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ULTRASONIC STUDY ON SUPERCONDUCTING
ALUMINUM CONTAINING DISLOCATIONS
Y. Hiki, H. Ohtsuka, Y. Kogure, T. Kino
To cite this version:
ULTRASONIC STUDY.ON SUPERCONDUCTING ALUMINUM CONTAINING DISLOCATIONS
Y. HIKI, H. OHTSUKA, Y. KOGURE AND T. KINOf
Faculty of Science, Tokyo Institute of Technology, Tokyo 152,
Japan
'Faculty of Science, Hiroshima University, Hiroshima 730, Japan
Resume - L ' a t t e n u a t i o n des ondes u l t r a s o n o r e s de megahertz dans un m o n o c r i s t a l T 7 T l T e h a u t e p u r e t e e t a i t mesuree en l e s e t a t s normal e t supraconducteur
(2.0
-
0.4 K). Le specimen e t a i t successivement deform6 p a r l a compression (0.14-
1.4 % ) e t l e s e f f e c t s des d i s l o c a t i o n s e t a i e n t e t u d i e s . L 1 a t t 6 n u a t i o n en l ' e t a t normal d i m i n u a i t g r a d u e l l e m e n t cause de l a d i f f u s i o n des e l e c t r o n s normaux p a r l e s d i s l o c a t i o n s . En l ' e t a t supraconducteur, l a l a c u n ee n e r g e t i q u e e t a i t t r o u v e e apparemment a l t e r e e p a r l e s d i s l o c a t i o n s . A b s t r a c t
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The megahertz u l t r a s o n i c a t t e n u a t i o n i n a h i g h - p u r i t y aluminum s i n g l e c r y s t a l has been measured i n t h e normal and superconducting s t a t e s (2.0-
0.4 K). The specimen was s u c c e s s i v e l y deformed by compression (0.14-
1.4 % ) , and t h e e f f e c t s o f t h e i n t r o d u c e d d i s l o c a t i o n s were s t u d i e d . The a t t e n u a t i o n i n t h e normal s t a t e decreased g r a d u a l l y due t o t h e i n c r e a s e d s c a t t e r i n g o f normal e l e c t r o n s by d i s l o c a t i o n s . I n t h e superconducting s t a t e , t h e energy gap was f o u n d t o be a p p a r e n t l y a l t e r e d b y d i s l o c a t i o n s .I
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INTRODUCTIONS u p e r c o n d u c t i v i t y commonly o r i g i n a t e s f r o m t h e p a i r i n g o f e l e c t r o n s through an e l e c t r o n - p h o n o n i n t e r a c t i o n . When l a t t i c e d e f e c t s a r e c o n t a i n e d i n a c r y s t a l , t h e superconducting p r o p e r t i e s o f t h e c r y s t a l s h o u l d somewhat be changed, s i n c e t h e s t a t e s o f e l e c t r o n s and phonons a r e a l t e r e d . The i n t e n t i o n o f t h e p r e s e n t s t u d y i s t o i n v e s t i g a t e t h e e f f e c t o f c r y s t a l d i s l o c a t i o n s on t h e s u p e r c o n d u c t i n g energy gap, which i s a r e p r e s e n t a t i v e q u a n t i t y o f a superconductor. Aluminum has been chosen as t h e t e s t i n g m a t e r i a l , because i t i s a t y p i c a l weak-coupling superconductor and t h e s t a t e s o f e l e c t r o n s and phonons i n t h e m a t e r i a l have been w e l l s t u d i e d . An u l t r a s o n i c a t t e n u a t i o n method was adopted t o determine t h e energy gap, s i n c e t h e method was enough p r e c i s e and a l s o v e r y c o n v e n i e n t f o r t h e p r e s e n t purpose. I 1
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EXPERIMENTAL METHODThe specimen was p r e p a r e d f r o m a z o n e - r e f i n e d s i n g l e - c r y s t a l aluminum b l o c k . A
c y l i n d r i c a l specimen o f 10 mm i n d i a m e t e r and h a v i n g t h e [ I 1 0 1 a x i a l c r y s t a l l o g r a - p h i c o r i e n t a t i o n was shaped, and i t was c u t t o a l e n g t h o f a b o u t 15 mm by a spark c u t t e r . The a x i a l o r i e n t a t i o n o f t h e specimen was a c c u r a t e w i t h i n 1 degree.
