COMPUTER SIMULATION STUDIES OF MIGRATION MECHANISMS IN IONIC GLASSES AND LIQUIDS

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COMPUTER SIMULATION STUDIES OF

MIGRATION MECHANISMS IN IONIC GLASSES AND LIQUIDS

C. Angell, P. Cheeseman, S. Tamaddon

To cite this version:

C. Angell, P. Cheeseman, S. Tamaddon. COMPUTER SIMULATION STUDIES OF MIGRATION

MECHANISMS IN IONIC GLASSES AND LIQUIDS. Journal de Physique Colloques, 1982, 43 (C9),

pp.C9-381-C9-385. �10.1051/jphyscol:1982972�. �jpa-00222501�

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 of Chemistvy Thωue University, West Lafayette, Indiana 47907, U.S.A.

Résumé.- Les mécanismes de m i g r a t i o n des c a t i o n s e t d e s 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 s i m u l é s o n t 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 m é t h o d e . 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 - v é e s 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 descrip- tion 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 diffi- cult 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 be- havior 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 num- ber 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 ob- served experimentally using far infra-red spectroscopy. Thirdly, we see a more or less temperature independent, constant slope, regime which connects the high fre- quency and low frequency extremes. This frequency-dependent regime conforms to the simple relation

a(f) = kf

(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 multi- component 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] (2) ij 1 3 1 0 13 ^ 1 : 13

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

C9-382 JOURNAL DE PHYSIQUE

The p a r a m e t e r s u s e d 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 p r i m a r y 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 a c c u r a c y a r e g i v e n i n e a r l i e r p u b l i c a - t i o n s (2,7)

T a b l e 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 Barium F l u o r o z i r c o n a t e

S p e c i e s a ^b . ( 10-13erg)

~j p

0.29 S p e c i e s a ^bi . ( l o a 1 3 e r g )

S i 0 Na A1 2 r Ba F

S i 1 . 3 3 3.42 2 r 1 . 2 8 3.80

0 1 . 4 2 2.117 0.814 Ba 1 . 4 9 3.325 2.85

Na 1.252 2.898 1 . 5 9 5 2.375 F 1 . 3 3 2.613 2.138 1.425

A1 1.358 3.372 2.070 2.850 3.325

cm-'

' ~ l k Ik

-

- 'E

0

a

Q) 10-

Z

F i g . 1 : E x p e r i m e n t a l f r e q u e n c y s p e c t r

-

f o r ~ a + i o n m o t i o n s 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 t e m p e r a t u r e s . F o r a a l k a l i s i l i c a t e g l a s s e s ,

~ ( f ) = 1 . 0 1 x 1 0 - ~ a ( f )

I

~

~

;

J ~ ~ ~ ~ ~ ~ ~ . ~ ~ ~ ~ ~ J

log f Hz

A l k a l i C a t i o n M i g r a t i o n . -

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 h a v e b e e n 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 " e x p e r i m e n t s " 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 o b s e r v e d i n

Na20-3Si02 g l a s s i s d e m o n s t r a t e d 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 p r i m a r y 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 o f i t s f a c e s . The d i a g r a m 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 m o t i o n s , 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 s e c o n d 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 " c h a n n e l s " c a n 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 t i m e 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 f r e q u e n c y is o b t a i n e d by a p r i n t - o u t of t h e number o f 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 f r e q u e n c y of 200 cm-I i n good a g r e e m e n t w i t h t h e o b s e r v e d 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). The d r i f t i n g motion c a n 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 t i m e , 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 o f t h e c a l c u l a t i o n , of 1 . 3 x i ~ - ~ c m i s ~ o b t a i n e d . ~ ~ ~ - Using t h e N e r n s t - E i n s t e i n e q u a t i o n 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 o f 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 e x p e r i m e n t 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 m o t i o n can

o c c u r , h e n c e t h e r e l a t i o n between l o n g r a n g e a n d l i m i t e d r a n g e ( n o n - d i f f u s i v e mo-

t i o n s ) we c o n d u c t e x p e r i m e n t s 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 c o n d u c t o r t h e m o t i o n 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 d e c o u p l e d

from t h a t o f t h e l a t t i c e , and change of a n i o n mass would h a v e n o e f f e c t . The s t r o n g

d e c r e a s e i n ~ a + 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

h a s b e e n 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 .

