On the theory of the stability of lamellar eutectics
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Fig. 2--Extensive oxide cracking on the surface of a specimen cycled at 1700~ Uncoated replica. Magnification 190 times.
On the Theory of the Stability of Lamellar Eutectics J. D. HUNT, D. T. J. H U R L E , K. A. JACKSON, AND E. JAKEMAN
FOLLOWINGthe
Fig. 3--A large crack on the surface of a specimen containing an oxidation-resistant aluminide coating that was cycled at 1700~ Uncoated replica. Magnification 190 times. E x t e n s i v e c r a c k i n g in a t h i c k e r oxide f o r m e d on the s u r f a c e of a s p e c i m e n t e s t e d at 1700~ is shown in Fig. 2. The " b r i c k w a l l " a p p e a r a n c e c o n s i s t s of long h o r i z o n t a l c r a c k s that a r e f i l l e d with oxide and s h o r t v e r t i c a l c r a c k s that p r o b a b l y f o r m e d d u r i n g cooling. R e s o l u t i o n of d e t a i l by d i r e c t s u r f a c e o b s e r v a t i o n and 318-VOLUME I,JANUARY 1970
d e m o n s t r a t i o n , by M o l l a r d and F l e m i n g s , 1 that e u t e c t i c m i c r o s t r u c t u r e s , f r e e of p r i m a r y d e n d r i t e s , could be obtained in P b - S n a l l o y s of n o n e u t e c t i c c o m p o s i t i o n s p r o v i d e d that the quotient of t e m p e r a t u r e g r a d i e n t to growth v e l o c i t y was sufficiently l a r g e , t h r e e t h e o r i e s w e r e p r o p o s e d independently to account for this phenomenon. Two of these t h e o r i e s 2'3 w e r e in the n a t u r e of f i r s t o r d e r p e r t u r b a t i o n c a l c u l a t i o n s while the t h i r d 4 conc e r n e d the conditions under which p r i m a r y d e n d r i t e s could grow f a s t e r than the coupled e u t e c t i c i n t e r f a c e . Thus the f i r s t two t h e o r i e s c o n s i d e r e d the conditions under which i n s t a b i l i t y would f i r s t set in while the t h i r d c o n s i d e r e d conditions r e l a t i n g to the t e r m i n a l , d e n d r i t i c , f o r m of the i n s t a b i l i t y . It is not p o s s i b l e to J. D. HUNT is at the University of Oxford, Oxford, England. D.T.J. HURLE is with the Royal Radar Establishment, Oxford, England. K. A. JACKSON is Head, Materials Physics Research Department, Bell Telephone Laboratories, Murray Hill, N . J . E . JAKEMAN is with the Royal Radar Establishment, Malvern, England. Manuscript submitted March 1l, 1969. METALLURGICAL TRANSACTIONS
r e l a t e the two a p p r o a c h e s d i r e c t l y but, of c o u r s e , if both a r e v a l i d they should l e a d to s i m i l a r p r e d i c t i o n s . The two p e r t u r b a t i o n a p p r o a c h e s z,3 l e a d to s i g n i f i cantly d i f f e r e n t p r e d i c t i o n s of the s p a t i a l wavelength of the i n s t a b i l i t y which f i r s t o c c u r s . Cline and T a r s h i s 3,s concluded that the w a v e l e n g t h of the i n i t i a l d i s t u r b a n c e was l a r g e c o m p a r e d to the wavelength of the l a m e l l a r s t r u c t u r e w h e r e a s H u r l e and J a k e m a n ~ concluded that it was equal to the l a m e
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