COMPUTER SIMULATION STUDIES OF MIGRATION MECHANISMS ...

JOURNAL DE PHYSIQUE Colloque

C9, supplément

au n°12,

Tome 43, décembre

1982

page

C9-381

COMPUTER SIMULATION STUDIES OF MIGRATION MECHANISMS IN IONIC GLASSES AND LIQUIDS C.A. A n g e l l , P.A. Cheeseman and S. Tamaddon Department U.S.A.

of Chemistvy

Thωue University,

West Lafayette,

Indiana

47907,

Résumé.- Les mécanismes de m i g r a t i o n des c a t i o n s e t des a n i o n s dans l e s v e r r e s e t l i q u i d e s du type s i l i c a t e e t f l u o r u r e simulés ont é t é é t u d i é s p a r des méthodes de dynamique m o l é c u l a i r e à l ' o r d i n a t e u r . On donne des exemples m o n t r a n t l a p u i s s a n c e de l a méthode. On montre l ' e x i s t e n c e d ' u n minimum de v i s c o s i t é aux p r e s s i o n s é l e vées pour des a l u m i n o s i l i c a t e s f o n d u s . Abstract. - Ion dynamics computer simulations of the migration of cation and anions in "computer glasses" and liquids of silicate and fluoride types are reported, and examples of the diagnostic power of the simulation method are given. The existence of high pressure minima in the viscosity of molten aluminosilicates is indicated.

Introduction. - In this paper we will review briefly the way in which the use of ion dynamics computer simulation studies can help develop concepts for, and models of, ionic motion in both rigid glasses and high-temperature ionic liquids. The description will cover (1) cases in which the physical properties of the normal substance are directly simulated, and (2) cases in which the special ability of the simulation programs to introduce changes in the system (for instance, a change of mass without change of interionic potential) which cannot be introduced in laboratory experiments, is used to reveal features of the migration mechanism which otherwise might be difficult to recognize. Considering migration in solid glasses first, we reproduce in Fig. 1 the a.c. conductivity (or absorptivity) over a wide frequency range for a well-studied system, Na20'3Si02 glass, in order to draw attention to those features of the observed behavior which the simulation should help to explain. Fig. 1 shows the electrical conductivity over a wide frequency range from 10~1-10 Hz based on data from a number of different studies to which reference can be found in Ref. 1. We see, firstly, a frequency-independent but strongly temperature-dependent part of the conductivity response which is related directly to the diffusivity of the alkali cation in this material. Secondly, we see a frequency-dependent region with a maximum at M0*--> Hz in which the conductivity is comparatively independent of temperature. This is observed experimentally using far infra-red spectroscopy. Thirdly, we see a more or less temperature independent, constant slope, regime which connects the high frequency and low frequency extremes. This frequency-dependent regime conforms to the simple relation a(f) = kf a

(1)

where a = 1.0. The simulation, then, should show features which correspond with each of these regions and hopefully will provide a mechanistic interpretation of their existence. Simulations of the cases of alkali migration in silicate glasses, and also for fluoride anion conduction in fluorozirconate glasses, were performed using a multicomponent ion dynamics program described in previous publications (2). The potential of interaction for the various possible pairs of ions in the simulated stretches is assumed to be a simple two term function (coulomb + exponential repulsion) U. .(r) = e z.z./r.. + b.. exp [(a. + a. - r..)/p] ij

1 3 1 0

13

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1

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13

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1982972

(2)

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JOURNAL DE PHYSIQUE

The p a r a m e t e r s used i n Eq. ( 2 ) i n t h i s s t u d y a r e c o l l e c t e d i n T a b l e 1 below. The number of i o n s i n t h e primary c o m p u t a t i o n a l box was of o r d e r 200, and d e t a i l s of t h e c a l c u l a t i o n and of l i m i t a t i o n s on i t s accuracy a r e given i n e a r l i e r p u b l i c a t i o n s (2,7) Table 1 A l k a l i S i l i c a t e and Alumino S i l i c a t e b . ( 10-13erg) a Species ~j Si 0 Na A1 Si 1.33 3.42 0 1.42 2.117 0.814 Na 1.252 2.898 1.595 2.375 A1 1.358 3.372 2.070 2.850 3.325

p = 0.29

-'E

Barium F l u o r o z i r c o n a t e bi . (loa13erg) Species a 2r Ba F 2r 1 . 2 8 3.80 Ba 1.49 3.325 2.85 F 1 . 3 3 2.613 2.138 1.425 cm-' 1 10 I00KXX) 'uDlo