A c c o r d i n g t o an a c t i v a t i o n a n a l y s i s o f t h e m a t e r i a l , t h e main i m p u r i t y c o n t a i n e d was 0.6 ppm S i and t h e specimen was c o n s i d e r e d t o be 99.9999 % i n t h e p u r i t y /I/. The e l e c t r i c a l r e s i s t i v i t y r a t i o , R(300 K)/R(4.2 K), o f t h e m a t e r i a l was a t l e a s t 20000, and t h e mean f r e e p a t h o f e l e c t r o n s was e s t i m a t e d t o be a b o u t 1 mm a t 4.2 K / 2 / . The specimen was annealed i n vacuum by i n c r e a s i n g and d e c r e a s i n g t e m p e r a t u r e r e p e a t - e d l y between 380°C and 680°C, and t h e d e n s i t y o f d i s l o c a t i o n s i n t h e annealed specimen was p r o b a b l y
l o 4
-l o 5
cm-'. The b o t h ends o f t h e specimen were f i n i s h e d by hand l a p p i n g u n t i l 1 t h e f l a t n e s s and p a r a l l e l i s m b e t t e r t h a n 2 vm/cm were o b t a i n e d . I n o r d e r t o i n t r o d u c e d i s l o c a t i o n s i n t o t h e specimen, i t was deformed by compression a l o n g i t s a x i s by u s i n g a l o a d i n g machine. The d e f o r m a t i o n r a t e wasC10-700 JOURNAL
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PHYSIQUEabout 0.05 mm/min, and t h e amounts o f the successive deformation were E = 0.14, 0.32, 0.69, 1.07, and 1.43 %, which were measured by a micrometer a f t e r t h e deformation. With using t h e above specimen i n t h e annealed s t a t e and i n t h e deformed s t a t e s , measurements o f u l t r a s o n i c a t t e n u a t i o n were made i n t h e temperature range between 0.4 and 2.0 K, A 3He pumping c r y o s t a t was used f o r t h e experiment, and a carbon thermometer c a l i b r a t e d by t h e 3He vapor pressure was used f o r the temperature meas- urements. The u l t r a s o n i c a t t e n u a t i o n i n t h e specimen was measured by a pulse r e - f l e c t i o n method w i t h l o n g i t u d i n a l sound o f 10 MHz frequency. The e l e c t r o n i c apparatus used were an u l t r a s o n i c generator and r e c e i v e r (Matec model 6000
+
760) and an exponential generator (Matec model 1204A). Special care was taken i n bonding an u l t r a s o n i c transducer (X-cut quartz,t
i n c h i n diameter) t o t h e specimen, The Nonaq stopcock grease was used a f t e r being dehydrated i n a heated and evacuated vessel. Care was a l s o taken i n keeping t h e i n p u t u l t r a s o n i c power as low as p o s s i b l e i n o r d e r t o d i m i n i s h t h e sound a t t e n u a t i o n a r i s i n g from t h e h y s t e r e s i s l o s s due t o d i s l o c a t i o n v i b r a t i o n . The accuracy o f t h e present a t t e n u a t i o n measurements was u s u a l l y b e t t e r than 0.01 dB/usec. The measurements were made w i t h i n c r e a s i n g t h e temperature a t a r a t e o f about 3 mK/min, and t h e accuracy o f t h e temperature meas- urements was b e t t e r than 5 mK.I 1 1
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RESULTS AND ANALYSESThis study i s e v e n t u a l l y intended t o determine t h e r e l a t i o n between t h e magnitude o f t h e superconducting energy gap and t h e d e n s i t y o f d i s l o c a t i o n s contained i n t h e c r y s t a l . D i s l o c a t i o n s a r e introduced i n t o t h e specimen by t h e compressional d e f o r - mation. Since t h e specimen i s very pure, t h e introduced d i s l o c a t i o n s can e a s i l y move and a r e a p t t o be a n n i h i l a t e d . A f t e r t h e deformation, t h e d e n s i t y o f d i s l o c a - t i o n s r a p i d l y decreases by some amount and then approaches t o a constant value /3/. Namely, o n l y a p a r t o f t h e introduced d i s l o c a t i o n s can s t a b l y remain i n t h e c r y s t a l . Such i n f o r m a t i o n can be obtained by measuring t h e u l t r a s o n i c a t t e n u a t i o n a t room temperature, since here t h e main o r i g i n o f t h e a t t e n u a t i o n i s the d i s l o c a t i o n damp- ing. A f t e r analyzing t h e data on t h e u l t r a s o n i c a t t e n u a t i o n versus t h e deformation and on t h e frequency dependence o f t h e a t t e n u a t i o n and a l s o t h e compressional s t r e s s - s t r a i n r e l a t i o n o f t h e specimen, t h e authors obtained the f o l l o w i n g r e l a t i o n between t h e d e n s i t y o f remaining d i s l o c a t i o n s ~ ( c m - ~ ) and t h e deformation E ( % ) :
Fig. 1
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Temperature dependence o f u l t r a s o n i c a t t e n u a t i o n a i n t h e c r y s t a l i n t h e annealed s t a t e (E = 0) and i n t h e deformed s t a t e s (compressional deformation E = 0.32, 1.43 %).The d e t a i l o f t h e procedure t o
here t h a t t h e E~ term repre- sents t h e a n n i h i l a t i o n e f f e c t .
