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Hall-effect on protons in ice
Volume 22, number 4
PHYSICS LETTERS
HALL-EFFECT
1 September 1966
ON PROTONS
IN ICE
B. B U L L E M E R and N. RIEHL Physik Department der Technischen Hochschule Mi~nchen
Received 25 July 1966 A positive sign of the Hall-effect indicates protonic c a r r i e r s . The mobility is 1.4 cm2/V sec at -8oc and about 20 times the value found elsewhere, due to trapping. Protons should be "free" longer than 4.2 x 10 -12 sec.
The c o n s i d e r a b l e m o b i l i t y of c h a r g e c a r r i e r s in ice (N0.1 c m 2 / V sec) [1] s u g g e s t s that a H a l l effect due to p r o t o n i c c u r r e n t s should be d e t e c t a b l e [1-5], but no m e a s u r e m e n t s w e r e r e p o r t e d . In i c e , the p r o b l e m s r e l a t e d to h i g h - r e s i s t a n c e H a l l - p r o b e s a r e c o m p o u n d e d by p o l a r i z a t i o n e f f e c t s and a v e r y u n f a v o u r a b l e s i g n a l - t o - n o i s e r a tio c a u s e d by p r o t o n i c d i s c h a r g e at the e l e c t r o d e s . The n o i s e p r o b l e m c a n be a m e l i o r a t e d by s u i t a b l e s a m p l e g e o m e t r y [3]. But f u r t h e r m o r e , above - 2 0 o c , the s u r f a c e c o n d u c t i v i t y of the i c e s a m p l e t e n d s to s h o r t - c i r c u i t the g e n e r a t e d H a l l - v o l t a g e . It a p p e a r s p r e f e r a b l e , t h e r e f o r e , to m e a s u r e the H a l l - current. The s a m p l e s w e r e cut f r o m p u r e i c e s i n g l e c r y s t a l s (of the s a m e t y p e d e s c r i b e d in [6]) in f o r m of r e c t a n g u l a r p l a t e s (86 × 39 × 7.6 m m 3) with the c - d i r e c t i o n along the l a r g e s t d i m e n s i o n . Two i d e n t i c a l e l e c t r o d e s y s t e m s w e r e a p p l i e d to the l a r g e s a m p l e f a c e s . T h e s e e l e c t r o d e s w e r e p r e p a r e d with " p r i n t e d c i r c u i t " m e t h o d s f r o m c o p p e r - c l a d epoxy l a m i n a t e s . The c o p p e r s u r f a c e s , g a l v a n i z e d in a c i d i c P d C 1 2 - s o l u t i o n and f i n a l l y c o v e r e d with P d - b l a c k p r o v i d e d r e l i a b l e c o n t a c t s without b e i n g f r o z e n to the c r y s t a l . A g u a r d - e l e c t r o d e p r o t e c t e d the H a l l - c u r r e n t JH f r o m being a f f e c t e d by s u r f a c e c u r r e n t s a n d f r o m a z e r o d r i f t which would o t h e r w i s e be c a u s e d by n o n - s y m m e t r i c p o l a r i z a t i o n in the c i r cuits driving Jd' When the m a g n e t i c f i e l d w a s t u r n e d on o r off, the Hall s i g n a l was found to o c c u r a f t e r a definite and t e m p e r a t u r e - d e p e n d e n t r e s p o n s e t i m e 7 r of the o r d e r of s o m e 10 s e c . Having p a s s e d a m a x i m u m , JH d e c a y e d s l o w l y (due to i m p e r f e c t d i s c h a r g e ) and d r o p p e d to z e r o a f t e r 50 s e c . The t i m e r r i s c o n s u m e d in r o t a t i n g the J d c u r r e n t l i n e s t h r o u g h the Hall a n g l e ~ in a p l a n e n o r m a l to the m a g n e t i c field. We t h e r e f o r e c o n c l u d e d that 1/~ r should v a r y with t e m p e r a t u r e l i k e the
s u r f a c e c o n d u c t i v i t y of ice [7] and t h i s was c o n f i r m e d by o b s e r v a t i o n ( a c t i v a t i o n e n e r g y ~30 kcal/mole). The r e l a t i v e d i r e c t i o n s of J H , J d and H r e s u l t in a p o s i t i v e s i g n f o r the m a j o r i t y c a r r i e r s in ice. At - 8 o c , the o b s e r v e d H a l l - c u r r e n t was (6 ± 1.6)× × 1012 A in one d i r e c t i o n of the d r i v i n g c u r r e n t and (5± 2)× 10 -12 A a f t e r c u r r e n t r e v e r s a l . A p p l i e d d r i v i n g v o l t a g e and m a g n e t i c f i e l d w e r e Ud = = 105 V and H = 8.5 kG. The f i g u r e s e e m s to i n d i c a t e a g r a t i f y i n g l i n e a r d e p e n d e n c e of H a l l - c u r r e n t on d r i v i n g v o l t a g e at - 2 o c . The d r i v i n g c u r r e n t , b e i n g g r e a t l y a f f e c t e d by s u r f a c e c o n d u c t i v i t y , a p p e a r s to be a p o o r s t a r t ing point f o r f u r t h e r a n a l y s i s . R a t h e r , the H a l l c o e f f i c i e n t R = 1/e n H was e v a l u a t e d u s i n g the r e l a t i o n R = (~H/aZF., w h e r e ~E and ~ a r e defined b y J : J d + J H : ~ / ~ + ~H(/ffXE), and w h e r e e the e l e m e n t a r y c h a r g e and n H the Hall c o n c e n t r a t i o n . I n s e r t i o n of n u m e r i c a l v a l u e s f o r J H , Ud and the s a m p l e d i m e n s i o n s r e s u l t e d in the following v a l u e s a t - 2 o c ( r e sp. - 8 ° C ) : ~H = 1.1 ( r e s p . 1.2) × × 10 -9 A c m / V z s e c , n H = 1 ( r e s p . 0.4)× 1010 c m -3. The v a l u e s of (~E w e r e obtained f r o m [4] 0 H IO"~A "5 -r i i
-4
I uf
-3
I u
o,o f f
! ! !
