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MECHANICAL RELAXATION BY MOBILE IONS
(Cu+ AND Ag+) IN FAST ION CONDUCTING
GLASSES
C. Liu, C. Angell
To cite this version:
JOURNAL DE PHYSIQUE
Colloque CIO, supplément au n012, Tome 46, décembre 1985
page
C10-493MECHANICAL RELAXATION BY MOBILE IONS (Cu+ AND Ag')
IN FAST ION
CONDUCTING GLASSES
C. LIU AND
C.A. ANGELL
Department of Chemistry, Purdue University, West Lafayette,
IN47907, U.S.A.
A b s t r a c t
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The d i s s i p a t i o n o f mechanical e n e r g y i n g l a s s e s of t h e " f a s t i o n conductor" t y p e (AgI-AgP03, AgI-Ap,B02 a n d AgC1-CsI) h a s b e e n s t u d i e d u s i n g a Rheovibron mechanical a n a l y z e r i n t h e t e m p e r a t u r e r a n g e -190 t o 200°C. I n most c a s e s a s i n g l e l o s s peak a t low t e m p e r a t u r e i s found f o r f i x e d - f r e q u e n c y s c a n s . The peak t e m p e r a t u r e a l m o s t c o i n c i d e s w i t h t h a t f o r e l e c t r i c a l c o n d u c t i v i t y re-l a x a t i o n b u t i s much b r o a d e r . The l o s s magnitude does n o t c o r r e l a t e w i t h peak t e m p e r a t u r e b u t depends on g l a s s c o n s t i t u t i o n . Idhere l o s s i s s m a l l , t h e r e l a x a - t i o n time f o l l o w s A r r h e n i u s Law w i t h
r0
= l/2irf0,where f, i s found from f a r IR s p e c t r a . F o r l a r g e l o s s g l a s s e s , i m p o r t a n t non-Arrhenius b e h a v i o r i s found.INTRODUCTION
Although t h e t e c h n o l o g i c a l need f o r s o l i d e l e c t r o l y t e s h a s l e d t o a n e x p l o s i v e i n - c r e a s e i n t h e number o f c o n d u c t i v i t y s t u d i e s i n c r y s t a l l i n e and v i t r e o u s i o n i c mater- i a l s , t h e r e h a s been r e l a t i v e l y l i t t l e a t t e n t i o n g i v e n t o t h e r e s p o n s e of t h e m o b i l e i o n s t o m e c h a n i c a l , a s opposed t o e l e c t r i c a l , s t r e s s e s . Apart from c l a s s i c s t u d i e s f o c u s s e d on normal o x i d e g l a s s e s , t h e r e h a s o n l y been t h e u l t r a s o n i c s s t u d y o f C a r i n i and c o l l e a g u e s o n AgI-Ag*O-B203 g l a s s e s /1/. T h i s i s u n f o r t u n a t e b e c a u s e t h e mechan- i c a l r e s p o n s e i s q u a l i t a t i v e l y d i f f e r e n t from t h e e l e c t r i c a l r e s p o n s e i n s o f a r a s t h e r e a l p a r t o f t h e modulus remains f i n i t e a t low f r e q u e n c i e s . An e l e c t r i c a l s t r e s s a c t i n g on t h e same i o n s w i l l b e c o m p l e t e l y d i s s i p a t e d by t h e unimpeded motion of t h e i o n s a c r o s s t h e sample. Furthermore, t h e m e c h a n i c a l r e s p o n s e i s a s e c o n d a r y r e l a x a - t i o n , t h e p r i m a r y r e l a x a t i o n b e i n g t h a t which l e a d s t o t h e g l a s s t r a n s i t i o n .
For t h e c l a s s i c a l (weakly-conducting) g l a s s e s , t h e i n v e s t i g a t i o n o f m o b i l e i o n motion i s t e d i o u s b e c a u s e o f t h e s m a l l magnitude of t h e l o s s . For f a s t i o n conduc- t o r s , on t h e o t h e r hand, t h e l o s s e s a r e much g r e a t e r , a n d l e s s - s e n s i t i v e i n s t r u m e n t s such a s a Rheovibron (Toyo I n s t r u m e n t s I n c . ) may be employed w i t h a r e s u l t a n t i n - c r e a s e i n r a t e o f d a t a a c q u i s i t i o n o f a t l e a s t one o r d e r o f magnitude.