RAD1u

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MI~RO

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100010-

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F i g . 1 : E x p e r i m e n t a l frequency s p e c t r for ~ a + i o n motions i n Na20.3Si02 g l a s s and l i q u i d s t a t e a t d i f f e r e n t temperatures. For a a l k a l i s i l i c a t e glasses, ~ ( f = ) 1.01 x 1 0 - ~ a ( f )

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6

8

;

10

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14

log f Hz A l k a l i C a t i o n M i g r a t i o n . - W e r e p o r t b a s i c f i n d i n g s f o r t h e dynamics sodium s i l i c a t e " g l a s s " v e r y b r i e f l y ( t h e y have been p u b l i s h e d p r e v i o u s l y ) ( 2 ) , i n o r d e r t o d e s c r i b e h e r e p r e v i o u s l y u n p u b l i s h e d "experiments" from which new i n s i g h t i n t o t h e m i g r a t i o n mechanism can b e o b t a i n e d . The c h a r a c t e r of t h e a l k a l i motions observed i n Na20-3Si02 g l a s s i s demonstrated by F i g . 2a i n which t h e t r a j e c t o r i e s f o r a l l t h e sodium i o n s i n t h e primary c o m p u t a t i o n a l b o x a r e p r o j e c t e d o n t o one of i t s f a c e s . The diagram shows two s t a g e s i n t h e e v o l u t i o n of t h e motions, t h e f i r s t a f t e r 0 . 1 p s h a s e l a p s e d s i n c e t h e b e g i n n i n g of t h e r u n and t h e second a f t e r t e n t i m e s a s l o n g i n which t h e development of t r a j e c t o r y "channels" can b e s e e n . E v i d e n t l y t h e i o n s a r e s p e n d i n g some t i m e o s c i l l a t i n g a n h a r m o n i c a l l y ( " r a t t l i n g " ) i n a p r e f e r r e d l o c a t i o n i n t h e s t r u c t u r e , and some time d r i f t i n g i n c e r t a i n p r e f e r r e d d i r e c t i o n s between s u c h s i t e s . The e f f e c t i v e o s c i l l a t i o n frequency is o b t a i n e d by a p r i n t - o u t of t h e number of r e v e r s a l s of t h e t r a j e c t o r y , and c o r r e s p o n d s t o a frequency of 200 cm-I i n good The agreement w i t h t h e observed s t r o n g f a r i n f r a - r e d band c e n t e r e d a t 220 cm-'(4). d r i f t i n g motion can b e d e s c r i b e d by t h e f a m i l i a r mean-squared d i s p l a c e m e n t ( a v e r a g e v a l u e ) a s a f u n c t i o n of time, which i s d e p i c t e d i n F i g . 2b. From t h e long-time s l o p e of t h i s c u r v e a d i f f u s i o n c o e f f i c i e n t a t t h e t e m p e r a t u r e of t h e c a l c u l a t i o n , of 1.3 x i ~ - ~ c m is ~ o b t~a i n~e d ~ . -Using ~ t h e Nernst-Einstein equation w i t h c o r r e l a t i o n f a c t o r f = 0 . 4 , t h i s v a l u e of DN,+ p r e d i c t s a n e l e c t r i c a l c o n d u c t i v i t y of 1 . 2 Q-'om-I which a g r e e s w i t h experiment w i t h i n 25% (a1500K = 0 . 9 5 Q-lcm-I). To u n d e r s t a n d what d e t e r m i n e s t h e r a n g e o v e r which t h e d r i f t i n g motion can o c c u r , hence t h e r e l a t i o n between l o n g r a n g e and l i m i t e d range ( n o n - d i f f u s i v e mot i o n s ) we conduct experiments i n which t h e mass of t h e o x i d e i o n i s a r t i f i c i a l l y changed t o a l a r g e number t o o b s e r v e how t h e sodium i o n m o b i l i t y i s a f f e c t e d . I n t h e i d e a l f a s t i o n conductor t h e motion of t h e c o n d u c t i n g s p e c i e s i s c o m p l e t e l y decoupled from t h a t of t h e l a t t i c e , and change of a n i o n mass would have no e f f e c t . The s t r o n g d i s p l a c e m e n t which i n f a c t f o l l o w s from a n i n c r e a s e i n o x i d e i o n mass decrease i n ~ a + h a s been d e s c r i b e d e a r l i e r ( 2 ) , and i n t h e p r e s e n t p a p e r we conduct f u r t h e r " e x p e r i ments" t o e l u c i d a t e t h e o r i g i n of t h i s e f f e c t .

