Tip-splitting instability in directional solidification based on bias field method

doi:10.1088/1674-1056/24/7/078107

Abstract

Tip splitting instability of cellular interface morphology in directional solidification is analyzed based on the bias field method proposed recently by Glicksman. The physical mechanism of tip instability is explained by analyzing the interface potential, the tangential energy flux, and the normal energy flux. A rigorous criterion for tip-splitting instability is established analytically, i.e., the ratio of the cellular tip radius to the cellular width α > √3/2/π≈0.3899, which is in good agreement with simulation results. This study also reveals that the cellular tip splitting instability is attributable to weak Gibbs–Thomson energy acting on the interface.

Keywords: directional solidification morphological stability tip-splitting analytical method

Received: 01 January 2015
Revised: 20 March 2015
Accepted manuscript online:

PACS:	81.30.Fb	(Solidification)
	47.20.Hw	(Morphological instability; phase changes)
	02.60.Cb	(Numerical simulation; solution of equations)

Fund:

Project supported by the National Basic Research Program of China (Grant No. 2011CB610401), the National Natural Science Foundation of China (Grant No. 51371151), and the Free Research Fund of State Key Laboratory of Solidification Processing, China (Grant No. 100-QP-2014).

Corresponding Authors: Wang Jin-Cheng
E-mail: jchwang@nwpu.edu.cn

Cite this article:

You Jia-Xue (游家学), Wang Zhi-Jun (王志军), Li Jun-Jie (李俊杰), Wang Jin-Cheng (王锦程) Tip-splitting instability in directional solidification based on bias field method 2015 Chin. Phys. B 24 078107

[1]	Losert W, Stillman D A, Cummins H Z, Kopczynski P, Rappel W J and Karma A 1998 Phys. Rev. E 58 7492
[2]	Mullins W W and Sekerka R F 1964 J. Appl. Phys. 35 444
[3]	Kurz W and Fisher D J 1998 Fundamentals of Solidification (4th Edn.) (Switzerland: Trans Tech Publications) p. 66
[4]	Seetharaman V, Eshelman M A and Trivedi R 1988 Acta Metall. 36 1175
[5]	Ben Jacob E and Garik P 1990 Nature 343 523
[6]	Karma A 2001 Branching in Nature (Fleury V, Gouyet J F and Le'onetti M; Ed.) (Berlin: Springer) p. 365
[7]	Singer H M and Bilgram J H 2004 Phys. Rev. E 70 031601
[8]	Singer H M, Singer I and Bilgram J H 2009 Phys. Rev. Lett 103 015501
[9]	Langer J S 1987 Phys. Rev. A 36 3350
[10]	Brener E and Temkin D 1995 Phys. Rev. E 51 351
[11]	Billia B and Trivedi R 1993 Handbook of Crystal Growth (Hurle D T J Ed.) Vol. 1 (Amsterdam: Elsevier) p. 899
[12]	Chen Y, Billia B, Li D Z, Nguyen-Thi H, Xiao N M and Bogno A A 2014 Acta Mater. 66 219
[13]	Wang Z J, Wang J C and Yang G C 2009 Script. Mater. 61 915
[14]	Glicksman M E 2011 J. Phys.: Conf. Ser. 327 012001
[15]	Glicksman M E 2012 Metall. Mater. Trans. A 43A 391
[16]	Glicksman M E 2012 Mater. Sci. Eng. 33 012097
[17]	Xu J J and Chen Y Q 2011 Phys. Rev. E 83 061605
[18]	Glicksman M E, Lowengrub J S, Li S and Li X 2007 JOM 59 27
[19]	Wang Z J, Wang J C and Yang G C 2008 Phys. Rev. E 78 042601
[20]	Kessler D A, Koplik J and Levine H 1985 Phys. Rev. A 31 1712
[21]	Martin O and Goldenfeld N 1987 Phys. Rev. A 35 1382
[22]	Trivedi R, Liu S and Williams S 2002 Nat. Mater. 1 157
[23]	Gurevich S, Karma A, Plapp M and Trivedi R 2010 Phys. Rev. E. 81 011603
[24]	Xing H, Wang J Y, Chen C L, Jin K X and Du L F 2014 Chin. Phys. B 23 03810
[25]	Boettinger W J, Warren J A, Beckermann C and Karma A 2002 Annu. Rev. Mater. Res. 32 163
[26]	Li J J, Wang J C and Yang G C 2008 Chin. Phys. B 17 3516
[27]	Wang Z J, Wang J C and Yang G C 2010 Chin. Phys. B 19 078101

