Dendrite solidification in the Sn-Pb system
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Fig. 6--Selected area diffraction pattern from the austenitemartensite interface showing reflections from both the phases. [ l l l ] y and [120]ce zones are present. M a r t e n s i t e p l a t e s with s i m i l a r m o r p h o l o g i e s and int e r n a l s t r u c t u r e h a v e p r e v i o u s l y been o b s e r v e d by T a m u r a et al. 5 in an F e - 3 0 pct Ni-0.4 pct C alloy, P a t t e r s o n and Wayman 6 in an F e - 2 1 . 7 pct N i - 1 pct C alloy
Dendrite Solidification in the Sn-Pb System
1. R. Brookand A. R. Entwisle:Z Iron Steellnst., 1965, vol. 203, p. 905. 2. A. R. Entwisleand J. A. Feeny: The Mechanism of Phase Transformation in Crystalline Solids, MonographNo. 33, p. 156, Institute of Metals, London, 1969. 3. D. S. Sarma:Ph.D. Thesis, SheffieldUniversity,1972. 4. K. W. Andrews,D. J. Dyson, and S. R. Keown:Interpretation of Electron Diffraction Patterns, 2nd Edition, p. 165, AdamHilger(London), 1971. 5. I. Tamura, Y. Hoshimura, M Ibaraki, and M. Yagaya: Trans. Jap. Inst. Metals, 1964, vol. 5, p. 47. 6. R. L. Patterson and C. M. Wayman:ActaMet., 1964, vol. 12, p. 1306. 7. M. Watanabe and C. M. Wayman:Met. Trans., 1971, vol.2, p. 2221. 8. R. L. Patterson and C. M. Wayman:ActaMet., 1966,vol. 14, p. 347.
e u t e c t i c i s o t h e r m . Now s u b s t i t u t e Eq. [1] into Eq. [2] and a s s u m e the liquidus slope, m , is constant. Then m -
R. M. SHARP
AND
M. C. FLEMINGS
(Tt -
T~
[1]
w h e r e T t is tip t e m p e r a t u r e , T o is e q u i l i b r i u m liquidus t e m p e r a t u r e of an alloy of c o n c e n t r a t i o n Co, D is diffusion c o e f f i c i e n t , G is t e m p e r a t u r e g r a d i e n t at the tip, and R the growth r a t e . F o r constant G, d e n d r i t e length is: T t - TE
L-
G
[2]
where TE is the eutectic temperature. L, the dendrite length, is distance from the dendrite (or cell) tip to the R. M. SHARP is Lecturer, School of Engineering, University of Auckland, New Zealand. M. C. FLEMINGS is Abex Professor of Metallurgy, Department of Metallurgy and Materials Science, Massachusetts Institute of Technology, Cambridge, Massachusetts. Manuscript submitted April 15, 1974. 936-VOLUME 6A, APRIL 1975
TE
[3]
CE
w h e r e C E is the e u t e c t i c c o m p o s i t i o n , and
In a r e c e n t l y published p a p e r , 1 V e r h o e v e n and Gibson have p r e s e n t e d s o m e data r e l a t i n g to the growth of d e n d r i t e s in the Sn-Pb s y s t e m . It is of i n t e r e s t t o c o m p a r e the m e a s u r e m e n t s of d e n d r i t i c length and a r e a f r a c t i o n of d e n d r i t e s with p r e d i c t i o n s f r o m equations given by Sharp and F l e m i n g s , 2 and F l e m i n g s , s in t h e i r a n a l y s i s of d e n d r i t i c growth. D e n d r i t e tip t e m p e r a t u r e is obtained f r o m Eq. [6] of Sharp and F l e m i n g s 2 as -DG n
T OCo_
D
L=-~-+
n~ (C O -
CE )
[4]
G
A r e a f r a c t i o n d e n d r i t e s is obtained by i n t e g r a t i n g Eq. [9] of Sharp and F l e m i n g s . z This is also given
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