~

F i g . 2 ( a ) : Nai t r a j e c t o r i e s , over s h o r t (0.14 ps) and l o n g (0.97 p s ) time p e r i o d s p r o j e c t e d o n t o a box s i d e .

(b) : Mean-squared displacement of a l l i o n s i n Na 0 . 3 S i 0 2 a t 1500 K. 2

I n t h e p r e s e n t work t h e mass of oxide i o n s i n t h e system h a s been s e l e c t i v e l y i n c r e a s e d from 1 6 t o 160 amu depending on whether t h e o x i d e performs a b r i d g i n g o r a nonbridging f u n c t i o n i n t h e g l a s s . T h i s can b e simply determined from e x a n i n i n g a p r i n t - o u t of t h e n e a r n e i g h b o r s of a l l oxides i n t h e system and a s s i g n i n g b r i d g i n g f u n c t i o n s t o a l l t h o s e which have two s i l i c o n i o n s w i t h i n a d i s t a n c e of 2.0 1. The s i m u l a t i o n i s t h e n c o n t i n u e d , s t a r t i n g from t h e same i n i t i a l c o n f i g u r a t i o n a f t e r e n t e r i n g t h e new s p e c i e s and s p e c i e s mass assignments i n t h e i n p u t d a t a . The r e s u l t s of t h e s e experiments a r e shown i n F i g . 3 , where t h e mean-squared displacement of t h e sodium i o n s over a p e r i o d of 2.0 p s f o r t h e two c a s e s of heavy b r i d g i n g and heavy n o n b r i d g i n g oxygens i s compared w i t h t h e r e s u l t found f o r t h e normal oxide mass c a s e . We s e e t h a t t h e sodium i o n motion i s s l i g h t l y a c c e l e r a t e d when t h e nonbridging oxygens a r e made heavy, b u t i s g r e a t l y d e p r e s s e d when t h e b r i d g i n g oxygens a r e made heavy.

Fi:. 3 ( a ) : Mean-squared displacement of Na i o n s f o r normal Na2OS3SiO2 a t 1500 K , and f o r c a s e s of ( i ) heavy b r i d g i n g o x i d e i o n s and ( i i ) heavy n o n b r i d g i n g o x i d e i o n s , showing b r a k i n g e f f e c t of t h e l a t t e r .

(b) : T r a j e c t o r i e s of Nai i o n s i n p r e s ence of heavy n o n b r i d g i n g i o n i c showing l o c a l i z a t i o n of Na+ i o n s ( r a t t l e and l i m i t e d d r i f t motion).