[1]	Multi-phase field simulation of competitive grain growth for directional solidification Chang-Sheng Zhu(朱昶胜), Zi-Hao Gao(高梓豪), Peng Lei(雷鹏), Li Feng(冯力), and Bo-Rui Zhao(赵博睿). Chin. Phys. B, 2022, 31(6): 068102.
[2]	Numerical study of growth competition between twin grains during directional solidification by using multi-phase field method Chang-Sheng Zhu(朱昶胜), Ting Wang(汪婷), Li Feng(冯力), Peng Lei(雷鹏), and Fang-Lan Ma(马芳兰). Chin. Phys. B, 2022, 31(2): 028102.
[3]	Negative compressibility property in hinging open-cell Kelvin structure Meng Ma(马梦), Xiao-Qin Zhou(周晓勤), Hao Liu(刘浩), and Hao-Cheng Wang(王浩成). Chin. Phys. B, 2021, 30(5): 056201.
[4]	General analytical method of designing shielded coils for arbitrary axial magnetic field Yi Zhang(张燚), Yu-Jiao Li(李玉姣), Qi-Yuan Jiang(江奇渊), Zhi-Guo Wang(汪之国), Tao Xia(夏涛), Hui Luo(罗晖). Chin. Phys. B, 2019, 28(11): 110702.
[5]	Negative linear compressibility of generic rotating rigid triangles Xiao-Qin Zhou(周晓勤), Lei Zhang(张磊), Lu Yang(杨璐). Chin. Phys. B, 2017, 26(12): 126201.
[6]	Effects of physical parameters on the cell-to-dendrite transition in directional solidification Wei Lei (魏雷), Lin Xin (林鑫), Wang Meng (王猛), Huang Wei-Dong (黄卫东). Chin. Phys. B, 2015, 24(7): 078108.
[7]	Dendrite to symmetry-broken dendrite transition in directional solidification of non-axially oriented crystals Xing Hui (邢辉), Wang Jian-Yuan (王建元), Chen Chang-Le (陈长乐), Jin Ke-Xin (金克新), Du Li-Fei (杜立飞). Chin. Phys. B, 2014, 23(3): 038104.
[8]	Probing the thermoelectric transport properties of n-type Bi₂Te₃ close to the limit of constitutional undercooling Feng Song-Ke (冯松科), Li Shuang-Ming (李双明), Fu Heng-Zhi (傅恒志). Chin. Phys. B, 2014, 23(11): 117202.
[9]	Efficient and rapid accuracy estimation of the Earth's gravitational field from next-generation GOCE Follow-On by the analytical method Zheng Wei (郑伟), Hsu Hou-Tse (许厚泽), Zhong Min (钟敏), Liu Cheng-Shu (刘成恕), Yun Mei-Juan (员美娟). Chin. Phys. B, 2013, 22(4): 049101.
[10]	The effect of interfacial energy anisotropy on planar interface instability in a succinonitrile alloy under a small temperature gradient Wang Li-Lin(王理林), Wang Zhi-Jun(王志军), Lin Xin(林鑫), Wang Meng(王猛), and Huang Wei-Dong(黄卫东) . Chin. Phys. B, 2012, 21(6): 066801.
[11]	What happens to the initial planar instability when the thermal gradient is increased during directional solidification? Wang Zhi-Jun(王志军), Wang Jin-Cheng(王锦程), Li Jun-Jie(李俊杰), Yang Gen-Cang(杨根仓), and Zhou Yao-He(周尧和) . Chin. Phys. B, 2011, 20(10): 108104.
[12]	Phase field investigation on the initial planar instability with surface tension anisotropy during directional solidification of binary alloys Wang Zhi-Jun(王志军), Wang Jin-Cheng(王锦程), and Yang Gen-Cang(杨根仓) . Chin. Phys. B, 2010, 19(1): 017305.
[13]	Lattice models of traffic flow considering drivers' delay in response Zhu Hui-Bing(祝会兵). Chin. Phys. B, 2009, 18(4): 1322-1327.
[14]	The effect of anisotropic surface tension on the morphological stability of planar interface during directional solidification Chen Ming-Wen(陈明文), Lan Man(兰曼), Yuan Lin(袁琳), Wang Yu-Yan(王玉燕), Wang Zi-Dong(王自东), and Xu Jian-Jun(徐鉴君). Chin. Phys. B, 2009, 18(4): 1691-1699.
[15]	Investigation on stability of directionally solidified CBr₄--C₂Cl₆ lamellar eutectic by using multiphase field simulation Zhu Yao-Chan(朱耀产), Wang Jin-Cheng(王锦程), Yang Gen-Cang(杨根仓), and Zhao Da-Wen(赵达文). Chin. Phys. B, 2007, 16(3): 805-811.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Tip-splitting instability in directional solidification based on bias field method

Cite this article:

Online attention