p r o j e c t e d o n t o a box s i d e . 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 o x i d e i o n s i n t h e s y s t e m 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 w h e t h e r t h e o x i d e p e r f o r m s a b r i d g i n g o r a n o n b r i d g i n g f u n c t i o n i n t h e g l a s s . T h i s c a n b e s i m p l y d e t e r m i n e d 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 o x i d e s i n t h e s y s t e m 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 a s s i g n m e n t s 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 e x p e r i m e n t s a r e shown i n F i g . 3 , where t h e mean-squared d i s p l a c e m e n t of t h e sodium i o n s o v e r 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 o x i d e 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 n o n b r i d g i n g oxygens a r e made h e a v y , 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 d i s p l a c e m e n t of (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 - Na i o n s f o r normal Na2OS3SiO2 a t 1500 K , e n c e of heavy n o n b r i d g i n g i o n i c showing 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 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 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 , l i m i t e d d r i f t m o t i o n ) .

showing b r a k i n g e f f e c t of t h e l a t t e r .

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 c o n d u c t i n g " c h a n n e l s " 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 n o n b r i d g i n g 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 c h a n n e l s 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 c h a n n e l s i s n o t made c l e a r by t h e s e e x p e r i m e n t s . 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 re-

s t r i c t i n g t h e a m p l i t u d e 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 t h r o u g h t h e b o t t l e n e c k , o r i t may simply b e 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 a p p r o a c h i n g 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 e x p e r i m e n t , 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 a c c o r d 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 n o n b r i d g i n g 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 ( t h o u g h 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 o b v i o u s 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 ) ) .

C9-384 JOURNAL DE PHYSIQUE

The m o t i o n s s e e n i n F i g . 3b a l s o h a v e 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 f r e q u e n c y d e p e n d e n t 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" r e g i m e , 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 c o n d u c t a n c e 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 m o t i o n , 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 b e c a u s e i n t h i s c a s e t h e r e i s o n l y one a n i o n i n t h e s y s t e m , i . e . , a n o b v i o u s m o b i l e 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 b e e n i n t r o - duced i n t o t h e s y s t e m . S i m u l a t i o n s c a r r i e d o u t o n 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 m o l a r 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 h a v e 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 z i r c o n i u m i s s u r r o u n d e d by 7 f l u o - r i d e i o n s , 4 o f which p e r f o r m 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 r e m a i n i n g 3 h a v e bariums a s t h e i r s e c o n d n e a r e s t n e i g h b o r s , t h e symmetry of t h e a r r a n g e m e n t b e i n g v a r i a b l e t h r o u g h o u t 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 w h e t h e r 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 w h e t h e r 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 m o b i l e , 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 w h e t h e r t h e y h a v e one o r two n e a r e s t n e i g h b o r z i r c o n i u m 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 dur- i 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 . A l s o 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 e x c h a n g e s 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 m o b i l e 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 d o t h e z i r c o n i u m o r t h e b a r i u m 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

" f r o z e n " 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 c o m p o s i t i o n which p r o d u c e 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 b e e n 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 s y s t e m s o d e f i n e d i s n o t a n e q u i l i b r i u m s y s t e m 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 b e e n 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 .

F i g . 5 : I s o t h e r m a l p r e s s u r e 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 l i q u i d a l u m i n o s i l i c a t e 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 i m p l y i n g 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

r a n g e .

b e h a v i o r o f 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 o f 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 g e o c h e m i c a l 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 o f i n t e r e s t which we w i s h t o examine i n t h i s c a s e i s w h e t h e r o r n o t t h e c h o i c e of c o m p o s i t i o n s w h i c h 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 o f t h e m a t e r i a l t o i n c r e a s e

a n o m a l o u s l y , 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 o b s e r v e d 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 c a u s e d 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 , w e r e 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 b e e n 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 t i m e . 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 02- which 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

r a n g e 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 , h e n c e t h e f l u i d i t y , would p a s s t h r o u g h maximum v a l u e s ( a s i n t h e c a s e o f w a t e r ) c o u l d b e i d e n t i f i e d .

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 e c o n o m i c a l l y 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 o f 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 o f 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 o n BeF2 g l a s s ( 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 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 + i o n s . The r a p i d d e c r e a s e i n D N ~ + 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. F o r s u c h 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.

E l s e w h e r e , we h a v e 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 o f 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. - T h i s 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 F o u n d a t i o n U.S.A. under NSF-MRL G r a n t 80-20249 and S o l i d S t a t e C h e m i s t r y G r a n t DMR 8007053.

F l u o r i d e g l a s s s t u d i e s w e r e a s s i s t e d by Hanscomb A i r F o r c e B a s e . REFERENCES

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