A structural model for binary silicate systems
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y e a r s , m a n y m o d e l s have b e e n p r o p o s e d which have had c o n s i d e r a b l e s u c c e s s in e l u c i d a t i n g the s t r u c t u r e of b i n a r y s i l i c a t e m e l t s over c e r t a i n r a n g e s of c o m p o s i t i o n . Among m a n y i m p o r t a n t c o n t r i b u t i o n s to this field, one should cite the work of M a s s o n et a1,1 Gaskell, z Fincham and Richardson, 3 Toop and Samis, 4 Frohberg et al ,s and Niwa and Yokokawa. 6 For binary silicate systems MO-Si02 (34 = Ca, Mg, Mn, Fe, Pb, and so forth) it is generally accepted in all such models that all Si atoms are tetrahedrally bonded to four oxygen atoms. For solutions very rich in the "basic" oxide MO, the melt consists essentially of M 2ยง 02-, and SiO~- (orthosilicate) ions. According to the model first introduced by Flood and Knapp, 7 the entropy in this composition region may be calculated by assuming a random distribution of 02- and SiO~- anions. As the concentration of SiO2 is increased, the SiO~- tetrahedra start to join together to form dimers S1207 , trimers Si30~, and so forth. In these polymeric anions, the silicons are joined by "bridging" oxygen atoms which are covalently bonded to two silicon atoms. By assuming only linear and branched chain polymers and using a modification of Flory's s model for polymeric melts, M a s s o n el a/I successfully modeled the MO-SiO2 melts for SiO2 concentrations up to about 40 tool pct SiO2. For greater concentrations of SiO2 Masson's model no longer holds because of the formation of cyclic polymers and of a three dimensional network of bridged silica tetrahedra. In the limit of pure molten SiO2, the s t r u c t u r e c o n s i s t s of a n e t w o r k of s i l i c a t e t r a h e d r a with each oxygen f o r m i n g a " b r i d g e " by bonding to two s i l i c o n a t o m s . : F o r s m a l l a d d i t i o n s of MO to SiO2, F i n c h a m and R i c h a r d s o n 3 p r o p o s e d that each added 02ion b r e a k s one oxygen b r i d g e a c c o r d i n g to the following reaction: 9
02- + O ~ ~- 2 O-
6-
[1]
P. L. LIN and A. D. PELTON are Research Associate and Associate Professor, respectively, Department of MetallurgicalEngineering, Ecole Polytechnique, Universit6de Montreal, Montr6al, Qu4bec, Canada. Manuscript submitted September 19, 1978. METALLURGICALTRANSACTIONSB
w h e r e O ~ r e p r e s e n t s a " b r i d g i n g " oxygen bonded to two s i l i c o n a t o m s and O- r e p r e s e n t s an oxygen bonded to only one s i l i c o n a t o m . A r e s u l t a n t " b r o k e n b r i d g e " is shown s c h e m a t i c a l l y in F i g . 1. F o r t h i s c o m p o s i tion r e g i o n n e a r p u r e 8iO2, F d r l a n d 9 p r o p o s e d that the e n t r o p y be c a l c u l a t e d by a s s u m i n g a r a n d o m d i s t r i bution of b r o k e n and u n b r o k e n b r i d g e s . Ideally, a m o d e l for MO-SiO2 m e l t s should apply to the e n t i r e c o m p o s i t i o n r e g i o n , should be m a t h e m a t i c a l l y and c o n c e p
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