The sodium i o n t r a j e c t o r i e s o b t a i n e d i n t h e l a t t e r c a s e a r e shown i n F i g . 3b. I t i s s e e n t h a t t h e d i s t a n c e t h a t t h e sodium i o n s t r a v e l i n t h i s c a s e i s l i m i t e d , s o t h a t t h e conducting "channels" have e f f e c t i v e l y d i s a p p e a r e d . T h i s i m p l i e s t h a t nonbridging oxygens i n t h e s t r u c t u r e s e r v e t o p r o v i d e t h e b a r r i e r s which l i m i t t h e motion o f t h e a l k a l i i o n s : i n c r e a s i n g t h e mass of t h e s e i o n s h a s e f f e c t i v e l y c l o s e d t h e channels f o r t h e c o n d i t i o n s of t h i s c a l c u l a t i o n . The e x a c t manner i n which t h e heavy mass s e r v e s t o c l o s e t h e channels i s n o t made c l e a r by t h e s e experiments. It may b e e i t h e r a v i b r a t i o n a l a m p l i t u d e e f f e c t , i n which t h e i n c r e a s e i n mass, by res t r i c t i n g t h e amplitude of d i s p l a c e m e n t , r e d u c e s t h e p o s s i b i l i t y of a sodium i o n s l i p p i n g through t h e b o t t l e n e c k , o r i t may simply be a r e s u l t of t h e i n c r e a s e d mass more e f f e c t i v e l y b a c k - s c a t t e r i n g t h e approaching a l k a l i c a t i o n s , a n i n e r t i a l e f f e c t d i s t i n c t from t h e f i r s t - m e n t i o n e d . The experiment, however, s e r v e s t o f o c u s a t t e n t i o n on t h e n o n b r i d g i n g oxygens a s t h e l i m i t i n g f a c t o r i n t h e m i g r a t i o n of t h e a l k a l i i o n s , a n o b s e r v a t i o n which i s , of c o u r s e , i n good accord w i t h t h e e x p o n e n t i a l i n c r e a s e i n c o n d u c t i v i t y a s t h e number of nonbridging oxygens i n t h e s t r u c t u r e i s reduced w i t h i n c r e a s i n g a l k a l i i o n c o n t e n t (though t h e r e a s o n f o r t h e s l o p e of 0.5 found f o r l o g o v s % a l k a l i i s n o t a s obvious a s i n t h e weak e l e c t r o l y t e m o d e l ( 5 ) ) .

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The motions s e e n i n F i g . 3b a l s o have r a t t l e , 190 cm-l, and d r i f t components, b u t t h e d r i f t i s now l i m i t e d and w i l l r e s u l t i n a frequency dependent l o s s dependent on t h e c h a n n e l l e n g t h s . T h i s w i l l c o n t r i b u t e i n t h e o ( f ) = kf" regime, which i s t h u s i d e n t i f i e d a s a n e c e s s a r y accompaniment of t h e g a t e d c h a n n e l conductance mechanism. F l u o r i d e Anion Motion. - T u r n i n g t o f l u o r i d e i o n motion, d i f f e r e n c e s from t h e c a s e d e s c r i b e d above must b e e x p e c t e d because i n t h i s c a s e t h e r e i s only one a n i