4.0
t h e a t t e n u a t i o n decreases s t e e p l y as t h e temperature i s lowered. This can be a t t r i - buted t o t h a t t h e number o f normal e l e c t r o n s r a p i d l y decreases w i t h temperature. By analyzing t h e temperature dependence o f a t t e n u a t i o n , t h e superconducting energy gap can be determined. The temperature dependence, and t h e r e f o r e t h e energy gap, seem t o be changed by t h e deformation. These t h i n g s are f u l l y mentioned i n t h e f o l l o w i n g . F i r s t l y , t h e u l t r a s o n i c a t t e n u a t i o n i n t h e normal s t a t e w i l l be considered. The a t t e n u a t i o n due t o t h e conduction e l e c t r o n s depends on t h e wave number o f sound q and the mean f r e e path o f e l e c t r o n s
l e .
A t low temperatures, t h e mean f r e e path i s s o l e l y determined by i m p u r i t y atoms and o t h e r l a t t i c e d e f e c t s since t h e c o n t r i b u t i o n o f phonons i s i n e f f e c t i v e . Thus, t h e a t t e n u a t i o n i s independent o f temperature as can be seen i n r i g . 1. The measured values o f normal-state a t t e n u a t i o n f o r t h e specimen i n successively deformed s t a t e s are shown i n F i g . 2. The r e s u l t s can be analyzed on t h e basis o f t h e Pippard theory o f sound a t t e n u a t i o n by e l e c t r o n s /4/. The expression given by t h e theory i s as t h e f o l l o w i n g :where a ' i s t h e a t t e n u a t i o n i n t h e l i m i t o f 1, -+ m. I n t h e present case, t h e e l e c t r o n mean f r e e path i s determined by i m p u r i t i e s and d i s l o c a t i o n s , and
here li and ld a r e those due t o i m p u r i t i e s and d i s l o c a t i o n s . Furthermore, d i s t h e s c a t t e r i n g cross-width o f a d i s l o c a t i o n f o r electrons, and A i s t h e d e n s i t y o f d i s - l o c a t i o n s i n t h e specimen. By using eqs. (1)
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(3) and by adopting t h e value li =1 mm already mentioned and by a d j u s t i n g t h e two q u a n t i t i e s a ' and d as parameters, we obtained t h e f i t t e d curve i n F i g . 2. The f i t t i n g seems t o be almost s a t i s f a c t o r y . The determined value o f t h e s c a t t e r i n g cross-width i s d = 5.10 x
l o - '
cm2
2b, where b i s t h e Burgers v e c t o r o f d i s l o c a t i o n , being a reasonable r e s u l t .The u l t r a s o n i c a t t e n u a t i o n i n t h e superconducting s t a t e i s now considered. The temperature dependence o f a t t e n u a t i o n can be analyzed on t h e b a s i s o f t h e BCS theory
/5/. The r a t i o o f t h e a t t e n u a t i o n
-
Vii
3.2
z
TI-
a
2.8
i n t h e superconducting s t a t e as and t h a t i n t h e normal s t a t e a, i s represented by t h e theory as3.6
-
1
[ 1 1 0 1
2.4
6
'0.4
0.8
1.2
t i n g can be r e f e r r e d t o another a r t i c l e presented a t t h i s confer-€
ence1 6 1 .
