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RELAXATION PHENOMENA IN GLASS
J. Stevels
To cite this version:
J. Stevels. RELAXATION PHENOMENA IN GLASS. Journal de Physique Colloques, 1985, 46 (C8),
pp.C8-613-C8-616. �10.1051/jphyscol:1985898�. �jpa-00225251�
Résumé - Cet article est une brève revue de l'état des connais- sances dans le domaine des phénomènes de relaxation diélectri- ques et mécaniques dans les verres.
JOURNAL DE PHYSIQUE
Colloque C8, supplement au n°12, Tome t6, decembre 1985 page C8-613
RELAXATION PHENOMENA IN GLASS
J.M. Stevels
Emeritus Professor, Eindhoven University of Technology, Eindhoven, The Netherlands
Abstract - An Abstract is given of the current state of the knowledge of di- electric and mechanical relaxation phenomena in glass.
J_. Some General Remarks.
Relaxation effects occur if in a system an extensive quantity (for instance a dielectric displacement or a mechanical strain) lags behind in phase compared to a corresponding intensive quantity (i.e. the electric field strength or the mechanical stress). The name retardation effect would be better but in literature the name relaxation is commonly used.
The phase difference is called loss angle, $ .
It can easily be shown that the energy loss per period in an A.C. electric field in a non-ideal dielectric medium is proportional to tan € .
This is the reason why the behaviour of tan 5 of glasses has been studied in a rather early stage. In the fifties, when the etectrics industry started to con- struct large transmitting valves, X-ray tubes and similar products, it was very important to know how tan £ behaves, not only as a function of the frequency of the applied field and the temperature, but also as a function of the composition of the glass.
Later it was realised that this knowledge may help a great deal in an under- standing of the structure and the transport phenomena in glass. Consequently the study of the electric relaxation phenomena has become more and more important.
The study of mechanical relaxation phenomena has also contributed much to the knowledge of the structure and behaviour of glasses.
2_. General theory.
The general phenomenological theory of the relaxation processes is well-known.
These processes can be described with a complex modulus K = K' - iK'1, in which K' and K'' may represent the real and the imaginary parts of the modulus. In the
"electric" case K'is the dielectric constant and in the "mechanical" case K'is Young's modulus. „,,
For both cases tan O = ^r~
and also tan d = JJ- . 1 + WZC^.
in which T is the relaxation time, CO = 2"jl f, in which f is the frequency of the A.C. field or, as the case may be the mechanical stress applied and A K is a quan- tity that will be discussed later. In the "electric" case tan £ is often called the dielectric loss, where as in the "mechanical" case tan S is called the "in- ternal friction".
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1985898
JOURNAL DE PHYSIQUE
Both c o l l o q u i a l names a r e n o t q u i t e c o r r e c t , b u t t h e y s u g g e s t t h e i r p h y s i c a l meaning q u i t e w e l l . What i s t h e s i g n i f i c a n c e o f Z
,
when c o n s i d e r e d on a mole- c u l a r o r a t o m i c s c a l e ?Suppose we have a n i o n ( o r a n electron o r a group o f m o l e c u l e s ) i n a p o t e n t i a l w e l l , t h a t is s e p a r a t e d from its s u r r o u n d i n g s by a p o t e n t i a l b a r r i e r Q. The i o n i n q u e s t i o n w i l l p i c k up e n e r g y from i t s s u r r o u n d i n g s owing t o its v i b r a t i o n i n t h e p o t e n t i a l w e l l and t o t h e c o l l i s i o n s w i t h t h e w a l l s .
A f t e r some time (relaxation t i m e
Z
1, it w i l l have l l c o l l e c t e d " s u f f i c i e n t e n e r g y t o jump o v e r t h e p o t e n t i a l b a r r i e r from c n e w e l l t o a n a d j a c e n t one.I f w 7
>>
1 , no jumps c a n be made because t h e AC f i e l d r e v e r s e s t o o q u i c k l y , i n o t h e r words, no energy i s absorbed and s o t a n = o .I f w t < < 1 , t h e jumps c a n b e made a t t h e b e g i n n i n g o f each new p e r i o d , and s i n c e t a n
6
i s p r o p o r t i o n a l t o E* ( i f E is t h e e l e c t r i c f i e l d a t t h e mcment o f t h e jump), a g a i n t a n3
= o .Tan
&
h a s a c o n s i d e r a b l e v a l u e o n l y i f W Z 1 , s o t h a t t a n6
a s a f u n c t i o no f
w
is a r a t h e r narrow b e l l - s h a ed c u r v e w i t h its maximum where & = -LFor r J t = 1 , ( t a n
b
max -A R z
For v a l u e s CL,
< 4 t h e m;rEe?Z1shows c o n s i d e r a b l e p o l a r i s a t i o n because o f t h e
jumping i o n s and f o r v a l u e s UJ > 1
p o l a r i s a t i o n i s a b s e n t .