o n i n t h e system, i . e . , a n obvious mobile s p e c i e s l i k e t h e a l k a l i c a t i o n , h a s n o t been i n t r o duced i n t o t h e system. S i m u l a t i o n s c a r r i e d o u t on a p r o t o t y p e b i n a r y f l u o r o z i r c o n a t e " g l a s s " w i t h molar p r o p o r t i o n s 64 ZrF4:36BaF2 b u t n o t d e s c r i b e d i n d e t a i l h e r e have i n d i c a t e d a s t r u c t u r a l o r g a n i z a t i o n i n which e a c h zirconium i s surrounded by 7 f l u o r i d e i o n s , 4 of which perform a b r i d g i n g f u n c t i o n - t o second n e a r e s t n e i g h b o r z i r conium i o n s . The remaining 3 have bariums a s t h e i r second n e a r e s t n e i g h b o r s , t h e symmetry of t h e arrangement b e i n g v a r i a b l e throughout t h e s t r u c t u r e . I n o r d e r t o d e t e r m i n e whether a l l f l u o r i d e i o n s i n t h e s t r u c t u r e a r e e q u a l l y m o b i l e , o r whether t h e n o n b r i d g i n g f l u o r i d e s a r e t h e most mobile, we h a v e , a s b e f o r e , i d e n t i f i e d t h e f l u o r i d e i o n s i n t h e s t r u c t u r e a c c o r d i n g t o whether they have one o r two n e a r e s t n e i g h b o r zirconium i o n s . The two c l a s s e s a r e t h e n d i s t i n g u i s h e d from one a n o t h e r i n t h e program, and a s i m u l a t i o n r u n i s i n i t i a t e d . Given s u f f i c i e n t t i m e t h e e x i s t e n c e of exchanges of f l u o r i d e s between d i f f e r e n t z i r c o n i u m c e n t e r s duri n g t h e p r o g r e s s of d i f f u s i o n s h o u l d e l i m i n a t e t h e d i s t i n c t i o n between t h e b r i d g i n g and n o n b r i d g i n g f l u o r i d e s , s o t h e d u r a t i o n of t h e r u n h a s been l l m i t e d . Also t h e t e m p e r a t u r e of t h e r u n was chosen s o t h a t s l o w e r of t h e two s p e c i e s undergo few o r no exchanges between Zr4+ c e n t e r s d u r i n g t h e r u n . The r e s u l t s a r e shown i n F i g . 4. T h i s e x p e r i m e n t , which we r e g a r d a s v e r y q u a l i t a t i v e and p r e l i m i n a r y , s u g g e s t s t h a t t h e b r i d g i n g f l u o r i d e i o n s a r e i n d e e d more mobile t h a n t h e n o n b r i d g i n g , a l t h o u g h t h e l a t t e r s t i l l d r i f t f u r t h e r i n t h e c o u r s e of t h e s h o r t r u n t h a n do t h e zirconium o r t h e barium s p e c i e s which e f f e c t i v e l y p r o v i d e a "frozen" m a t r i x w i t h i n which t h e f l u o r i d e i o n s can m i g r a t e . It remains f o r f u r t h e r work t o show how t h i s a b i l i t y i s i n f l u e n c e d by changes of composition which produce more n o n b r i d g i n g f l u o r i d e s .

