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VERY LOW FREQUENCIES INTERNAL FRICTION
MEASUREMENTS OF ICE Ih
J. Tatibouet, J. Perez, R. Vassoille
To cite this version:
VERY LOW FREQUENCIES INTERNAL FRICTION MEASUREMENTS OF ICE I h
J. Tatibouet, J . Perez and R. VassoilleGroupe d 'Etudes de W t a Z Z u r g i e Physique e t Physique des MaMriaux, I . N. S. A.,
B&. 502, E.R.A. 463, 69621 ViZZeurbanne Cedex, France
A b s t r a c t Very low f r e q u e n c i e s i n t e r n a l f r i c t i o n measurement
( 1
-
10' 4 - ~ z ) i n i c e p e r m i t t e d t o i n c r e a s e t h e knowledge of t h e i n t e r n a l f r i c t i o n of i c e , e s p e c i a l l y t h e r e l a x a t i o n phenomenon. The a c t i v a t i o n e n e r g y of t h e r e l a x a t i o n i s 0.25 eV, a c a r a c t e r i s - t i c v a l u e of t h e m i g r a t i o n of r o t a t i o n a , l d e f e c t s . I t f o l l o w s a C u r i e Law. E x p e r i m e n t s a f t e r d i f f e r e n t c o o l i n g r a t e p u t i n e v i d e n c e t h e r o l e o f i n t r i n s i c d e f e c t s . 1 . I n t r o d u c t i o n-
U n t i l t o day i n t e r n a l f r i c t i o n of I c e Ih h a s been s t u d i e d i n t h e k i l o h e r t z [ l , 2 , 3 3 and H e r t z141
f r e q u e n c i e s r a n g e s . bleasurenient have a l s o been made by u l t r a s o n i c waves t e c h n i c sf5].
E x p e r i m e n t s made on s i m p l e c r y s t a l s a t 1 H e r t z between 100 and 273 K show 3 noteworthy f e a t u r e s . i ) a r e l a x a t i o n peak o b s e r v e d by o t h e r s a u t h o r s a t h i g h e r f r e q u e n - c i e s [ I , 2, 33. i i ) an i n c r e a s e of t h e i n t e r n a l f r i c t i o n a t h i g h t e m p e r a t u r e (230- 273 K ) . i i i ) A t h i g h t e m p e r a t u r e , i n t e r n a l f r i c t i o n becomes a m p l i t u d e de- p e n d a n t . The h i g h e r t h e t e m p e r a t u r e , t h e more p r o n o u n c e d . t h i s a m p l i t u d e dependence.
.High t e m p e r a t u r e phenomena a r e a t t r i b u t e d t o t h e movement o f d i s l o c a - t i o n s u n d e r t h e c y c l i c s t r e s s and s e v e r a l i n t e r ~ r e t a t i o n s have been y e t developped 1 6 ,
71.
The o r i g i n of t h e i n t e r n a l f r i c t i o n peak i s n o t f u l l y e x p l a i n e d . Bass[8] h a s i n t e r p r e t e d t h e m e c h a n i c a l r e l a x a t i o n by a r e a r r a n g e m e n t o f w a t e r m o l e c u l e s w i t h t h e h e l p of t h e r o ~ a t i o n n a l ( o r Bjerrum) d e f e c t s , i n r e s p e c t of t h e B e r n a l and Fowler r u l e s . From an a n a l o g o u s way, Gosar
19)
h a s c o n s i d e r e d t h a t e a c h w a t e r molecule i s a p o i n t d e f e c t i n t h e i c e l a t t i c e , and h a s ; : e n e r a l i z e d t h e model of Bass by i n t r o d u c i n g t h e c o n c e p t of e l a s t i c d i p o l e s p r e v i o u s l y d e v e l o p p e d . He c a l c u l a t e d t h e f r e e e n e r g y of t h e c r y s t a l by i n t r o d u c i n g t h e p r o t o n d e s o r d e r e n t r o p y w i t h t h e h e l p of g r a p h t h e o r y a s Nagle 110) d i di t
f o r t h e d i e l e c t r i c r e l a x a t i o n .C5-542 JOURNAL DE PHYSIQUE
So we have t r i e d t o e x t e n d t h e e x p e r i m e n t a l s t u d y of t h e i n t e r n a l f r i c t i o n peak i n I c e by u s i n g measurements t e c h n i c s a t v e r y low f r e - q u e n c i e s ( 1
-
t
~
KZ). The p r i n c i p a l aim of t h i s work was t o compare-
~
t h e i n f l u e n c e of i n t r i n s i c o r e x t r i n s i c r o t a t i o n n a l d e f e c t s on t h e r e - l a x a t i o n t i m e a s s o c i a t e d t o t h e i n t e r n a l f r i c t i o n peak.2. E x p e r i m e n t a l r e s u l t s .
2 . 1
.
