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采用相场法数值模拟研究了定向凝固过程中随机噪声条件下枝晶侧向分枝生成行为与强制扰动条件下侧向分枝调控规律. 模拟结果表明: 随机噪声条件下, 侧向分枝整体上并无规则性, 但产生频率存在一定分布范围, 且在一定时间段内会出现生成频率一致且具有极强相关性的一组侧向分枝, 即波包; 不同波包之间不具有相关性, 但不同波包内部的侧枝生成频率基本相同, 且与侧枝整体频谱曲线峰值位置处的频率基本相当; 强制周期扰动条件下, 当扰动频率处于侧向分枝整体生成频率范围内时, 可激发枝晶产生规则侧向分枝, 且扰动频率与波包内侧枝生成频率一致时侧向分枝最发达. 研究结果可为向定向凝固枝晶形态的调控提供理论指导.Growth behaviors of dendritic sidebranches under random noises and characteristics of sidebranches modulated by external forces in directional solidification are studied by using phase field simulations. Simulation results show that, under random noises no regular sidebranches appears all the time, but sidebranches can be formed within a suitable range of frequencies. Moreover, strongly correlated sidebranches are formed at a fixed frequency and in a certain period, usually called a burst, to appear. There is no correlation between different bursts, but the frequency of every sidebranch within a burst is the same as its precursor, and this fixed frequency is consistent with the peak frequency of the whole spectrum of sidebranch. By introducing a time-periodic external force with a frequency in the range of the whole spectrum, regular dendritic sidebranches can be induced, and they can be most developed if the frequency of the external force is the same with that in a burst. The simulation results can provide guidance to control dendritic morphologies in solidification.
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Keywords:
- phase field method /
- directional solidification /
- dendrite /
- sidebranches
[1] Pieters R, Langer J S 1986 Phys. Rev. Lett. 56 1948
[2] Langer J S 1987 Phys. Rev. A 36 3350
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[17] Karma A, Lee Y H, Plapp M 2000 Phys. Rev. E 21 3996
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[20] Wang J C, Li J J, Yang Y J, Zhang Y X, Yang G C 2008 Sci. China E 38 16 (in Chinese) [王锦程, 李俊杰, 杨玉娟, 张玉祥, 杨根仓 2008 中国科学 E 38 16]
[21] Greenwood M, Haataja M, Provatas N 2004 Phys. Rev. Lett. 93 246101
[22] Steinbach I 2008 Acta Mater. 56 4965
[23] Wang Z J, Wang J C, Yang G C 2008 Acta Phys. Sin. 57 1246 (in Chinese) [王志军, 王锦程, 杨根仓 2008 57 1246]
[24] Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478
[25] Wang Y Q, Wang J C, Li J J 2012 Acta Phys. Sin. 61 118103 (in Chinese) [王雅琴, 王锦程, 李俊杰 2012 61 118103]
[26] Echebarria B, Karma A, Gurevich S 2010 Phys. Rev. E 81 021608
[27] Steinbach I, Pezzolla F, Nestler B 1996 Physica D 94 135
[28] Kim S G, Kim W T, Suzuki T 2004 J. Cryst. Growth 261 135
[29] Yang X L, Dong H B, Wang W 2004 Mater. Sci. Engineer. A 386 129
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[1] Pieters R, Langer J S 1986 Phys. Rev. Lett. 56 1948
[2] Langer J S 1987 Phys. Rev. A 36 3350
[3] Martin O, Goldenfeld N 1987 Phys. Rev. A 35 1382
[4] Kessler D A, Koplik J, Levine H 1984 Phys. Rev. A 30 3161
[5] van Saarloos W, Caroli B, Caroli C 1993 J. Phys. I 3 741
[6] Bisang U, Bilgram J H 1996 Phys. Rev. E 54 5309
[7] Dougherty A, Kaplan P D, Gollub J P 1987 Phys. Rev. Lett. 58 1652
[8] Honjo H, Ohta S, Sawada Y 1985 Phys. Rev. Lett. 55 841
[9] Pocheau A, Bodea S, Georgelin M 2009 Phys. Rev. E 80 031601
[10] Georgelin M, Bodea S, Pocheau A 2007 Europhys. Lett. 77 46001
[11] Bouissou P, Chiffaudel A, Perrin B, Tabeling P 1990 Europhys. Lett. 13 89
[12] Börzsönyi T, Tóth-Katona T, Buka á, Gránásy L 1999 Phys. Rev. Lett. 83 2853
[13] Börzsönyi T, Tóth-Katona T, Buha á, Gránásy L 2000 Phys. Rev. E 62 7817
[14] Williams L M, Muschol M, Qian X, Losert W, Cummins H Z 1993 Phys. Rev. E 48 489
[15] Kobayashi R 1993 Physica D 63 410
[16] Kobayashi R 1994 Exp. Math. 3 59
[17] Karma A, Lee Y H, Plapp M 2000 Phys. Rev. E 21 3996
[18] Zhao D P, Jing T, Liu B C 2003 Acta Phys. Sin. 52 1737 (in Chinese) [赵代平, 荆涛, 柳百成 2003 52 1737]
[19] Boettinger W J, Warren J A 1999 J. Cryst. Growth. 200 583
[20] Wang J C, Li J J, Yang Y J, Zhang Y X, Yang G C 2008 Sci. China E 38 16 (in Chinese) [王锦程, 李俊杰, 杨玉娟, 张玉祥, 杨根仓 2008 中国科学 E 38 16]
[21] Greenwood M, Haataja M, Provatas N 2004 Phys. Rev. Lett. 93 246101
[22] Steinbach I 2008 Acta Mater. 56 4965
[23] Wang Z J, Wang J C, Yang G C 2008 Acta Phys. Sin. 57 1246 (in Chinese) [王志军, 王锦程, 杨根仓 2008 57 1246]
[24] Li J J, Wang Z J, Wang Y Q, Wang J C 2012 Acta Mater. 60 1478
[25] Wang Y Q, Wang J C, Li J J 2012 Acta Phys. Sin. 61 118103 (in Chinese) [王雅琴, 王锦程, 李俊杰 2012 61 118103]
[26] Echebarria B, Karma A, Gurevich S 2010 Phys. Rev. E 81 021608
[27] Steinbach I, Pezzolla F, Nestler B 1996 Physica D 94 135
[28] Kim S G, Kim W T, Suzuki T 2004 J. Cryst. Growth 261 135
[29] Yang X L, Dong H B, Wang W 2004 Mater. Sci. Engineer. A 386 129
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