Calculated liquidus and solidus curves for the Hf-Zr, Hf-U, and Zr-U systems
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ated Liquidus and Solidus Curves for the Hf-Zr, Hf-U, and Zr-U Systems D.
to attain equilibrium is difficult to estimate and is frequently underestimated by the investigators. In & n u m b e r of binary metallic s y s t e m s ,3,4 solidus c u r v e s calculated f r o m s i m p l e solution m o d e l s have been later found to be m o r e reliable than solidus c u r v e s d e t e r m i n e d by t h e r m a l analysis. Ltquidus c u r v e s det e r m i n e d by t h e r m a l analysis on the o t h e r hand are n o r m a l l y reliable b e c a u s e of rapid diffusion in the l i q u i d state. I n a d d i t i o n to t h e a b o v e - m e n t i o n e d d i f f i c u l t y in a c curately determining t h e s o l i d u s c u r v e s , a n u m b e r of g e n e r a l e x p e r i m e n t a l difficulties e x i s t s in e s t a b l i s h i n g t h e p h a s e b o u n d a r i e s in t h e H f - Z r , H f - U , a n d Z r - U s y s t e m s . T h e nonavailability o f high purity m a t e r i a l s i n bulk q u a n t i t i e s , t h e h i g h t e m p e r a t u r e s i n v o l v e d , a n d t h e r e a c t i v i t y of t h e s e m e t a l s a r e a m o n g t h e m a j o r problems. A s p a r t o f a l o n g - t e r m p r o j e c t to critically e v a l u a t e published s o l i d u s and l i q u i d u s c u r v e s for b i n a r y a l l o y a n d oxide s y s t e m s exhibiting c o m p l e t e s o l i d a n d l i q u i d solubility, t h e a v a i l a b l e liquid-solid t w o - p h a s e b o u n d a r i e s for the H f - Z r , Hf-U, and Zr-U s y s t e m s have b e e n c o m p a r e d w i t h the b o u n d a r i e s c a l c u l a t e d f r o m i d e a l s o l u t i o n m o d e l . T h e i m p o r t a n c e o f t h e s e syst e m s in r e a c t o r m e t a l l u r g y , t h e r e p o r t e d i n a c c u r a c y of the p u b l i s h e d s o l i d u s c u r v e s , and the near-ideality of t h e s e s y s t e m s m o t i v a t e d t h e p r e s e n t i n v e s t i g a t i o n , In the p a s t , d i f f e r e n t a p p r o a c h e s b a s e d on i d e a l s o l u tion m o d e l h a v e b e e n a p p l i e d w i t h g o o d - t o - e x c e l l e n t s u c c e s s to p r e d i c t t h e liq,,id-solid t w o - p h a s e b o u n d -
a r i e s for a n u m b e r of b i n a r y metallic4-9 and o x i d et°'1~ s y s t e m s characterized by m o n o t o n i c variations in the liquidus and solidus curves. A l t h o u g h such s y s t e m s are not a l w a y s ideal, and the enthalpies and e x c e s s entropies of m i x i n g in the liquid and solid p h a s e s are not negligible, the deviations f r o m ideality in the twop h a s e s are often relatively s m a l l and of c o m p a r a b l e magnitude. Recently, Steininger4 has derived the following general expression for the t h e r m o d y n a m i c relationship b e t w e e n the liquidus and solidus c o m p o s i tions for nonideal but homogeneous and monotonic systems:
R T [in (NS /NS4 ) - In (NL / N L ) ]
CHATTERJI
T H E s y s t e m s H f - Z r , H f - U , a n d Z r - U a r e r e p o r t e d 1'2
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