A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

doi:10.1088/1674-1056/ab6718

中国物理B ›› 2020, Vol. 29 ›› Issue (2): 28103-028103.doi: 10.1088/1674-1056/ab6718

• INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY • 上一篇下一篇

A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

Zhaodong Zhang(张兆栋), Yuting Cao(曹宇婷), Dongke Sun(孙东科), Hui Xing(邢辉), Jincheng Wang(王锦程), Zhonghua Ni(倪中华)

1 School of Mechanical Engineering, Southeast University, Nanjing 211189, China;
2 MOE Key Laboratory of Material Physics and Chemistry under Extraordinary, Shaanxi Key Laboratory for Condensed Matter Structure and Properties, Northwestern Polytechnical University(NPU), Xi'an 710129, China;
3 State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China

收稿日期:2019-09-09 修回日期:2019-10-31 出版日期:2020-02-05 发布日期:2020-02-05
通讯作者: Dongke Sun, Hui Xing, Zhonghua Ni E-mail:dksun@seu.edu.cn;huixing@nwpu.edu.cn;nzh2003@seu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51728601 and 51771118), the Fund of the State Key Laboratory of Solidification Processing in NPU (Grant No. SKLSP201901), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2242019K1G003).

A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

Zhaodong Zhang(张兆栋)¹, Yuting Cao(曹宇婷)¹, Dongke Sun(孙东科)¹, Hui Xing(邢辉)², Jincheng Wang(王锦程)³, Zhonghua Ni(倪中华)¹

1 School of Mechanical Engineering, Southeast University, Nanjing 211189, China;
2 MOE Key Laboratory of Material Physics and Chemistry under Extraordinary, Shaanxi Key Laboratory for Condensed Matter Structure and Properties, Northwestern Polytechnical University(NPU), Xi'an 710129, China;
3 State Key Laboratory of Solidification Processing, Northwestern Polytechnical University, Xi'an 710072, China

Received:2019-09-09 Revised:2019-10-31 Online:2020-02-05 Published:2020-02-05
Contact: Dongke Sun, Hui Xing, Zhonghua Ni E-mail:dksun@seu.edu.cn;huixing@nwpu.edu.cn;nzh2003@seu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant Nos. 51728601 and 51771118), the Fund of the State Key Laboratory of Solidification Processing in NPU (Grant No. SKLSP201901), and the Fundamental Research Funds for the Central Universities, China (Grant No. 2242019K1G003).

摘要/Abstract

摘要： Pattern selection during crystal growth is studied by using the anisotropic lattice Boltzmann-phase field model. In the model, the phase transition, melt flows, and heat transfer are coupled and mathematically described by using the lattice Boltzmann (LB) scheme. The anisotropic streaming-relaxation operation fitting into the LB framework is implemented to model interface advancing with various preferred orientations. Crystal pattern evolutions are then numerically investigated in the conditions of with and without melt flows. It is found that melt flows can significantly influence heat transfer, crystal growth behavior, and phase distributions. The crystal morphological transition from dendrite, seaweed to cauliflower-like patterns occurs with the increase of undercoolings. The interface normal angles and curvature distributions are proposed to quantitatively characterize crystal patterns. The results demonstrate that the distributions are corresponding to crystal morphological features, and they can be therefore used to describe the evolution of crystal patterns in a quantitative way.

关键词: lattice Boltzmann, crystal growth, phase field, melt flow, pattern selection

Abstract: Pattern selection during crystal growth is studied by using the anisotropic lattice Boltzmann-phase field model. In the model, the phase transition, melt flows, and heat transfer are coupled and mathematically described by using the lattice Boltzmann (LB) scheme. The anisotropic streaming-relaxation operation fitting into the LB framework is implemented to model interface advancing with various preferred orientations. Crystal pattern evolutions are then numerically investigated in the conditions of with and without melt flows. It is found that melt flows can significantly influence heat transfer, crystal growth behavior, and phase distributions. The crystal morphological transition from dendrite, seaweed to cauliflower-like patterns occurs with the increase of undercoolings. The interface normal angles and curvature distributions are proposed to quantitatively characterize crystal patterns. The results demonstrate that the distributions are corresponding to crystal morphological features, and they can be therefore used to describe the evolution of crystal patterns in a quantitative way.

Key words: lattice Boltzmann, crystal growth, phase field, melt flow, pattern selection

中图分类号: (Methods of crystal growth; physics and chemistry of crystal growth, crystal morphology, and orientation)

81.10.-h

81.30.Fb (Solidification) 68.08.De (Liquid-solid interface structure: measurements and simulations)

张兆栋, 曹宇婷, 孙东科, 邢辉, 王锦程, 倪中华. A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method[J]. 中国物理B, 2020, 29(2): 28103-028103.

