Eutectic solidification
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Eutectic Solidification J.N.CLARK,
J. T. EDWARDS, AND R. ELLIOTT
Jackson and Hunt r e l a t e the p a r a m e t e r s v, X, and AT in their l a m e l l a r e u t e c t i c growth theory by the equation, A-"T-T = v X Q L + a L / ) t m
[1]
w h e r e v is the growth v e l o c i t y , ~ the i n t e r l a m e l l a r spacing, AT the interface undercooling and m Q L and J. N. C L A R K a n d J. T. E D W A R D S are Research Student and Postdoctoral Student, respectively, and R. E L L I O T T is Lecturer, Metallurgy D e p t . , U n i v e r s i t y o f Manchester, Manchester, England. Manuscript submitted July 15, 1 9 7 4 . 232-VOLUME
6 A , J A N U A R Y 1975
a r e c o n s t a n t s for a given alloy concentration. In o r d e r to d e r i v e a relationship b e t w e e n any two of the p a r a m e t e r s f r o m Eq. [1], it i s n e c e s s a r y to specify an additional condition. T h r e e conditions have been s u g g e s t e d after c o n s i d e r i n g Eq. [1] and a s i m i l a r equation d e r i v e d for rod growth. Each of t h e s e conditions g i v e s a relationship b e t w e e n any two of the p a r a m e t e r s that a g r e e s qualitatively with e x p e r i m e n t for an alloy of e u t e e t i c c o m p o s i t i o n . More recently, a t t e m p t s have been m a d e to distinguish b e t w e e n the three conditions by studying the variation of v~. z with c o m p o s i t i o n and c o m p a r i n g the experiraental relationship with that p r e dicted for each condition. The r e s u l t s obtained so far have e m p h a s i z e d the l i m i t a t i o n s of the t h e o r y in i t s p r e s e n t state. N o n - f a c e t i n g / n o n - f a c e t i n g s y s t e m s e x amined 2'3 have shown only r e a s o n a b l e a g r e e m e n t b e aL
Table I. Expanded Table of P and M Function
x 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17 0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34 0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50
P n = 10,000
M n = 10,000
0.00000 0.00014 0.00046 0.00091 0.00147 0.00212 0.00284 0.00362 0.00446 0.00534 0.00626 0.00721 0.00819 0.00918 0.01019 0.01121 0.01224 0.01327 0.01429 0.01532 0.01633 0.01734 0.01833 0.01930 0.02026 0.02120 0.02212 0.02301 0.02388 0.02472 0.02553 0.02631 0.02705 0.02777 0.02845 0.02909 0.02970 0.03027 0.03080 0.03129 0.03174 0.03215 0.03252 0.03285 0.03313 0.03337 0.03357 0.03372 0.03383 0.03390 0.03392
0.000013 0.01846 0.02450 0.02850 0.03145 0.03374 0.03556 0.03702 0.03821 0.03917 0.03994 0.04056 0.04104 0.04140 0.04166 0.04183 0.04192 0.04194 0.04189 0.04178 0.04162 0.04141 0.04116 0.04087 0.04054 0.04017 0.03978 0.03936 0.03891 0.03843 0.03794 0.03742 0.03689 0.03633 0.03577 0.03518 0.03459 0.03398 0.03336 0.03273 0.03209 0.03144 0.03078 0.03012 0.02946 0.0.2878 0.02810 0.02742 0.02674 0,02605 0.02536
x 0.51 0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0s 0.63 0.64 0.65 0.66 0.67 0.68 0.69 0.70 0.71 0.72 0.73 0.74 0.75 036 0.77 0.7
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