I n t h i s r e p o r t we d e s c r i b e e s s e n t i a l f e a t u r e s o f t h e m e c h a n i c a l r e s p o n s e o f t h r e e t y p e s of f a s t i o n c o n d u c t o r s o v e r wide t e m p e r a t u r e r a n g e s .
EXPERIMENTAL SECTION
The p r i n c i p l e s o f t h e measurement a r e i l l u s t r a t e d i n F i g . 1. Two sample c o n f i g u r a - t i o n s a r e i n common u s e . The f i r s t u t i l i z e s a f i b e r which i s h e l d between s t a i n l e s s s t e e l jaws connected t o t h e f r e q u e n c y g e n e r a t i n ~ a n d s t r e s s / s t r a i n d e t e c t i n g e l e m e n t s o f t h e Rheovibron. A s i n u s o i d a l s t r a i n cllis a p p l i e d , and t h e l a g of t h e s t r e s s a2
b e h i n d t h e s t r a i n is r e c o r d e d a s t h e l o s s t a n g e n t i l l u s t r a t e d i n t h e lower p a r t of t h e f i g u r e . The second, from which t h e same i n f o r m a t i o n c a n b e a c q u i r e d , u s e s t h e
C10-494
J O U R N A L
DEPHYSIQUE
. .
F i g . 1 - P r i n c i p l e s of measurement. F i g . 2
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Loss s c a n s f o r AgI-&PO3 g l a s s e s . f l e x u r e c o n f i g u r a t i o n i l l u s t r a t e d i n t h e c e n t e r s e c t i o n o f F i g . 1. The jawlsample assembly is e n c l o s e d i n a v a r i a b l e t e m p e r a t u r e m e t a l b l o c k , and t h e l o s s t a n g e n t and dynamic modulus a t c o n s t a n t f r e q u e n c y a r e r e a d a t f r e q u e n t i n t e r v a l s d u r i n g a slow t e m p e r a t u r e s c a n from -200 t o+
200°C ( a s n e e d e d ) .RESULTS
Complete s c a n s , f r o m t h e low t e m p e r a t u r e regime where t h e "mobile i o n " l o s s is r e - c o r d e d , up t o t h e h i g h t e m p e r a t u r e l i m i t where t h e v i s c o e l a s t i c r e l a x a t i o n o c c u r s ( l a r g e l o s s w i t h s a m p l e s t r e t c h i n g ) i s i l l u s t r a t e d i n F i g . 2 . Two c o m p o s i t i o n s i n t h e s y s t e m AgPO3- Ag1 a r e r e p r e s e n t e d . The agreement o f t h e v i s c o e l a s t i c l o s s tem- p e r a t u r e w i t h t h e u s u a l (DSC) ~ l a s s t e m p e r a t u r e Tg, i s shown i n t h e i n s e r t . D e t a i l s of t h e low t e m p e r a t u r e peak o f i n t e r e s t t o t h i s work a r e shown i n F i g . 3 . Some d a t a f o r t h e s y s t e m C u z O ~ P ~ O ~ - C u ( I o r C l ) a r e shown i n F i g . 4 .
The s t o r a g e and l o s s d a t a a r e combined t o g i v e t h e r e a l and i m a g i n a r y p a r t s of t h e t e n s i l e modulus, E' and E" r e s p e c t i v e l y , i n F i g . 5. R e s u l t s a r e shown f o r two f r e q u e n c i e s , a l t h o u g h t h e f r e q u e n c y dependence of t h e r e s p o n s e is o n l y c l e a r l y s e e n i n t h e i m a g i n a r y p a r t .
Comparison w i t h e l e c t r i c a l r e s p o n s e s i s made i n F i p . . 6 f o r a c o m p o s i t i o n i n t h e AgI-AgP03 s y s t e m u s i n g a n i n v e r s e t e m p e r a t u r e s c a l e t o c a s t t h e d a t a i n a form simi- l a r t o t h a t o b t a i n e d f o r f r e q u e n c y s c a n s a t c o n s t a n t t e m p e r a t u r e . The l a t t e r a r e shown, i n t h e i n s e r t , f o r t h e e l e c t r i c a l modulus, M" (M* = II&*). F i g . 6 b r i n g s o u t t h e i m p o r t a n t f a c t t h a t , w h i l e b o t h r e s p o n s e s show maxima i n t h e i r l o s s c u r v e s a t F i g . 3 - L o s s " s p e c t r a " due t o O 0 3 C u I û4Cuzo 03PA
Motet 04AgI.O.6 AgPO, 04290.C 0.021
.