E x p e r i m e n t a l p r o c e d u r e-
I n t e r n a l f r i c t i o n measurements a t v e r y low f r e q u e n c i e s were made w i t h an i n v e r t e d t o r s i o n a l pendulum w i t h a v e r y weak i n e r t i a l moment. T h i s pendulum working i n f o r c e d o s c i l l a - t i o n s i s p r e s e n t e d a t t h e p r e s e n t c o n f e r e n c e [ l l ] . The t o r q u e i s t r a n s - m i t t e d t o t h e specimen by a magnet between two Helmholtz c o i l s . The s t r a i n i s d e t e c t e d by mean of p h o t o v o l t a i c c e l l s .S t r a i n and s t r e s s s i g n a l s a r e b o t h s e n t t o a c a l c u l a t o r which com- p u t e s i n t e r n a l f r i c t i o n and a v a l u e p r o p o r t l o n n a l t o t h e modulus.
3
The specimen ( p a r a l l e l e p i p e d a l 8 X 2 X 60 mm ) a r e m e c h a n i c a l l y
c u t t e d from s i n g l e c r y s t a l s grown by Bridgman inethod i n t h e G l a c i o l o g y L a b o r a t o r y i n Grenoble. The r e s i s t i v i t y of t h e employed w a t e r i s more t h a n l o ~ ~ ~ / c m .
2 . 2 . R e s u l t s . - F i g u r e l showsthe g e n e r a l shape of an i n t e r n a l f r i c t i o n spectrum a t t h e i n t e r m e d i a t e f r e q u e n c y of 1 0 - ~ Ha. We f i n d na- t u r a l l y t h e same f e a t u r e s t h a t when e x p e r i m e n t s a r e made a t l
Hz.
The r e l a x a t i o n peak i s s h i f t e d t o w a r d s t h e lower t e m p e r a t u r e s by f r e q u e n c y e f f e c t a s t h e i n t e r n a l f r i c t i o n a s s o c i a t e d t o t h e d i s l o c a t i o n s movement which inc:reases a t t e m p e r a t u r e a s low a s 200 K (230-
240 X a t 1Hz).
4"'
F i g . 1 : I n t e r n a l f2iction/tempe- Fig. 2 : High Temperature I n t e r -
r a t u r e 10-
Hz.
n a l F r i c t i nS
&",
=5
10-.
...d i s l o c a t i o n d e n s i t y . Indeed we have v e r i f i e d t h a t a f t e r e v e r y measure- ment a t 1oe2 and I O - ~
Hz
we found a g a i n e x a c t l y t h e i n i t i a l v a l u e ob- t a i n e d a t 1Hz.
I n a f i r s t a p p r o a c h , t h e h i g h t e m p e r a t u r e i n t e r n a l f r i c t i o n i s t h e more i m p o r t a n t t h e f r e q u e n c y i s low i n agreement w i t h t h e i n t e r p r e t a t i o n g i v e n i n r e f e r e n c e [ 6 ) .The aim of t h i s work b e i n g t h e s t u d y of t h e r e l a x a t i o n peak, we have n o t developped t h i s p o i n t and we s h a l l f o c u s e d on t h e low tempera- t u r e i n t e r n a l f r i c t i o n ; we have r e p r e s e n t e d on f i g u r e 3 t h i s peak v e r s u s t e m p e r a t u r e a t d i f f e r e n t f r e q u e n c i e s . We n o t i c e t h e s h i f t oP t h e t e m p e r a t u r e peak t o w a r d s t h e low t e m p e r a t u r e and t h e i n c r e a s e of t h e r e l a x a t i o n i n t e n s i t y w i t h d e c r e a s i n g f r e q u e n c y . I n o r d e r t o p u t i n e v i - dence t h e r o l e of i n t r i n s i c d e f e c t s o u t of e q u i l i b r i u m i n t h e r e l a x a - t i o n phenomena, we have made measurements of i n t e r n a l f r i c t i o n d u r i n g
a t e m p e r a t u r e r i s e a f t e r two d i f f e r e n t c o o l i n g r a t e s from an e q u i l i - ;jrlurn s ~ a t e (we have choosen t h a t o b t a i n e d a f t e r 1 h 30 a t 230 K ) .
i ) low c o o l i n g r a t e = 0.3 K/min. i i ) f a s t c o o l i n g r a t e = 2.7
m min.
'eYt
F i g . 3 : R e l a x a t i o n Peak v s tempe- P i p . 4 : R e l a x a t i o n Peak a f t e r r a t u r e a t d i f f e r e n t f r e - d i f f e r e n t c o o l i n g ra$e.
q u e n c i e S.