The r e s u l t s o f t h e f i t were extremely good f o r both cases F i g . 2-
Normal-state a t t e n u a t i o n versus o f annealed and deformed s t a t e s o f deformation. The curve i s t h e r e s u l t o f t h e specimen, I n t h e above analy- parameter f i t based on t h e Pippard theory. s i s , the zero-temperature energyT
=
1.2
K
-
P /
o
a s =-
2 an 1 + ~ X P [ A ( T ) / ~ ~ T ~ I'
( 4 ) where kg i s t h e Boltzmann constant, T, i s t h e t r a n s i t i o n temperature. Also A(T) i s t h e superconducting energy gap depending on tempera- t u r e , and A(T) i s a f u n c t i o n o f Tc and t h e zero-temperature energy gap A,. An example o f t h e f i t o fC10-702 JOURNAL
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PHYSIQUEgap A, i s one o f t h e f i t t i n g parameters, and i t s v a l u e i s o b t a i n e d e x p e r i m e n t a l l y . The determined energy gaps f o r t h e specimen i n t h e annealed and i n t h e deformed s t a t e s a r e g i v e n i n F i g . 4. Each o f t h e values was o b t a i n e d by a n a l y z i n g more t h a n
two e x p e r i m e n t a l r u n s o f a t t e n - REFERENCES
5
-
o2
3.6
3.4
/I/ Kino, T., Hashimoto, E., Kamigaki, N., Kiso, Y. and M a t s u s h i t a , R., Trans. Jpn. I n s t . M e t a l s 18 (1977) 305.
/2/ N a k a m i c h i Y I . and Kino, T., J. Phys. Soc. Jpn. 49 (1980) 1350.
/3/ H i k i , Y., Kosugi, 'T., Mizuno, K. and Kino, T., S m a d a Conference V, P o i n t D e f e c t s and D e f e c t I n t e r a c t i o n s i n M e t a l s ( U n i v e r s i t y o f Tokyo Press, Tokyo, 1982) p. 753. /4/ Pippard, A. B., P h i l . Mag. 46 (1955) 1104.
/5/ Bardeen, J., Cooper, L. N. z d S c h r i e f f e r , J. R., Phys. Rev. 108 (1957) 1175. /6/ Kogure, Y., Takeuchi, N., H i k i , Y., Mizuno, K. and Kino, T., T s Proceedings.
Note : Perhaps authors should explain that Figure 4 results depend on method of analyzing the data.
u a t i o n - v s - t e m p e r a t u r e measure- ment. The c u r v e s i n t h e f i g u r e r e p r e s e n t t h e r e l a t i o n . 2Ao/kBT, = A
+
BA, (5) where A i s t h e d i s l o c a t i o n d e n s i t y c a l c u l a t e d f r o m eq. ( I ) , and A and B a r e c o n s t a n t s . F o r t h e l e f t and t h e r i g h t curves, A = 3.37 and 2.54; B = 1.45 and 1.81 xlo-',
r e s p e c t i v e l y . The experimental r e s u l t s show t h a t t h e superconducting energy gap i n c r e a s e s i n p r o p o r t i o n t o t h e d e n s i t y o f d i s l o c a t i o n s , and t h e n suddenly drops by f a i r l y3.0
CI 02.0
al
U1 I-
a
u
-
a
1.0
0 - '
0.4
0.6
0.8
1.0
1
.
2
l a r g e amount, and a g a i n i n -T ( l 0
creases w i t h t h e d i s l o c a t i o n d e n s i t y . Perhaps i t i s p o s s i b l e t h a t t h e o b t a i n e d r e s u l t o f F i g . F i g . 3-
An example o f t h e BCS f i t f o r t h e 4 depends on t h e method o f ana- a t t e n u a t i o n versus temperature data. l y z i n g t h e d a t a and can bea l t e r e d when o t h e r methods a r e
, adopted. T h i s p o i n t i s now be-
i n g c o n s i d e r e d by t h e a u t h o r s . 1