F i g . 4 : " S i n g l e ass" mean-square d i s p l a c e m e n t v s . t i m e p l o t s a t 1200 K f o r i o n s i n t h e s y s t e m ZrF4 BaF2 i n which t h e F- component h a s been s e p a r a t e d i n t o b r i d g i n g (Zr-F-Zr) and n o n b r i d g i n g (Zr-F-(Ba)) t y p e s , d e f i n e d a t t - 0 . S i n c e t h e system s o defined i s n o t an equilibrium system o n l y a s i n g l e p a s s s t a r t i n g a t t = 0 h a s been made, which a c c o u n t s f o r g r e a t e r n o i s e l e v e l .

+

Fig. 5 : Isothermal pressure dependence of t h e i o n i c d i f f u s i v i t i e s i n a liquid aluminosilicate of low p r e s s u r e open network type. Note t h e w a t e r - l i k e d i f f u s i v i t y maximum f o r t h e network i o n s a t 200-300 k b a r implying a v i s c o s i t y minimum i n t h e same p r e s s u r e range.

Motion of Network I o n s i n Molten S i l i c a t e s . - Turning now t o t h e s t u d y of c e r t a i n problems of i n t e r e s t i n f u l l y f l u i d i o n i c glass-forming s y s t e m s , we examine t h e b e h a v i o r of some v e r y h i g h t e m p e r a t u r e s i l i c a t e s y s t e m s . These a r e of i n t e r e s t n o t o n l y a s g l a s s - f o r m i n g m a t e r i a l s , b u t a s geochemical s y s t e m s o f t h e t y p e which a r e r e s p o n s i b l e f o r most of t h e e a r t h ' s c o n t i n e n t a l c r u s t , ( a l u m i n o s i l i c a t e s w i t h v a r i o u s charge-compensating c a t i o n s s u c h a s ~ a + ,K+, Ca*). The q u e s t i o n of i n t e r e s t which we wish t o examine i n t h i s c a s e i s whether o r n o t t h e c h o i c e of compositions which f a v o r , a t low t e m p e r a t u r e s , expanded network s t r u c t u r e s , w i l l behave l i k e w a t e r i n t h e i r r e s p o n s e t o i n c r e a s e s i n p r e s s u r e , i . e . , w h e t h e r i n c r e a s e i n p r e s s u r e w i l l c a u s e t h e f l u i d i t y of t h e m a t e r i a l t o i n c r e a s e anomalously, r a t h e r t h a n d e c r e a s e , a s i s t h e c a s e w i t h most l i q u i d s . L a b o r a t o r y s t u d i e s on l i q u i d j a d e i t e , NaA1Si206 which observed t h a t p r e s s u r e i n c r e a s e s t o 40 k b a r caused a r a p i d l o w e r i n g o f t h e v i s c o s i t y a t 1350" C , were r e p o r t e d by K u s h i r o i n 1976, and s i m i l a r r e s u l t s h a v e been found f o r s e v e r a l o t h e r s i l i c a t e m e l t s s i n c e t h a t time. Such b e h a v i o r would b e r e f l e c t e d i n o u r s i m u l a t i o n s t u d i e s by i n c r e a s e s w i t h p r e s s u r e i n t h e i o n i c d i f f u s i v i t i e s f o r t h e i o n i c s p e c i e s siW, ~ l ~and ' , 02which make up t h e q u a s i l a t t i c e of t h e l i q u i d . However, w i t h t h e u n l i m i t e d p r e s s u r e range o f t h e i o n dynamics method, t h e p r e s s u r e a t which t h e m o b i l i t i e s , hence t h e f l u i d i t y , would p a s s through maximum v a l u e s ( a s i n t h e c a s e of w a t e r ) could b e identified. I n F i g . 5 we show r e s u l t s f o r NaAlSi206 a t 6000 K , a n h i g h t e m p e r a t u r e b e i n g chosen i n o r d e r t h a t t h e i o n s d i s p l a c e s u f f i c i e n t l y i n economically r e a s o n a b l e computing t i m e s f o r t h e c a l c u l a t e d d i f f u s i o n c o e f f i c i e n t s t o b e r e a s o n a b l y r e l i a b l e . The r e s u l t s i n d e e d show t h e e x i s t e n c e of m o b i l i t y maximum i n t h e v i c i n i t y of 2-300 k b a r . Examination of t h e a v e r a g e c o o r d i n a t i o n number of t h e si4+ i o n s w i t h s t r u c t u r e s u g g e s t t h a t t h e m o b i l i t y maximum c o r r e l a t e s w i t h a maximum p r e v a l e n c e of t h e u n s t a b l e c o o r d i n a t i o n s t a t e 5 , c o n s i s t e n t w i t h t h e o b s e r v a t i o n s by Brawer on BeF2 glass (6). Another f e a t u r e of i n t e r e s t i n F i g . 5 i s t h e c o n t r a s t i n p r e s s u r e dependences i o n s . The r a p i d d e c r e a s e i n D N ~ + of t h e network i o n s and t h e i n t e r s t i t i o n a l ~ a + a t a l l p r e s s u r e s i s c l e a r l y a consequence of t h e c o l l a p s e of t h e open c h a n n e l s t r u c t u r e w i t h d e c r e a s i n g volume. For such i o n s t h e S t o k e s - E i n s t e i n e q u a t i o n would e v i d e n t l y f a i l even t o p r e d i c t t h e s i g n of t h e p r e s s u r e dependence. Elsewhere, we have shown how t h e s e anomalous c h a r a c t e r i s t i c s may be removed by a d d i t i o n of e x c e s s o x i d e i o n t o c h e m i c a l l y b r e a k down t h e framework s t r u c t u r e , a r e s u l t which i s a l s o c o n s i s t e n t w i t h l a b o r a t o r y e x p e r i m e n t s a t lower t e m p e r a t u r e . ACKNOWLEDGEMENT. - This work was s u p p o r t e d i n p a r t by t h e N a t i o n a l S c i e n c e Foundation U.S.A. under NSF-MRL Grant 80-20249 and S o l i d S t a t e Chemistry Grant DMR 8007053. F l u o r i d e g l a s s s t u d i e s were a s s i s t e d by Hanscomb A i r Force Base. REFERENCES 1.

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