~ ~ ' a t III HZF i g . 5 - Real and imaginary p a r t s o f F i g . 6 - Comparison o f e l e c t r i c a l and mechan- complex t e n s i l e modulus. (E' i s d i s - i c a l l o s s moduli p l o t t e d v s . 1 / T t o g i v e same c r e p a n t a t 35 H z ) . Sample i s 0.6 s h a p e a s i s o t h e r m a l s p e c t r a shown i n i n s e r t . AgI.0.4(Ag20.2B203).
a p p r o x i m a t e l y t h e same t e m p e r a t u r e ( i . e . t h e most p r o b a b l e r e l a x a t i o n time i s n o t v e r y d i f f e r e n t ) t h e m e c h a n i c a l r e s p o n s e i s much b r o a d e r , p a r t i c u l a r l y on t h e h i g h t e m p e r a t u r e (low f r e q u e n c y ) s i d e . Indeed, t h e r e a r e t e m p e r a t u r e s a t which t h e e l e c - t r i c a l l o s s h a s a l m o s t v a n i s h e d w h i l e t h e mechanical l o s s i s s t i l 3 ' h a l f i t s maximum v a l u e . The e l e c t r i c a l r e l a x a t i o n i s d e s c r i b e d by B ( t ) = exp- [ ( t / ~ ) 4 w i t h
6
= 0.45A cornparison of l o s s peaks amongst s y s t e m s of d i f f e r e n t c o n s t i t u t i o n , i n c l u d i n g t h e r e c e n t l y developed a l l - h a l i d e g l a s s e s of t h e t y p e AgI-AgC1-CsC1, i s made i n F i g . 7. T h i s f i g u r e b r i n g s o u t t h e i m p o r t a n t p o i n t t h a t s y s t e m s o f comparable r e - l a x a t i o n t i m e may have v e r y d i f f e r e n t l o s s magnitudes (implying t h a t d i f f e r e n t f r a c - t i o n a l modulus changes a r e n o t c o r r e l a t e d w i t h t h e i o n i c m o b i l i t y ) .
DISCUSSION
The o u t s t a n d i n g f e a t u r e s o f t h e p r e s e n t f i n d i n g s a r e (1) t h e magnitude of t h e l o s s i n some b u t n o t a l 1 c a s e s compared t o p r e v i o u s g l a s s s t u d i e s , (2) t h e f a c t t h a t most p r o b a b l e t i m e s f o r e l e c t r i c a l and m e c h a n i c a l r e l a x a t i o n a r e c l o s e l y s i m i l a r w h i l e t h e s p e c t r a l w i d t h s a r e v e r y d i f f e r e n t a n d ( 3 ) t h e f a c t t h a t d e s p i t e t h e d i f f e r e n t w i d t h s (which c o u l d b e t a k e n t o i n d i c a t e d i f f e r e n t a c t i v a t i o n e n e r g y d i s t r i b u t i o n s I l / ) t h e a c t i v a t i o n e n e r g i e s f o r t h e two t y p e s o f r e l a x a t i o n a r e i n d i s t i n g u i s h a b l e . We d i s - c u s s t h e s e i n t u r n .
Data f o r a s i n g l e system, e . g . AgI-AgP03, F i g . 3, would s u p g e s t t h a t t h e l o s s , which i s p r o p o r t i o n a l t o t h e f r a c t i o n a l change i n modulus due t o r e l a x a t i o n , s c a l e s w i t h t h e l o g o f t h e r e l a x a t i o n time. However, t h e new d a t a f o r t h e a l l - h a l i d e s y s - tem show t h i s i s n o t s o . Thus, a t t e n t i o n must b e r e d i r e c t e d from t h e m o b i l i t y of t h e s i l v e r i o n s towards t h e n a t u r e o f t h e m a t r i x w i t h i n which t h e y move. We n o t e t h e r e a r e no asymmetric a n i o n s i n t h e c a s e o f t h e h a l i d e g l a s s w h i l e t h e r e a r e tri- a n g u l a r (BOS) g r o u p s i n t h e v e r y l o s s y b o r a t e compared w i t h t e t r a h e d r a l (PO+) groups i n t h e p h o s p h a t e g l a s s .