----
:2,7
K/min-
: 0 , 3 ~ / m i nC5-544 JOURNAL DE PHYSIQUE 3 . D i s c u s s i o n
-
From o u r e x p e r i m e n t a l r e s u l t s we h a v e d o n e a n a t t e m p t t o g i v e a more c o m p l e t e c a r a c t e r i z a b i o n o f t h e r e l a x a t i o n p e a k , h a v i n g d o n e e x p e r i m e n t s on a l a r g e r f r e q u e n c y r a n g e . A s r e c a l l e d p r e c e d i n g l y t h e m e c h a n i c a l r e l a x a t i o n i n I c e d u e t o t h e r e o r i e n t a t i o n o f w a t e r mo- l e c u l e d u e t o t h e a p p l i c a t i o n o f a c y c l i c s t r e s s , w i t h t h e h e l p o f r o - t a t i o n a l ( o r I3jerrum) d e f e c t s . As t h e o r i g i n o f t h e s e d e f e c t s c a n b e e i t h e r i n t r i n s i c o r e x t r i n s i c t h e r e l a x a t i o n t i m e c a n be g i v e n by [ 4 ] :where Em and EF a r e r e s p e c t i v e l y t h e m i g r a t i o n and forrnatj.on e n e r g i e s o f B j e r r u m d e f e c t s (13 = 0 . 2 1 eV ; EF = 0 . 3 4 eV) p21 and C i s t h e con-
-4 f o r f r e q u t ? n c i e s f r o m 1 0 t o 1 0
Hz.
E x p e r i m e n t a l r e s u l t s show t h a t r e - l a x a t ~ o n phenomena c a n be r e a s o n a b l y d e s c r i b e d by a C u r j e Law a s t g =&-.
T h i s f a c t d o e s n o t seem t o c o n f i r m t h a t t h e r e i s a p h a s e $ , r a n s i t i o n n e a r 110-
1.20 K a s ct was n o t i c e d p r e v i o u s l y .4'
'he v a l u e o f A c a l c u l a t e d f r o m t,ur d a t a i s 1.5 I O - ~ eV which 1s i n good a g r e e m e n t w i t h t h e ~ t i e o r i c a l v a l u e f r o m t h e e l e c -501,,,y',-
,
,
b r a s t a t i c model o f B a s s (83. -4F i g . 8 / t g B )
5 0 100 150 20 0 Kw i t h / J = d j p o l e moment o f h y d r o g e n bond, C44 = e l a s t i c c o n s t a n t , V = vo-
0
lumr o f u n i t c e l l and = d i e l e c t r i c c o n s t a n t .
C5-546 JOURXAL DE PHYSIQUE
E x p e r i m e n t s on a l a r g e f r e q u e n c y r a n g e c o n f i r m e d t h e r o l e o f t h e B j e r - rum d e f e c t s on r e l a x a t i o x i .
An a c c u r a t e v a l u e o f Lhe m i j i r a t i o n e n e r g y o f t h e s e d e f e c t s i s i
found ( E = C , 2 5
-
0 , 0 1 eV) and a C u r i e l a w i s o b s e r v e d . I n o r d e r t om p r e c i s e t h e r o l e o f " f r o z e n " r o t a t i o n a l d e f e c t s we i n t e n d t o d o expe- r i m e n t s w i t h d o p e d i c e c r y s t a l s . 6 . R e f e r e n c e s 3 K n x e r f I . O . , Nagun S., Z i e g l e r G. ( 1 9 5 5 ) N a t u r w i s s .
15,
427. 2 S e h i l l e r P , , ( 1 9 5 8 ) Z. f u r P h y s i k Bd 1 5 3 , p . 1-15.3 KuroPva D . ( 1 9 6 4 ) C o n t r i b u t i o n n o 667
.
I n s t . Low Temp. S c i . HohkaYdo University A 1 8 , p . 1-624 V a s s o i l l e It., T a t i b o u G t J . , P e r e z J., Gobin P.F. ( 1 9 7 4 ) Cl1 Xcad. S c i . P a r i s S 6 r i e B ,
278
no 1 0 , 409-412. 5 T a t i b o u S t J . , V a s s o i l l e R., P e r e zJ.
( 1 9 7 5 ) J . o f G l a c i o l o g y v o l . 1 6 , 7 3 , 161-169. 6 V a s s o i l l e R., May C . , P e r e z J. (1978) J. o f G l a c i o l o g y , v 0 1 21 85,375-3 84-
7
i'erez <J., Maf C . , T a t i b o u g t J , , V a s s o i l l e R., ( 1 9 8 0 ) J . o f G l a c i o - l o g y , v o l . 2 5 ,E,
133-149.8 B a s s R., ( 1 9 5 8 ) z. P h y s . , 1 5 3 , 1 6 ; P r o c . Roy. Soc. London, A ,
247,
426-464.9 G o s a r P., ( 1 9 7 4 ) P h i l . Mag., 29,
no
2, 221-240. 1 0 Nagle J . F . ( 1 9 6 6 ) J. Math. I'hys.,2 ,
1 181-14921 1 E t i e n n e S., C a v a i l l 6 J.Y., P e r e z J . , S a l v i a M., ( 1 9 8 1 ) , 1 c I F U ~ S 7 . , Lausanne
.
1 2 Hobbs P.V. ( 1 9 7 4 ) I c e P h y s i c s , O x f o r d , C l a r e d o n I'ress.
