Montecarlo calculations of ionic structure in silicate and alumino-silicate melts
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T H E i m p o r t a n c e of m e t a l - s l a g r e a c t i o n s in steelmaking processes, is such that numerous investigations on slags have been made, and a wealth of experimental data on their physical properties (density, viscosity, surface tension, and so forth) is reported in the literature. For the structure of molten silicates and alumino-silicatesions on the contrary, the only papers knownto the Authors are those by Waseda1,2,'I and by Yanagase and Suginohara.a As far as it is knownto the Authors, this is the first contribution to the knowledge, by means of the Montecarlo method, of the ionic species present in molten silicates and alumino-silicates.
t i e s " , is i n d i c a t e d a s an end a l o m . We can now define one ion of this s t r u c t u r e a s a s e t of Si a n d / o r A1 a t o m s which can be connected by at l e a s t one path within the t e t r a h e d r a l l a t t i c e which does not p a s s t h r o u g h a n end atom. Since ions of d i f f e r e n t lengths a r e p r e s e n t s i m u l t a n e o u s l y i n s i l i c a t e s and a l u m i n o - s i I i c a t e s , the p a r a m e t e r b e s t s u i t e d to d e s c r i b e the ionic s t r u c t u r e of t h e s e c o m p o u n d s is a d i s t r i b u t i o n function g i v i n g the f r a c t i o n of the ions having a c e r t a i n d i m e n s i o n as a function of the d i m e n s i o n . Given a c e r t a i n l a t t i c e conf i g u r a t i o n of Si, A1 and v a c a n c i e s , then:
x'(n) - ~V(n)
[i]
SILICATE MODEL The s a m e l a t t i c e model p r e v i o u s l y used 4 has b e e n here adopted to r e p r e s e n t the s y s t e m s u n d e r study. A c c o r d i n g to the model, when rn m o l e c u l e s of m e t a l oxide M e O (Me = F e , Mn,Mg, Ca) a r e added to a c r y s t a l c o n t a i n i n g n m o l e c u l e s of SiO2, the oxygen l a t t i c e in the SiO2 c r y s t a l i n c r e a s e s f r o m 2n to (2n + m) s i t e s . T h i s l a t t i c e c o n t a i n s t h e r e f o r e (2n + m ) / 2 t e t r a h e d r a l s i t e s and only n a t o m s of Si; the r e m a i n i n g u n o c c u p i e d s i t e s which we define " v a c a n c i e s " , r e p r e s e n t the e n e r g e t i c effects of m e t a l c a t i o n s : t h e r e f o r e t h e r e a r e so as m a n y types of " v a c a n c i e s " as t h e r e a r e m e t a l cations. The s a m e s c h e m e can be adopted for a l u m i n o - s i l i cates (SiO2 .AIzO3 .MeO) a s s u m i n g that a l u m i n u m is t e t r a c o o r d i n a t e d ; in effect the t e t r a c o o r d i n a t i o n of a l u m i n u m has a l r e a d y b e e n p o s t u l a t e d i n Ref. 4 in s y s t e m s where the m o l a r f r a c t i o n of m e t a l oxide is g r e a t e r than that of A12Os. A s y s t e m c o n t a i n i n g m m o l e c u l e s of MeO, n m o l e c u l e s of SiO2 and p m o l e c u l e s of A12Os contains t h e r e f o r e (m + 2n + 3p) a t o m s of oxygen and thus (m + 2n + 3p)/2 t e t r a h e d r a l s i t e s . Of t h e s e , (n + 2p) a r e occupied by Si a n
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