Non-isothermal finite diffusion-controlled growth in ternary systems
- PDF / 1,430,411 Bytes
- 8 Pages / 612 x 792 pts (letter) Page_size
- 10 Downloads / 228 Views
ber of analytic solutions to the p r o b l e m of diffusion controlled phase growth in b i n a r y s y s t e m s a r e a v a i l a b l e in the l i t e r a t u r e . 1,2 Recently, a n a l y t i c a l solutions for the g e n e r a l c a s e of t e r n a r y diffusion controlled growth have been developed by Kirkaldy 3 and Coates. 4,s These solutions a r e , however, r e s t r i c t e d to i s o t h e r m a l growth and do not c o n s i d e r the effects of overlapping diffusion fields, or impingement. The s p e c i a l case of proeutectoid f e r r i t e growth in t e r n a r y F e - C - X alloys, where X is a substitutional alloying element, has been studied in g r e a t detail. 4-9 In these alloys, the diffusion coefficient of C is g r e a t e r than 104 t i m e s that of the substitutional element. Simplified closed form e x p r e s s i o n s have been developed for the s t e a d y state growth of f e r r i t e . 4'6 At high s u p e r s a t u r a t i o n l e v e l s , for these alloys, it has been proposed that the substitutional e l e m e n t m a y no longer be in local equilibrium at the ~/V phase boundaries (paraequilibrium). ~~ At low s u p e r s a t u r a t i o n l e v e l s and for other types of alloy s y s t e m s , local equilibrium at the two phase growth i n t e r f a c e is usually a s s u m e d , lz Except for the initial s t a g e s of growth, the effect of impingement is of p a r t i c u l a r i m p o r t a n c e . The effect has been a p p r o x i m a t e d in c e r t a i n s p e c i a l c a s e s . 13 However, a m o r e flexible and p o s s i b l y m o r e a c c u r a t e approach is to employ a n u m e r i c a l model for diffusion controlled growth which accounts for impingement effects. Tanzilli and Heckel ~4 developed such a computer model for application to finite i s o t h e r m a l b i n a r y diffus i o n - c o n t r o l l e d , two phase, m o v i n g - i n t e r f a c e p r o b l e m s . To the b e s t of our knowledge, s i m i l a r computer models for finite t e r n a r y phase growth have not been developed. In many c a s e s , phase growth o c c u r s under nonisot h e r m a l conditions. Several heating and cooling s t e p s may be employed or phase growth m a y occur during E. RANDICHis INCO Fellow, and J. I. GOLDSTEIN is Associate Professor, Department of Metallurgyand MaterialsScience, Lehigh University, Bethleham, PA 18015. Manuscript submitted October 21, t974. METALLURGICALTRANSACTIONS A
the cooling of a l l o y s f r o m high t e m p e r a t u r e s . Computer m o d e l s have been developed by Goldstein and Ogilvie ~ and Wood ~ for finite diffusion c o n t r o l l e d phase growth in b i n a r y s y s t e m s during n o n i s o t h e r m a l conditions. These computer models w e r e developed to study Widmanstatten growth in iron m e t e o r i t e s and because of their publication in the geologic l i t e r a t u r e have been g e n e r a l l y overlooked by the m e t a l l u r g i c a l community. The p u r p o s e of this paper is two-fold: 1) to d e s c r i b e a n u m e r
Data Loading...
