Materials Transactions Online

Materials Transactions, Vol.48 No.09 (2007) pp.2272-2279
© 2007 The Japan Institute of Metals

Cellular and Dendritic Growth in Constrained Solidification

Yasunori Miyata

Nagaoka University of Technology, Department of Mechanical Engineering, Nagaoka 940-2188, Japan

A theoretical model is developed to predict the characteristics of a needle (cellular or dendrite) interface during the controlled and arrayed solidification of binary alloys. Both heat and mass transport fields near a growing needle front have been considered. The effect of solute, diffused from nearby dendrites, on dimensions of needle is also taken into account. Minimum undercooling criterion of tip of interface has been developed to select a solution to determine the dimensions, satisfying the local equilibrium conditions at the interface. Solutions are classified into two categories; one is responsible to the cellular growth and the other to the dendrite growth. Good correlations are obtained between theory and experiments.

(Received 2007/3/1; Accepted 2007/4/23; Published 2007/7/11)

Keywords: dendrite, morphology, solidification, modeling, theory, primary-arm spacing, tip radius of curvature, undercooling, supercooling

PDF(Free)PDF (Free) Table of ContentsTable of Contents


  1. B. Chalmers: Principles of Solidification, (Wiley, New York, NY, 1964) pp. 126–185.
  2. T. F. Bower, H. D. Brody and M. C. Flemings: Trans. AIME 236 (1960) 624–634.
  3. M. H. Burden and J. D. Hunt: J. Cryst. Growth 22 (1974) 99–108.
  4. M. H. Burden and J. D. Hunt: J. Cryst. Growth 22 (1974) 109–116.
  5. R. Trivedi: J. Cryst. Growth 49 (1980) 219–232.
  6. W. Kurz and D. J. Fisher: Acta Metall. 29 (1981) 11–20.
  7. S.-Z. Lu and J. D. Hunt: J. Cryst. Growth 123 (1992) 17–34.
  8. U. Bisang and J. H. Bilgram: Phys. Rev. 42 (1996) 5309–5326.
  9. A. A. Wheeler, W. J. Boettinger and G. B. McFadden: Phys. Rev. A 45 (1992) 7424- .
  10. S. G. Kim, W. T. Kim and T. Suzuki: Phys. Rev. E 60 (1999) 7186- .
  11. M. E. Glicksman and S. P. Marsh: Handbook of Crystal Growth, ed. by D. T. J. Hurle, vol. 1B, Chap. 15(Elsevier Science Pub., 1993).
  12. Y. Miyata, M. E. Glicksman and S. H. Tirmizi: J. Cryst. Growth 110 (1991) 683–691.
  13. Y. Miyata and M. Takeda: Mater. Trans. 42 (2001) 180–188.
  14. Y. Miyata and M. Takeda: Mater. Trans. 42 (2001) 189–196.
  15. Y. Miyata, H. Takahashi and M. Herai: Submitted to J. Japan Inst. Metals.
  16. Y. Miyata, T. Suzuki and J. Uno: Metall. Trans. A16 (1985) 1799–1805.


© 2007 The Japan Institute of Metals
Comments to us :