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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
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[2] Langer J S 1987 Phys. Rev. A 36 3350
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[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]
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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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