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ULTRASONIC ATTENUATION AND VELOCITY
STUDIES IN THE α-α SOLID SOLUTION PHASES
OF THE Nb-H SYSTEM
F. Mazzolai, H. Birnbaum
To cite this version:
F. Mazzolai, H. Birnbaum. ULTRASONIC ATTENUATION AND VELOCITY STUDIES IN THE
α-α SOLID SOLUTION PHASES OF THE Nb-H SYSTEM. Journal de Physique Colloques, 1981,
ColZoque C5, suppZPment au nO1O, Tome 42, octobre 1981 page C5-769
ULTRASONIC ATTENUATION AND VELOCITY STUD1
ES IN
THE u-a'
SOLID SOLUTION
PHASES OF
THE
Nb-H SYSTEM
F.M. ~ a z z o ~ a i * and H.K. Birnbaum
University o f IZZinois a t Urbana-Champaign, Mnterials Research Laboratory, U~bana, I L 61 801, (I. S. A. A b s t r a c t . - U a t a a r e r e p o r t e d or) t h e e l a s t i c c o n s t a n t s and u l t r a s o n i c a t t e n u a t i o n o f a s i n g l e c r y s t a l o f Nb d e t e r m i n e d as a f u n c t i o n o f t h e h y d r o g e n c o n t e n t ( 0
<
H/Nb<
0.71) a t 528 K and as a f u n c t i o n o f t e m p e r a t u r e ( 3 8 0 _17
( 528 T() f o r H/Nb = 0.31, 0.45, 0.53 a n d 0.71. A r e l a x a t i o n p r o c e s s i s o b s e r v e d w h i c h a p p e a r s t o be a Z e n e r - t y p e o f e f f e c t . 1. I n t r o d u c t i o n . - The n a t u r e o f t h e p h a s e t r a n s i t i o n s i n t h e g r o u p Vb m e t a l-
h y d r o g e n s y s t e m s has been e x t e n s i v e l y i n v e s t i g a t e d w i t h a number o f e x p e r i m e n t a l t e c h n i q u e s ( 1 ) . H y d r o g e n b e h a v i o r i n t h e e x t e n s i v e r a n g e o fa
a n d a' s o l i d s o l u t i o n s i n Nb has been i n t e r p r e t e d u s i n g a l a t t i c e gas model w h e r e t h e H i n t e r a c t i o n s a r e t r e a t e d i n t h e mean f i e l d a p p r o x i m a t i o n ( 2 ) . T h i s t r e a t m e n t c a n a c c o u n t f o r t h e e x i s t e n c e o f t h e a - a - m i s c i b i l i t y gap ( 3 ) as w e l l a s f o r m i c r o s c o p i c a n d m a c r o s c o p i c modes ( 4 - 7 ) . A t h i g h H c o n c e n t r a t i o n s a s e r i e s of h y d r i d e s t r u c t u r e s corm, whose a p p e a r a n c e h a s been a t t r i b u t e d t o t h e H-H d i p o l a r i n t e r a c t i o n s ( 8 ) . . I n t h e p r e s e n t p a p e r we r e p o r t on p a r t o f an i n v e s t i g a t i o n o f t h e s e p h a s e t r a n s i t i o n s u s i n g m e a s u r e m e n t s o f a c o u s t i c a t t e n u a t i o n a n d e l a s t i c c o n s t a n t s , w h i c h i n p r e v i o u s s t u d i e s had o n l y been i n v e s t i g a t e d f o r v a l u e s o f t h e a t o m i c r a t i on
e q u a l t o 0.78 ( 9 ) a n d l e s s t h a n a b o u t 0.05 ( 1 0 - 1 2 ) . 2. E x p e r i m e n t a l.-
M e a s u r e m e n t s w e r e c a r r i e d o u t on s i n g l e c r y s t a l s h a v i n g p o l i s h e d f a c e s p a r a 1 l e l t o[ l o o ]
