Transient growth of second phases during solution treatment
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T H E solution t r e a t m e n t p r o c e s s n o r m a l l y c o n s i s t s of heating a two-phase aggregate (a + ~) to a t e m p e r a t u r e w h e r e only one of the p h a s e s (c~) is s t a b l e , t h e r e b y effecting a t i m e - d e p e n d e n t t r a n s f o r m a t i o n to a single p h a s e s t r u c t u r e . It would, t h e r e f o r e , be expected that the c o n t e n t of u n s t a b l e phase (lJ) would d e c r e a s e c o n t i n u o u s l y with t i m e . In other w o r d s , for an i n i t i a l s t r u c t u r e of isolated fi p a r t i c l e s in an ~ m a t r i x , it would be a n t i c i p a t e d that the c~:~ i n t e r f a c e s would m i g r a t e in such a m a n n e r as to d e c r e a s e the v o l u m e s of the ~ p a r t i c l e s * . *This,of course,assumesthat the kineticsare not influencedby coarsening,or that all of the particlesare of the samesize S t r i c t l y speaking, the i n t e r f a c e m i g r a t i o n is c o n t r o l l e d by the diffusional t r a n s p o r t of m a s s in the v i c i n i t y of the i n t e r f a c e ; it is the d i f f e r e n c e in the fluxes in the two p h a s e s on opposite s i d e s of the i n t e r face which d e t e r m i n e s the i n t e r f a c e m i g r a t i o n velocity. O r d i n a r i l y , the flux at the i n t e r f a c e in the u n s t a b l e phase (/3) is negligible and the a - p h a s e flux c a u s e s the phase to d e c r e a s e continuously in v o l u m e . If, howe v e r , a l a r g e flux in the /3 phase r e s u l t s f r o m l a r g e v a r i a t i o n s in solubility with t e m p e r a t u r e a n d / o r a l a r g e i n t e r d i f f u s i o n coefficient at the solution t r e a t m e n t t e m p e r a t u r e , it is p o s s i b l e for the ~:~ i n t e r f a c e to move i n i t i a l l y in the d i r e c t i o n of i n c r e a s i n g / 3 - p h a s e content. T h i s s i t u a t i o n is d e s c r i b e d in F i g . 1 in t e r m s of the c o n c e n t r a t i o n - d i s t a n c e profile in the v i c i n i t y of the ot:~ i n t e r f a c e . The i n i t i a l condition is given by the dashed line: C = C~o X < 0 i R. W. HECKEL, formerly Professor of MetallurgicalEngineering, Drexel University, Philadelphia, Pa., is now Professor and Head, Department of Metallurgyand Materials Science, Carnegie-MellonUniversity, Pittsburgh, Pa. 15213. A. J. HICKL, formerly Graduate Student, Drexel University, is now United States Steel Fellow, Department of Metallurgyand Materials Science,Carnegie-MellonUniversity. R. J. ZAEHRINGis Technician, Department of MetallurgicalEngineering, Drexel University. R. A. TANZlLLI is Consulting Engineer, General Electric Co., Re-Entry and Environmental Systems Division,Philadelphia, Pa. Manuscript submitted February 15, 1972. METALLURGICALTRANSACTIONS
C = Cao
X>0
with the a : # i n t e r f a c e p o s i t i o n , 4, o c c u r r i n g at X = 0. The solid line r e p r e s e n t s the c o n c e n t r a t i o n - d i s t a n c e p r o f i l e a f t e r the s t a r t of i n t e r d i f f u s i o
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