Zhaodong Zhang(张兆栋), Yuting Cao(曹宇婷), Dongke Sun(孙东科), Hui Xing(邢辉), Jincheng Wang(王锦程), Zhonghua Ni(倪中华). A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method[J]. Chin. Phys. B, 2020, 29(2): 28103-028103.

参考文献 29

[1]	Gao Y, Lu Y, Kong L, Deng Q, Huang L and Luo Z 2018 Acta Metall. Sin. 54 278
[2]	Wang J, Guo C, Zhang Q, Tang S, Li J and Wang Z 2018 Acta Metall. Sin. 54 204
[3]	Provatas N, Wang Q, Haataja M and Grant M 2003 Phys. Rev. Lett. 91 155502 doi: 10.1103/PhysRevLett.91.155502
[4]	Chen Y, Billia B, Li D Z, Nguyen-Thi H, Xiao N M and Bogno A A 2014 Acta Mater. 66 219 doi: 10.1016/j.actamat.2013.11.069
[5]	Xing H, Dong X, Wu H, Hao G, Wang J, Chen C and Jin K 2016 Sci. Rep. 6 26625 doi: 10.1038/srep26625
[6]	Echebarria B, Folch R, Karma A and Plapp M 2005 Phy. Rev. E 70 061604
[7]	Beckermann C, Diepers H J, Steinbach I, Karma A and Tong X 1999 J. Comput. Phys. 154 468 doi: 10.1006/jcph.1999.6323
[8]	Tong X, Beckermann C, Karma A and Li Q 2001 Phy. Rev. E 63 1
[9]	Zhu M F, Lee S Y and Hong C P 2004 Phys. Rev. E 69 061610 doi: 10.1103/PhysRevE.69.061610
[10]	Chen S, Chen H, Martinez D and Matthaeus W H 1991 Phys. Rev. Lett. 67 3776 doi: 10.1103/PhysRevLett.67.3776
[11]	Qian Y H, d'Humiéres D and Lallemand P 1992 Europhys. Lett. 17 479 doi: 10.1209/0295-5075/17/6/001
[12]	Miller W 2001 J. Cryst. Growth 230 263 doi: 10.1016/S0022-0248(01)01353-7
[13]	Chakraborty S and Chatterjee D 2007 J. Fluid. Mech. 592 155 doi: 10.1017/S0022112007008555
[14]	Sun D K, Zhu M F, Pan S Y and Raabe D 2009 Acta Mater. 57 1755 doi: 10.1016/j.actamat.2008.12.019
[15]	Sakane S, Takaki T, RojasR, Ohno M, Shibuta Y, Shimokawabe T and Aoki T 2017 J. Cryst. Growth 474 154 doi: 10.1016/j.jcrysgro.2016.11.103
[16]	Medvedev D, Fischaleck T and Kassner K 2007 J. Cryst. Growth 303 69 doi: 10.1016/j.jcrysgro.2006.10.227
[17]	Zhang X, Kang J, Guo Z, Xiong S and Han Q 2018 Comput. Phys. Commun. 223 18 doi: 10.1016/j.cpc.2017.09.021
[18]	Rojas R, Takaki T and Ohno M 2015 J. Comput. Phys. 298 29
[19]	Takaki T, Sato R, Rojas R, Ohno M and Shibuta Y 2018 Comput. Mater. Sci. 147 124 doi: 10.1016/j.commatsci.2018.02.004
[20]	Cartalade A, Younsi A and Plapp M 2016 Comput. Math. Appl. 71 1784 doi: 10.1016/j.camwa.2016.02.029
[21]	Younsi A and Cartalade A 2016 J. Comput. Phys. 325 1 doi: 10.1016/j.jcp.2016.08.014
[22]	Sun D K, Xing H, Dong X and Han Q 2019 Int. J. Heat Mass Transfer 133 1240 doi: 10.1016/j.ijheatmasstransfer.2018.12.095
[23]	Xing H, Ji M, Dong X, Wang Y, Zhang L and Li S 2020 Mater. Des. 185 108250 doi: 10.1016/j.matdes.2019.108250
[24]	Sun D K, Zhu M F, Pan S Y, Yang C R and Raabe D 2011 Comput. Math. Appl. 61 3585 doi: 10.1016/j.camwa.2010.11.001
[25]	d'Humiéres D 2002 Phil. Trans. R. Soc. Lond. A 360 437 doi: 10.1098/rsta.2001.0955
[26]	Guo Z and Zheng C 2002 Int. J. Comput. Fluid D 22 465
[27]	Chai Z H and Zhao T S 2012 Phys. Rev. E 86 016705 doi: 10.1103/PhysRevE.86.016705
[28]	Maier R S, Bernard R S and Grunau D W 1996 Phys. Fluids 8 1788 doi: 10.1063/1.868961
[29]	Dardis O and McCloskey J 1998 Phys. Rev. E 57 4834 doi: 10.1103/PhysRevE.57.4834

A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

A numerical study on pattern selection in crystal growth by using anisotropic lattice Boltzmann-phase field method

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