T h i s means t h a t i n t h e former c a s ~ m o d u l u s K ' i s h i g h e r t h a n i n t h e l a t t e r c a s e , t h e d i f f e r e n c e b e i n g i n d i c a t e d by A K.
A s t o t h e t e m p e r a t u r e , r e l a x a t i o n p r o c e s s e s a r e t y p i c a l r a t e p r o c e s s e s , which means t h a t t h e r e l a x a t i o n time -C c a n u s u a l l y be e x p r e s s e d i n a formula o f t h e
t y p e = T o e C/RT
i n which Q i s t h e above p o t e n t i a l b a r r i e r , RT h a s t h e wellknown s i g n i f i c a n c e and fS i s a c h a r a c t e r i s t i c r e l a x a t i o n time.
% s i c a l l y b o t h t e t a n
&
- T and t a n8 -
& c u r v e s show a maximum i n t h e area where W 5 = w ~ , € ' / R ~ = 1.I n p r a c t i c a l e x p e r i m e n t s t h e t e m p e r a t u r e may be k e p t c o n s t a n t and w be v a r i e d , b u t t h i s means t h a t d i f f e r e n t t y p e s o f a p p a r a t u s have t o be used, which makes t h e e x p e r i m e n t s l a b o r i o u s and e x p e c s i v e . It is much e a s i e r t o keep tu c o n s t a n t and t o v a r y T; v e r y o f t e n t h i s c a n be doce w i t h t h e same equipment.
There is a n o t h e r r e a s o n why t h e l a t t e r t y p e o f e x p e r i m e n t s were found i n t e r e s - t i n g . The knowledge o f t h e t a n
6 -
T c u r v e p r o v i d e s a n e a s y method o f determi- n i n g t h e v a l u e o f Q.For t h e 1 1 e l e c t r f 6 1 1 _cse d i f f e r e n t a p p a r a t u s i n t h e wide r a n g e . o f f r e q u e n c i e s f = s-I t o 10 s a r e a v a i l a b l e t o measure koc; t a n v a n e s w i t h T f o r o c e g i v e n f r e q u e n c y o v e r a t e m p e r a t u r e r a n g e from Helium t e m p e r a t u r e s (4 1 0 t o , f o r example 300°c.-
Fo_? t h e "mechanicalf1 c a s e m e a ~ u r e m e n t s _ ~ c a n b e made by t o r s i o n e x p e r i m e n t s ( f " 1 s )
,
Sending e x p e r f m s n t . ~ (f fZ 10 s )and a c o u s t i c v i b r a t i o n e x p e r i m e n t s ( f.S 2000 t o 3000 s- ) :
T h i s p r o v i d e s sufficient v a r i a t i o r , f o r a s t u d y o f t h e dependfnce o f t a n
d
o n t e m p e r a t u r e , because t h e methods n e c t i o n e d c a n be used i n t h e t e m p e r a t u r e r a n g e frorr.-
1OoOc
t o 800'~.If i t i s known how Q behaves i n a . s e r i e s o f g l a s s e s i n which t h e c o m p o s i t i o n s a r e v a r i e d i n a s y s t e m a t i c way, i n t e r e s t i n g c o n c l u s i o n s c a n o f t e n be drawn a b o u t t h e s t r u c t u r e o f t h e s e g l a s s e s , and it c a n b e shown what t h e mechanism o f t h e r e l a x a t i o n phenomenon i s o n a r a t o m i c s c a l e .
From t h e above formulae i t c a n be d e r i v e d , t h a t R T = -
m Q
I n -0
i f Tm i s t h e t e m p e r a t u r e where t a n
6
is maximal a s a f u n c t i o n o f T and w is t h e g i v e n f r e q u e n c y o f t h e A.C. f i e l d a p p l i e d .I n o t h e r words, i f Tm is known, i.e. t h e ~ o s i t i o n o f ( t a n
6
)rnax i n t h e t a n6 -
T diagram, Q c a n be c a l c u l a t e d w i t h a c o n s t a r t p r o p o r t i o n a l i t y f a c t o r , namely Q = (-R I nw x
.) Tm.I n macy c a s e s however,T, is n o t known. I n t h a t c a s e Q c a n be determind w i t h t h e formula = R ( l n f i
-
l n f 2 i f t h e s i t u a t i o n o f T and T f o r two t a n6
-T1 ITmq - I ITm '"1 m2
L 1
c u r v e s i s measured z t two d i f f e r e n t f r e q u e n c i e s f l and f l .
3 . P r a c t i c a l R e s u l t s .
