Simulation for the Fluctuation Effect on the Dendrites Growth with Phase Field Method

Abstract:

The dendrite growth process was simulated with the Phase Field Model coupled with the fluctuation. The effect of fluctuation intensity on the dendrite morphology and the thermal fluctuation together with the phase field fluctuation on the forming of side branches were investigated. Result shows that with the decrease of thermal fluctuation amplitude, the furcation of dendrites tip also decreased, transverse dendrites become stronger and lengthways dendrites becomes degenerate, Doublon structure disappeared, finally a quite symmetrical dendrites structure formed. Thermal fluctuation can result in the unsteadiness of dendrites side branches, it is also the main reason of forming side branches, yet phase field fluctuation has little contribution to the side branches, it is usually ignored in the calculation; when the value of F_u is appropriate, the thermal noise can lead the side branches, but cannot change the steady behavior of the dendrites’ tip.

• Periodical: Materials Science Forum (Volumes 704-705)
• Pages: 1338-1348
• DOI: https://doi.org/10.4028/www.scientific.net/MSF.704-705.1338
• Online since: December 2011
• Authors: Hua Hou, Yu Hong Zhao
• Keywords: Dendrites, Fluctuation, Phase-Field Method, Side Branches

References

[1] M.N. Barber , A. Barbieri, J.S. Langer: Phys. Rev. A Vol. 39 (1987), p.5314.

[2] R . Pieters: Phys. Rev. A Vol. 37 (1988), p.3126.

[3] J .S. Langer: J. Cryst. Growth Vol. 42 (1977), p.42.

[4] E. Brener, D Temkin: PhysicaA Vol. 263 (1999), p.338.

[5] C. S . Zhu, T. Jing, B.C. Liu: Foundry Vol. 53 (2004), p.1040.

[6] C.S. Z hu, Z. P . Wang: Mechanical Engineering Transaction Vol. 41 (2005), p.30.

[7] R.J. Braun, B.T. Murray : Crystal Growth Vol. 174 (1997), p.41.

[8] R. Kobayasi: Physica D Vol. 63 (1993), p.410.

[9] A. Karma, W. J. Rappel: Phys. Rev. E Vol. 60 (1999), p.3164.

[10] S. Tokunaga , H. Sakaguchi : Journal of Crystal Growth Vol. 275 (2005), p.197 List of Figures (a) Without noise (b) with noise Fig. 1 Influence of noise on dendrite Fig . 2Dendrite growth of Ammonium bromide.

[10] Fig. 3 Experiment of dendrite growth with noise.

[10] (a) Fu =1×10-2 (b) Fu =5×10-3 (c) Fu =1×10-3 (d) Fu =5×10-4 (e) Fu =5×10-5 (f) Fu =1×10-5 Fig. 4 Dendrite morphology with different fluctuation amplitude (a) Without noise (b) Phase field noise (c) Thermal noise Fig. 5 Dendrite morphology with different noise Fig. 6 Dendrite morphology without noise and with a=1. 0 Fig. 7 Dendrite morphology with a=1. 0 and Fu=1×10-3 Fig. 8 Dendritic tip velocity with different time Fig. 9 Dendritic tip radius with different time.

DOI: 10.17816/cardar100224-64442