Continuity equation for evolving particle size distributions
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rant, this r a t i o is l a r g e l y a d i r e c t i o n r e f l e c t i o n of the r e l a t i v e , t i m e - i n t e g r a t e d n u c l e a t i o n k i n e t i c s at the two t y p e s of s i t e . T h u s its dependence upon u n d e r c o o l i n g is just that p r e d i c t e d by the Cahn ' a n a l y s i s . F i g u r e s l(a) to (c) a l s o show that the r a t i o i n i t i a l l y d e c r e a s e s and then i n c r e a s e s slightly with r e a c t i o n t i m e . The d e c r e a s e could r e s u l t f r o m such f a c t o r s as a p o s s i b l e longer i n c u b a t i o n t i m e for the f a c e - n u c l e ated a l l o t r i o m o r p h s , s l o w e r growth r a t e s of these c r y s t a l s to d e t e c t a b l e size a n d / o r continuing n u c l e a tion at g r a i n f a c e s a f t e r the a v a i l a b l e edge n u c l e a t i o n s i t e s have b e e n s a t u r a t e d . The r i s e in the r a t i o at l a t e r r e a c t i o n t i m e s is a t t r i b u t e d to e r r o n e o u s l y c o u n t ing as e d g e - n u c l e a t e d those f a c e - n u c l e a t e d a l l o t r i o m o r p h s which have had sufficient t i m e to grow into contact with a g r a i n edge. Support of this r e s e a r c h by the N a t i o n a l Science F o u n d a t i o n t h r o u g h G r a n t DMR77-11374 is g r a t e f u l l y acknowledged.
1. J. W. Cahn: Acta Met., 1956, vol. 4, p. 449. 2. P. H. Clemm and J. C. Fisher: Acta. Met., 1955, vol. 3, p. 70. 3. C. J. Middleton and G. W. Form: Met. Sei., 1975, vol. 9, p. 521. 4. G. W. Parker and D. H. Kirkwood: ChemiealMetallurgy in Iron and Steel, p. 248, Iron and Steel Institute, London, 1973. 5. W. F. Lange III and H. I. Aaronson: Met. Trans., in press. 6. H. 1. Aaronson, N. A. Gjostein, H. W. Paxton, and R. W. Heckek Rev. Sci. Instrum., 1957, vol. 28, p. 579. 7. W. F. Lange III and H. I. Aaronson: unpublished research, Michigan Technological University, 1978. 8. J. R. Bradley, J. M. Rigsbee, and H. I. Aaronson: Met. Trans. A, 1977, vol. 8A, p. 323. 9. K. R. Kinsman and H. I. Aaronson: Transformation and Hardenability in Steels, p. 39, Climax Molybdenum Co., Ann Arbor, MI, 1967.
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Continuity Equation for Evolving Particle Size Distributions
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Fig. 1-Variation of the ratio of the number of edge-nucleated to the number of face-nucleated ferrite allotriomorphs as a function of reaction time at various reaction temperatures in: (a
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