a n d [ 1 1 0 ] c r y s t a l l o g r a p h i c p l a n e s . T h e s e c r y s t a l s had b e e n a n n e a l e d a t 2173 K i n a vacuum o f a b o u t Pa f o r p u r i f i c a t i o n .H
was i n t r o d u c e d a t 528 K t h r o u g h a s p u t t e r c l e a n e d a n d Pd e v a p o r a t e d s u r f a c e o f t h e Nb c r y s t a l . T r a n s d u c e r s w e r e b o n d e d t o t h e t h r e e o r t h o g o n a l f a c e s o f t h e c r y s t a l a l l o w i n g m e a s u r e m e n t o f t h e Cll, CL = 1 / 2 (Cll+
C12 + 2 C 4 4 ) , I a n d C = 1 / 2 (Cll-
C12). B o n d i n g was a c c o m p l i s h e d u s i n g a t h i n l a y e r o f B i t o w e l d t h e s p u t t e r e d s u r f a c e s o f t h e Nb c r y s t a l o n t o t h e g o l d *Permanent address : I s t i t u t o d i Acustica "O.M. Corbino", v. Cassia 1216, Rome,I t a l
v
JOURNAL DE PHYSIQUE a t t e n u a t i o n d a t a t o Eq. ( 2 ' ) f o r a l l c o m p o s i t i o n s was o b t a i n e d w i t h t h e r e l a x a t i o n p a r a m e t e r s T o = 5 x 1 0 - l 3 s e c . a n d W = 0.22 eV. I n c o n t r a s t t h e f i t t o t h e L a n d a u t h e o r y ,
Ea.
( 2 ) ( w h i c h s h o u l d p r e d i c t a l i n e a r r e l a t i o n i n F i g . 5 ) was p o o r . The a b o v e v a l u e s f o r r 0 a n d W a r e i n good a g r e e m e n t w i t h NMR m e a s u r e m e n t s o f H m o b i l i t y i n t h e a' p h a s e . F o r a c o m p l e t e l y random s o l i d s o l u t i o n , Eq. ( 9 ) r e d u c e s t o 2 2 b o = yn ( I - n ).
( 5 ) F i g u r e 6 shows t h a t t h e e x p e r i m e n t a l d a t a , e x c e p t f o r n = 0.31 f i t t h i s r e l a t i o n , s u g g e s t i n g t h a t i n t h e t e m p e r a t u r e r a n g e o f t h e p r e s e n t m e a s u r e m e n t s t h e s o l i d s o l u t i o n i s e s s e n t i a l l y random. 5. C o n c l u s i o n s . - A l l t h e e x p e r i m e n t a l o b s e r v a t i o n s a p p e a r t o be i n good a g r e e m e n t w i t h t h e Z e n e r r e l a x a t i o n m e c h a n i s m i n t h e c o m p o s i t i o n r a n g e a b o v e H/Nb = 0.31. N e a r t h e c r i t i c a l c o m p o s i t i o n f o r t h e a-a' t r a n s i t i o n h o w e v e r , t h e b e h a v i o r a p p e a r s t o b e more c o m p l e x as t h e r e l a x a t i o n s t r e n g t h i s c o n s i d e r a b l y s m a l l e r t h a n p r e d i c t e d a n d t h e v a l u e o f TS i s s i g n i f i c a n t l y h i g h e r t h a n o b t a i n e d by e x t r a p o l a t i o n f r o m t h e h i g h e r c o m p o s i t i o n s .A c k n o w l e d g e m e n t s . - T h i s work was s u p p o r t e d by DOE c o n t r a c t OE-AC-2- 76ER01198.
R e f e r e n c e s
1. T. ~ c h a b e r and H. W e n z l : T o p i c s i n A p p l i e d P h y s i c s , v o l . 28 S p r i n g e r , B e r l i n ( 1 9 7 8 ) .
