恒德, 王淀佐, 李依依, 左铁镛 2001 材料导报 15 5]
[3] Cao R C, Ke W, Xu Y B 2001 Acta Metal. Sin. 51 2 (in Chinese) [曹荣昌, 柯伟, 徐永波 2001 金属学报 51 2]
[4] Asta M, Beckermann C, Karma A, Kurz W, Napolitano R, Plapp M 2009 Acta Mater. 57 941
[5] Amoorezaei M, Gurevich S, Provatas N 2012 Acta Mater. 60 657
[6] Ivantsov G R, Nauk D A 1947 SSSR 58 567
[7] Kessler D A, Koplik J, Levine H 1988 Adv. Phys. 37 255
[8] Pomeau Y, Ben-Amar M 1992 Solids far from Equilibrium (Cambridge: Cambridge University Press) pp365-378
[9] Lipton J, Glicksman M E, Kurz W 1984 Mater. Sci. Eng. 65 57
[10] Lipton J, Glicksman M E, Kurz W 1987 Metall Trans. A 18 341
[11] Lipton J, Kurz W, Trivedi R 1987 Acta Metall 35 957
[12] Plapp M 2011 Philos. Mag. 91 25
[13] Yamanaka A, Aoki T, Ogawa S, Takaki T 2011 J. Cryst. Growth 318 40
[14] Du L F, Zhang R, Xing H, Zhang L M, Zhang Y, Liu L 2013 Acta Phys. Sin. 62 106401 (in Chinese) [杜立飞, 张蓉, 邢辉, 张利民, 张洋, 刘琳 2013 62 106401]
[15] Boussinot G, Brener E A, Temkin D E 2010 Acta Mater. 58 1750
[16] Zhang X G, Zong Y P, Wu Y 2012 Acta Phys. Sin. 61 088104 (in Chinese) [张宪刚, 宗亚平, 吴艳 2012 61 088104]
[17] Wang X D, Ouyang J, Su J, Zhou W 2013 Chin. Phys. B 22 106103
[18] Wang Z J, Wang J C, Yang G C 2010 Chin. Phys. B 19 078101
[19] Li J J, Wang J C, Yang G C 2008 Chin. Phys. B 17 3516
[20] Karma A, Rappel W J 1998 Phys. Rev. E 57 4323
[21] Echebarria B, Folch R, Karma A, Plapp M 2004 Phys. Rev. E 70 061604
[22] Bergeon N, Tourret D, Chen L, Debierre J M, Guérin R, Ramirez A, Billia B, Karma A, Trivedi R 2013 Phys. Rev. Lett. 110 226102
[23] Amoorezaei M, Gurevich S, Provatas N 2010 Acta Mater. 58 6115
[24] Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478
[25] Wang M, Jing T, Liu B 2009 Script. Mater. 61 777
[26] Eiken J 2009 Int. J. Cast. Met. Res. 22 1
[27] Karma A 2001 Phys. Rev. Lett. 87 115701
[28] Kara M, Kurki-Suonio K 1981 Acta Crystallogr. A: Cryst. Phys. Diffr. Theor. Gen. Crystallogr. 37 201
[29] Sun D Y, Mendelev M I, Becker C A, Kudin K, Haxhimali T, Asta M, Hoyt J J, Karma A, Srolovitz D J 2006 Phys. Rev. B 73 024116
[30] Fu Z, Xu Q, Xiong S 2007 Mater. Sci. Forum. 546-549 133
[31] Ohno M 2012 Phys. Rev. E 86 051603
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