I n c o n s i d e r i n g t h e meaning of t h e much g r e a t e r s p e c t r a l w i d t h f o r mechanical compared w i t h e l e c t r i c a l r e l a x a t i o n we n o t e a g a i n t h e q u a l i t a t i v e d i f f e r e n c e between t h e two r e s p o n s e s . Given t i m e , t h e e l e c t r i c a l r e s p o n s e c o m p l e t e l y r e l a x e s a n a p p l i e d s t r e s s , i . e . t h e r e i s no zero-frequency e l e c t r i c a l modulus. By c o n t r a s t , t h e mechan- i c a l r e s p o n s e r e l a x e s t h e modulus t o a zero-frequency v a l u e j u s t 5-15% l e s s t h a n t h e h i g h frequency v a l u e . Furthermore, t h e mechanical r e l a x a t i o n , u n l i k e t h e e l e c t r i c a l ,
C10-496
JOURNAL
DE
PHYSIQUE
-160 I I I I I
a0 IO 2 0 30 4 0 50 60 70 80 90 la0
F i g . 7
-
Cornparison o f l o s s peaks f o r F i g . 8-
E l e c t r i c a l and mechanical r e l a x a - d i f f e r e n t g l a s s e s . t i o n t i m e s and r e l a t i o n t o IR spectrum.i n t h e r a n g e 0.45-0.50 f o r a l 1 c a s e s . The adequacy of t h e KWW form f o r t h e mechani- c a l s p e c t r a h a s n o t y e t been p r o p e r l y e v a l u a t e d due t o l a c k o f s u f f i c i e n t measuring f r e q u e n c y r a n g e and p r e c i s i o n . However, s h o u l d t h i s form b e a p p r o p r i a t e , t h e n t h e peak h a l f w i d t h s imply
B
v a l u e s a s s m a l l a s 0.2 which w i l l h a v e t o b e r a t i o n a l i z e d by t h e o r y . Comparable w i d t h s i n 1/T have been found i n t h e u l t r a s o n i c r a n g e111,
though, by GHz f r e q u e n c i e s , a r e m a r k a b l e n a r r o w i n g t o g i v e s i n g l e r e l a x a t i o n t i m e b e h a v i o r h a s v e r y r e c e n t l y been o b s e r v e d / 2 / .
F i n a l l y , we examine t h e t e m p e r a t u r e dependence o f t h e r e l a x a t i o n p r o c e s s . The r e l a x a t i o n t i m e s 1/2lTf a r e p l o t t e d v s . t h e 1/T v a l u e s a t which t h e l o s s maxima a r e found, i n F i g . 8, f o r a l 1 t h e s y s t e m s d i s c u s s e d i n t h i s p a p e r . F i g . 8 shows t h a t t h e l e a s t l o s s y g l a s s e x h i b i t s A r r h e n i u s b e h a v i o r f o r b o t h c o n d u c t i v i t y and m e c h a n i c a l r e l a x a t i o n s w i t h a s i m p l e e x t r a p o l a t i o n t o t h e A ~ + q u a s i - l a t t i c e " r a t - t l i n g " t i m e ( 1 / 2 r f 0 ) o b s e r v a b l e i n t h e f a r IR ( F i g . 8 i n s e r t ) . The more l o s s y g l a s s e s show r e g i o n s of non-Arrhenius b e h a v i o r . For t h e b o r a t e g l a s s , extended-range mechanical r e l a x a t i o n s t u d i e s / 1 , 2 / p e r m i t c h a r a c t e r i z a t i o n d o m t o T = 1 0 - I l s e c
,
s e e F i g . 8. These d a t a s u p p o r t e x t r a p o l a t i o n s of t h e n o n l i n e a r A r r h e n i u s p l o t s t o t h e same f a r IR f r e q u e n c y . These r e s u l t s a r e a n a l y z e d i n more d e t a i l e l s e w h e r e / 3 / . ACKNOWLEDGMENTSSupported by ONR Grant No. N84k0289 and NSF-MRL Grant No. DMR 8316988 REFERENCES
/ 1 / ( a ) C a r i n i , G . , C u t r o n i , PI., F e d e r i c o , M. a n d G a l l i , G., S o l i d S t a t e Corn. 44 (1982) 1427.
( b ) C a r i n i , G., C u t r o n i , M . , F e d e r i c o , M, G a l l i , G. and Tripodo, G . , J . Non- C r y s t . S o l i d s 56 (1983) 393.
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