-
The above g e n e r a l t h e o r y h o l d s f o r b o t h c r y s t a l l i n e and v i t r e o u s systems.
I n c r y s t a l s t h e r e l a x i n g p a r t i c l e s a r e r e g u l a r y d i s t r i b u t e d i n t h e m a t e r i a l . T h e i r s u r r o u n d i n g s on a n a t o m i c s c a l e a r e e x a c t l y t h e same, s o t h a t one w e l l - d e f i n e d Q v a l u e and as a r e s u l t a v e r y s h a r p t a n & peak i n t h e t a n -T diagram c a n be e x p e c t e d .
A s i n v i t r e o u s systems t h e s e c o n d i t i o n s a r e n o t f u l f i l l e d , t h e r e is a w i d e r d i s t r i b u t i o n o f t h e Q v a l u e s , which r e s u l t s i n much w i d e r t a n
3
peaks i n t h e t a n8
-T diagram.S t r a n g e enough, v e r y few i n v e s t i g a t i o n s have been c a r r i e d o u t w i t h c r y s t a l s , whereas f o r v i t r e o u s s y s t e m s e x t e n s i v e m a t e r i a l i s a v a i l a b l e .
F i g u r e 1 g i v e s a r e p r e s e n t a t i v e b u t s i m p l i f i e d o v e r a l l p i c t u r e f o r t a n
6
asa f u n c t i o n o f frequency a t two t e m p e r a t u r s (30C' and 50 K ) f o r t h e complicated g l a s s e s used f o r t e c h n i c a l a p p l i c a t i o n s
These a r e s e c t i o n s o f a g e n e r a l s t e r i c a l model, where t a n
6
i s p l o t t e d a s a f u n c t i o n o f T and f .An a n l y s e s o f t h e c u r v e s o f f i g . 1 shows t h a t t h e r e a r e 3 t y p e s o f r e l a x a t i o n phenomena i n ( n o n - r a d i a t e d ) g l a s s e s , namely t h e m i g r a t i o n l o s s e d ( c u r v e s I acd 2 ) , t h e l o s s e s due t o l o c a l motions ( c u r v e 3 ) and t h e network l o s s e s ( c u r v e 4 ) . 4 . s n c h a r a c t e r i s t i c s o f t h e v a r i o u s t y p e s o f r e l a x a t i o n phenomena i n v i t r e o u s
-
systems.4 . 1 M i g r a t i o n l o s s e s .
--- ---
Migraf;ion,losses u s u a l l y o c c u r i n t h e f r e q u e n c y range f = 10' s-' (and l o w e r ) t o f =-lo0 s-' and t h e y are- due mainly t o t h e jumping o f t h e ~ a + i o n s i n t h e i n t e r s t i c e s o f t h e network ( t h r o u g h ~ i + and K+ i o n s may a l s o g i v e some c o n t r i b u - t i o n ) .
They a r e c h a r a c t e r i s e d by a c t i v a t i o n e n e r g i e s from 0.6 t o 1 . 2 eV. depending o n t h e composition o f t h e g l a s s . S i n c e t h i s v a l u e i s f a i r l y h i g h , t h e m i g r a t i o n l o s s e s are h a r d l y s e n s i t i v e t o t h e t e m p e r a t u r e .
b n y c a s e s a r e known where b e s i d e s t h e a c t i v a t i o n e n e r g y o f t,he d i e l e c t r i c r e l a x a t i o n a l s o t h a t o f t h e s e l f - d i f f u s i o n f o r ~ a + i o n s o r t h a t o f t h e D.C.
e l e c t r i c c o n d u c t i v i t y o r both a r e known. I n t h e s e c a s e s t h e s m , e v a l u e i s found f o r e a c h g l a s s , which shows t h a t . t h e mechanism o f t h e jumping o f t h e ~ a + i o n s is r e a l l y r . e s p o n s i b l e f o r a l l t h e s e t h r e e e f f e c t s .
F i g . 1
.
Showing t h e g e n e r a l shape o f t a nd
o f g l a s s e s as a f u n c t i o n o f t h e frequencey a t 300 K and 50 K. The f u l i y drawn c u r v e s g i v e t h e t o t a l l o s s e s . The f o u r d i f f e r e n t c o n t r i b u t i o n s are g i v e n by d o t t e d l i n e s .C8-616 JOURNAL DE PHYSIQUE
I n a number o f r e c e n t p a p e d ) a b o u t measurements w i t h b l o c k i n g and non-block- i n g e l e c t r o d e s , i t was showr t h a t t h e m i g r a t i o n l o s s e s ( c u r v e s 1 + 2 ) a r e r e a l l y a s u p e r p o s i t i o n o f ( 1 ) "conduction l o s s e s f 1 ( t h e Na+ i o n s jump under t h e i n f l u e n c e o f a D.C. f i e l d p r i n c i p a l l y i n one d i r e c t i o d a n d ( 2 ) t h e " d i p o l e r e l a x a t i o n l o s s e s " ( t h e Na+ i o n s jump t o and f r o i n a l i m i t e d a r e a and f o l l o w t h e f r e q u e n c y o f a n A.C. f i e l d a p p l i e d ) .