2. H. Wagner and H. H o r n e r : Advan. Phys. 23, 587 ( 1 9 7 4 ) . 3. H. H o r n e r a n d H. Wagner: J. P h y s . C: 7, 3305 ( 1 9 7 4 ) . 4. H. Z q p e l a n d H. P e i s l : A c t a Met. 28, 589 ( 1 9 7 0 ) . 5. J. V o l k l a n d G,. A l e f e l d : I 1 Nuovo C i m e n t o , 33B, 1 9 0 ( 1 9 7 6 ) . 6. H. C o n r a d , G. B a u e r , G. A l e f e l d , T.S. S p r i n g e r and W. S c h m a t z : Z. P h y s i k , 266, 239 ( 1 9 7 4 ) . 7. W. M u n z i n g , N. Stump and G. G o e l t z : J. A p p l . C r y s t a l l o g r . , 11, 588 ( 1 9 7 8 ) . 8. M.A. P i c k a n d R. B a u s c h : J . Phys. F: 6, 1 7 5 1 ( 1 9 7 6 ) . 9. M. Ammano a n d H.K. B i r n b a u m : P r o c e e d i n g s o f t h e I n t e r n a t . C o n f . on " I n t e r n a l F r i c t i o n and U l t r a s o n i c A t t e n u a t i o n i n S o T i d s , " U n i v e r s i t y o f T o k y o P r e s s , 1977.
1 0 . E.S. F i s h e r , D.G. W e s t l a k e and S.T. O c k e r s : Phys. S t a t . S o l . ( a ) 28, 5 9 1 ( 1 9 7 5 ) .
11. A. M a g e r l , B. B e r r e and G. A l e f e l d : Phys. S t a t . S o l . ( a ) 36, 1 6 1 ( 1 9 7 6 ) .
1 2 . D.M. S c l a e d e r a n d J.F. S m i t h : To be p u b l i s h e d .
13. L.D. L a n d a u a n d I . M . K h a l a t n i k o v : Dokp, Acad. Nauk USSR 96, 469, ( 1 9 5 4 ) .
1 4 . I. Y a k o v l e v and I.S. V e l i c h k i n a : Sov. Phys. Usp. 63, 552, ( 1 9 5 7 ) . 15. A.S. N o w i c k a n d B.S. B e r r y : A n e l a s t i c R e l a x a t i o n i n C r y s t a l l i n e
S o l i d s , chap. 16, A c a d e m i c P r e s s , N.Y. ( 1 9 7 2 ) .
16. C.W. G a r l a n d : Phys. A c o u s t i c s V a l . 7, Acad. P r e s s , N.Y. ( 1 9 7 0 ) . 1 7 . F.M. M a z z o l a i , P.G. B o r d o n i and F.A. L e w i s : J. Phys. F: M e t a l
P h y s . 11,337 ( 1 9 8 1 ) .
Ref. ( )
+ Ref. ( )
Ref. (
2.4 - A s measured
2.3
--
Corrected for relax-2.2
< 'I
Fig. 1
T(K)
Fig. 2
Fiq. 1 V a r i a t i o n o f the e l a s t i c con- s t i n t s w i t h H/Nb a t 528 K.
o Data from Ref.
19);
X Data from Ref. C121. - --
As measured values f o r t h e e l a s t i c constants c o r r e c t e d f o r t h e thermal expansion and t h e volume change caused by H absorption.- - -
-
Unrelaxed values o f t h ee l a s t i c constants.
JOURNAL DE PHYSIQUE Fig. 4 T-'
.
lo3 (K-') 2.00 2.25 2.50 2.75 Fig. 5-Plots o f C'TS
a f u n c t i o n o f ( T - T I ) -.
Reported values o f T a r e obtained f r o m the b e i t f i t o f t h e experimental p l o t s t o a l i n e a r r e l a t i o n s h i p between C 1 and (T-TI)-].r-- ---- T----l-- ----T--- n=0.71 Tc ' 351 K +/ +loMHz w =0.22eV Experimental data
-1
-
-
"
Fig. 4-Comparison o f t h e temper-a t u r e dependence of measured a t t e n u a t i o n w i t h the p r e d i c t i o n s
\
-10
-
o f t h e Landau and Zener t h e o r i e s .I"
The data should be f i t t e d t o aFig. 6-Comparison o f t h e composition dependence o f A, w i t h t h e dependence p r e d i c t e d by t h e t h e o r y o f Zener e f f e c t f o r a completely disordered a l l o y s .
/
2
s t r a i g h t l i n e i n t h e forms shown. -32 ;N .!,a i s the a t t e n u a t i o n above -153'a
background as estimated fromI measurements a t t h e h i g h e s t
I temperatures.
0.5
