Nucleation limitation and hardenability
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The r e l a t i o n b e t w e e n n u c l e a t i o n t h e o r y and h a r d e n a b i l i t y of s t e e l s h a s b e e n c r i t i c a l l y e x a m ined. The effect on h a r d e n a b i l i t y of m o s t e l e m e n t s with the e x c e p t i o n of b o r o n and s t r o n g c a r b i d e f o r m i n g a - s t a b i l i z e r s , is found to be s e m i q u a n t i t a t i v e l y c o n s i s t e n t with c l a s s i c a l n u c l e a t i o n t h e o r y . The " a n o m a l o u s " e f f e c t s of b o r o n , c h r o m i u m and m o l y b d e n u m , a r e d i s c u s s e d in t e r m s of p o s s i b l e p h y s i c a l i n t e r f e r e n c e of p r e c u r s o r r e a c t i o n s with f e r r i t e formation.
T H E r e l a t i o n s h i p b e t w e e n n u c l e a t i o n t h e o r y and h a r d e n a b i l i t y r e m a i n s a c h a l l e n g i n g topic f o r s c i e n t i f i c i n v e s t i g a t i o n . The e a r l y r e v i e w s of H o b s t e t t e r 1 and C h r i s t i a n 2 and the r e c e n t and c o m p r e h e n s i v e r e v i e w b y R u s s e l l a p r o v i d e much of the s o u r c e m a t e r i a l for t h i s work. The p u r p o s e s of t h i s c o n t r i b u t i o n a r e : 1) To u s e the g e n e r a l t h e o r y to d r a w s o m e b r o a d i n f e r e n c e s about n u c l e a t i o n e f f e c t s in h a r d e n a b i l i t y . 2) To f o r m u l a t e e x p l i c i t l y the t h e r m o d y n a m i c s of n u c l e a t i o n in t h r e e component s y s t e m s (the m i n i m u m n u m b e r of c o m p o n e n t s which p e r m i t s the t e r m " h a r d e n a b i l i t y " to t a k e i t s full meaning). 3) To c o m p u t e r e l a t i v e h a r d e n a b i l i t y e f f e c t s of s e lected alloying elements. 4) To c o m p a r e the o r d e r s - o f - m a g n i t u d e of n u c l e a t i o n t i m e s and a l l o y i n g e l e m e n t e f f e c t s with t h o s e e x p e c t e d on the b a s i s of c l a s s i c a l h e t e r o g e n e o u s n u c l e a t i o n t h e o r y , and a s a c o m p l e m e n t , to c o n s t r u c t a p l a u s i b l e m o d e l f o r the c r i t i c a l nucleus f o r p r o e u t e c t o i d f e r r i t e in a u s t e n i t e . 5) To d r a w attention to a l l o y s y s t e m s which d e p a r t f r o m p r e d i c t i o n s of the e l e m e n t a r y t h e o r y and to s p e c u l a t e on the c a u s e s of t h e s e d e p a r t u r e s . THERMODYNAMICS O F NUCLEATION The t h e o r y of t h e r m a l l y a c t i v a t e d n u c l e a t i o n f o c u s s e s on the (unstable) e q u i l i b r i u m b e t w e e n the c r i t i c a l nuc l e u s (of p h a s e a) and the p a r e n t p h a s e (/3). The i n t e r f a c e is a s s u m e d to be s h a r p , and the p r e c i p i t a t e and m a t r i x a r e a s s u m e d to be u n i f o r m in c o m p o s i t i o n . The f r e e e n e r g y of the n u c l e u s is a m a x i m u m with r e s p e c t to growth o r d e c o m p o s i t i o n , and a m i n i m u m with r e s p e c t to any o t h e r p r
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