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the last s e v e r a l y e a r s u n d e r s t a n d i n g of the b e h a v i o r of b i n a r y s i l i c a t e m e l t s h a s i n c r e a s e d s i g n i f i c a n t l y a s a r e s u l t of the a p p l i c a t i o n of the p r i n c i p l e s of p o l y m e r t h e o r y to t h e s e s y s t e m s . A l t h o u g h i t has long b e e n r e a l i z e d that any s i l i c a t e melt m u s t c o n t a i n a r a n g e of s i z e s of s i l i c a t e a n i o n s ,1 t h e o r e t i c a l l y b a s e d quantification of this size r a n g e d i s t r i b u t i o n only b e c a m e p o s s i b l e a s a r e s u l t of the a p p l i c a t i o n of p o l y m e r t h e o r y . T h i s has been d e s c r i b e d in a s e r i e s of p a p e r s by W h i t e w a y , S m i t h and M a s s o n ,2-~ w h e r e i n , f r o m s t a t i s t i c a l p r i n c i p l e s , the m o s t p r o b a b l e s i z e d i s t r i b u t i o n of s i l i c a t e a n i o n s is c a l c u l a t e d a s a f u n c tion of the d e g r e e of p o l y m e r i z a t i o n of the s i l i c a t e m e l t . Two c a s e s a r e c o n s i d e r e d in the WSM m o d e l ; one in w h i c h the SiO~- ion is c o n s i d e r e d to be a b i f u n c t i o n a l m e r u n i t , i.e. f = 2 , and the o t h e r in w h i c h the SiO~- ion is c o n s i d e r e d to be a t e t r a f u n c t i o n a l m e r u n i t , i.e. f = 4 . In the f o r m e r c a s e only two of the S i - O - g r o u p s on any SiO~- c a n r e a c t to f o r m p o l y s i l i c a t e ions and h e n c e only l i n e a r c h a i n ion f o r m a t i o n is p o s s i b l e and in the l a t t e r c a s e all four of the S i - O g r o u p s on a n SiO~- m a y r e a c t , thus p e r m i t t i n g the f o r m a t i o n of b r a n c h i n g c h a i n i o n s . T h e d e g r e e of p o l y m e r i z a t i o n of a s i l i c a t e m e l t is q u a n t i f i e d by o~ w h i c h is t h e f r a c t i o n of p o t e n t i a l l y - r e a c t i v e S i - O g r o u p s p r e s e n t in the c o m p l e t e l y d e p o l y m e r i z e d s t a t e w h i c h have r e a c t e d to form d o u b l y - b o n d e d o x y g e n s a n d f r e e o x y g e n s a c c o r d i n g to l [ I [ -Si-O- + -O-Si- -- - S i - O - S i - + 02-. l l l l D. R. GASKELL is Associate Professor of Metallurgy, Laboratory for Research on the Structure of Matter, and Department of Metallurgy and Materials Science, University of Pennsylvania, Philadelphia, PA 19174. Manuscript submitted December 19, 1975. METALLURGICAL

TRANSACTIONSB

[I]

SiO~- AS A BIFUNCTIONAL MER UNIT (f = 2) In its completely depolymerized state, a binary silicate melt containingN moles of SiO2 and (l-N) moles of basic metal oxide MO comprises N moles of SiO~ions and (I- 3N) moles of 02- ions when N -< 1/3. As the number of moles of potentially-reactive Si-Ogroups is 2N, the degree of polymerization, ~, is g i v e n as (9/-

2n o 2N

w h e r e n o is t h e n u m b e r of m o l e s of 0 2- ions f o r m e d by the p o l y m e r i z a t i o n R e a t i o n [1 ]. A l s o , a s