U s u a l l y t h e c o n d u c t i o n l o s s e s f o r one and t h e same g l a s s a t a g i v e n tempera- t u r e have t o be l o c a t e d a t much lower f r e q u e n c i e s t h a n t h e d i p o l e r e l a x a t i o n l o s s e s . T h i s is why t h e l f o r m e r a r e u s u a l l y o v e r r u l e d by t h e l a t t e r , a t l e a s t i n t h e r a r g e o f f = 10' s- t o 1
o6
s-I.
4 . 2 Losses due t o l o c a l motions.
--- ...
F i g . 1 a l s o shows t h e d i e l e c t r i c l o s s e s due t o l o c a l motions ( c u r v e 3 ) , i n o l d e r l i t e r a t u r e c a l l e d deformation l o s s e s .
These l o s s e s a r e caused by a n atoms llwagglingll between s e v e r a l p o s i t i o n s i n t h e i r own i n t e r s t i c e s s e ~ a r a t e d by r a t h e r low p o t e n t i a l b a r r i e r s . The Q v a l u e s i n v o l v e d a r e v e r y low i n d e e d . They v a r y between 0.05 and 0 . 2 eV.
T h i s means t h a t t h e y a r e v e r y s e n s i t i v e t o t h e t e m p e r a t u r e .
F i g . 1 shows t h a t t h e y c a n be s t u i e d onky a? r a t h e r low t e m p e r a t u r e s ( 5 0 K) and a t medium f r e q u e n c i e s ( f = lo3 iqt o 10
<
1.A t room t e m p e r a t u r e t h e y cannot be d e t e c t e d because t h e y a r e droxned i n t h e l o s s e s r e p r e s e n t e d by c u r v e 4 .
4,s N~tw:rll_l:s_sez.
F i n a l l v f i n . 1 shows t h e network l o s s e s ( c u r v e 4 ) , i n o l d e r l i t e r a t u r e c a l l e d t h e v i b r a t i o n l o s s e s .
A s t h e y a r e due t o t h e r e l a x a t i o n o f mcvements o f p a r t s o f t h e network, t h i s t y p e o f l o s s e s is found m a i n l y i n t h e r e g i o n where t h e g l a s s a p p r o a c h e s its a n n e a l i n g r a n g e .
The v a l u e o f a c t i v a t i o n e n e r g y Q is v e r y h i g h and u s u a l l y between 2.2 and 4 e V . It i s n o t s u p r i s i n g t h a t t h i s v a l u e is a b o u t as high as t h e u s u a l a c t i v a t i o n e n e r g i e s f o r v i s c o u s flow.
T h i s i s a v e r y s t r o n g e v i d e n c e t h a t t h e r e l a x a t i o n indeed is due t o movements o f p a r t s o f t h e network ( r u p t u r e and r e c o m b i n a t i o n ) .
5. Concluding r e m m . -
I n t h e p r e c e e d i n g t e x t some g e n e r a l remarks a b o u t t h e f o u r d i f f e r e n t t y p e s o f r e l a x a t i o n s phenomena i n v i t r e o u s systems a r e made.
I n t h e l a s t f i f t e e n y e a r s t h e behaviour o f many v i t r e c c s s y s t e m s h a s been s t u d i e d . These i n c l u d e s i l i c a t e , b o r a t e and phosphate g l a s s e s , a s w e l l a s t h e complicated g l a s s e s used f o r t e c h n i c a l a p p l i c a t i o n s .
Many d e t a i l s a b o u t t h e s t r u c t u r e o f t h e s e s y s t e m s have been r e v e a l e d . A s u r v e y o f t h i s work i s g i v e n i n a paper by t h e a u t h o r t o b e p u b l i s h e d b e f o r e l o n g i n t h e J o u r n a l o f Non
-
C r y s t a l l i n e S o l i d s , 1985.2
References.
1. J . M . S t e v e l s (19571, Encyclop. o f P h y s i c s
3,
p. 373.2. M. Tomozawa and R. H. Dorenus (1974) ( 1 9 7 6 ) , J. Non
-
C r y s t a l l i n e S o l i d s14,
5 4 ,
21,
287.M.H. b a r and J . M . S t e v e l s ( 1 9 7 8 ) , J. Non- C r y s t a l l i n e S o l i d s
