镁基合金自由枝晶生长的相场模拟研究

段培培; 邢辉; 陈志; 郝冠华; 王碧涵; 金克新

doi:10.7498/aps.64.060201

摘要

利用定量相场模型, 以Mg-0.5 wt.%Al合金为例模拟了基面((0001)面)内镁基合金的等温自由枝晶生长过程. 通过研究该合金体系数值模拟的收敛性, 获得了最优化值耦合参数λ = 5.5及网格宽度Δx/W0 = 0.4, 并在该参数下系统研究了各向异性强度和过饱和度对枝晶尖端生长速度、尖端曲率半径、Péclet数及稳定性常数σ* 的影响. 结果表明, 由微观可解性理论得到的稳定性系数σ* 与ε6 拟合值σ*≅ ε6 1.81905, 更接近理想值σ * (ε6) ≅ε6 1.75. 此外, 当过饱和度Ω σ * 不随ε6 的变化而变化, 而当Ω > 0.6时, 稳定性系数σ * 随着ε6 的增加而减小. 这反映了枝晶的生长由扩散控制向动力学控制的转变. 随着过饱和度的增加, 枝晶形貌由雪花状枝晶向圆状枝晶转变.

关键词:

Abstract

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.

Keywords:

作者及机构信息

1.
西北工业大学应用物理系, 陕西省凝聚态结构与性质重点实验室, 西安 710129

基金项目: 中央高校基本科研业务费专项资金 (批准号: 3102014KYJD026)、国家自然科学基金 (批准号: 61078057, 51172183, 6147130, 11102164)、陕西省自然科学基金(批准号: 2012JQ8013)、西北工业大学专项研究基金(批准号: NPU-FFR-JC20110273, JC201155, JC20120246)和西北工业大学新人新方向(批准号: 13GH014602)资助的课题.

Authors and contacts

1.
Shaanxi Key Laboratory of Condensed Matter Structures and Properties, Northwestern Polytechnical University, Xi'an 710129, China

Funds: Project supported by the Fundamental Research Funds for the Central Universities, China (Grant No. 3102014KYJD026), the National Natural Science Foundation of China (Grant Nos. 61078057, 51172183, 6147130, 11102164), the Natural Science Foundation of Shaanxi Province in China (Grant No. 2012JQ8013), NPU Foundation for Fundamental Research, China (Grant Nos. NPU-FFR-JC20110273, JC201155, JC20120246), and the Program of New Staff and Research Area Project of NPU, China (Grant No. 13GH014602).

参考文献

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[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
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[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]
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[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

施引文献

[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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