~2
-,-! / f
!
60
Ud
Fig. 1. Hall-current versus driving voltage at -2oc with 8.5 kG applied for pure ice single crystal. 411
Volume 22, number 4
PHYSICS LETTERS
with a s m a l l c o r r e c t i o n a c c o r d i n g to [7]. F o r the d r i f t m o b i l i t y of the c u r r e n t c a u s i n g the H a l l - e f f e c t we obtained PdH=0.8 (resp. 1.4) c m 2 / V sec. Thus we found a c a r r i e r c o n c e n t r a t i o n l o w e r by a f a c t o r 20 and d r i f t m o b i l i t i e s h i g h e r by a s i m i l a r f a c t o r than the v a l u e s d e r i v e d f r o m d i s s o c i a t i o n f i e l d e f f e c t [4]. Indeed, as the m e c h a n i s m of conductivity in i c e i n v o l v e s a t r a p p i n g p r o c e s s , the a c t u a l v e l o c i t y o b s e r v e d in a g a l v a n o m a g n e t i c e x p e r i m e n t has to e x c e e d the ( a v e r a g e ) d r i f t v e l o c i t y . T h e r e f o r e , the o b s e r v e d f a c t o r of 20 should indicate the r a t i o of t i m e t r a p p e d to t i m e f r e e f o r the c a r r i e r . This a r g u m e n t is supp o r t e d by o b s e r v a t i o n of the e x i s t e n c e of a t r a p f i l l e d l e v e l with s p a c e - c h a r g e - l i m i t e d c u r r e n t s in i c e [6]. C a l c u l a t i o n on a s i m p l e m o d e l b a s e d on t h e s e i d e a s p e r m i t to deduce a m i n i m u m f r e e c a r r i e r life t i m e of 2.6 r e s p . 4 . 2 × 1 0 -12 sec at -2 r e s p . - 8 ° C f r o m the Hall angle ~o = ~HH/C;E. And if we
PEAK
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IN
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MAGNETIZATION
1September 1966
a d m i t s o m e s p e c u l a t i o n , t h i s m i g h t e x p l a i n the o b s e r v a t i o n of i n c r e a s i n g m o b i l i t y with d e c r e a s ing t e m p e r a t u r e [6, 7] (e.g. a supply of t h e r m a l e n e r g y would tend to d e c r e a s e the c o r r e l a t i o n b e t w e e n s u c c e s s i v e p r o t o n jumps).
References 1. M. Eigen and L. De Maeyer, Proc. Roy. Soc.A 247 (1958) 505. 2. J.M. Ziman, Electrons and Phonons (Oxford 1963) p. 486. 3. H. Gobrecht. A. Tausend and G. Clauss, Z. Physik 176 (1963) 155. 4. M.Eigen and L.De Maeyer, H. -Ch.Spatz, Ber. Bunsengesell. Phys. Chem. 68 (1964) 19. 5. E.W. Saunders, ERL-64-16 Res. Rep. Univ.Calif. (1964) ; AD-601050.
6. H.Engelhardt and N.Riehl, Physics Letters 14 (1965) 20; Phys. Kondens. Materie 5 No. 2 (1966). 7. B.Bullemer and N.Riehl, submitted to Solid State Commun.
OF
SUPERCONDUCTING
NIOBIUM
N. TSUDA, S. KOIKE * and T. SUZUKI
Institute f o r Solid State Physics, University of Tokyo, Tokyo, Japan Received 26 July 1966
The peak effect in dB/dH at Hc2 was observed. This is explained in terms of the interaction of the Abrikosov lattice with dislocations using the two fluid model. The interaction energy is estimated to be about 3 x 10-8 erg/cm.
It i s well known that a peak a p p e a r s n e a r the u p p e r c r i t i c a l f i e l d in the c u r v e of r e s i s t i v i t y plott e d a g a i n s t m a g n e t i c f i e l d [1-3]. It o r d i n a r i l y a p p e a r s as a r e s u l t of the e x i s t e n c e of g a s e o u s i m p u r i t i e s such a s oxygen o r cold w o r k and it s shape depends on the t r a n s p o r t c u r r e n t density. In the p r e s e n t note, a s h a r p peak in the m a g n e t i z a t i o n found in a single c r y s t a l of niobium will be d e s c r i b e d . A s a m p l e of about 6 m m d i a m . and 10 m m long was d e g a s s e d in 5 x 10-9 m m H g at 1700°C until the peak d i s a p p e a r s at 4.2OK. Then it was c o m p r e s s e d . T h e r e s i s t a n c e r a t i o P300/P4..2 of the s a m p l e d e f o r m e d by 9% was about 340. The m a g n e t i z a t i o n was obtained by m e a s u r i n g the f i r s t d e r i v a t i v e of the m a g n e t i c induction, that i s , the induced v o l t a g e in the coil * On leave from Tokyo College of Science.
412
a r o u n d the s a m p l e by the a p p l i c a t i o n of m a g n e t i c f i e l d sweeping at a c o n s t a n t sp eed w as r e c o r d e d . It was found that the p e a k a s shown in fig. 1 w as due to the i m p u r i t i e s such a s o x y g en s o r d i s l o c a t i o n s and not due to s u r f a c e s t a t e s o r v a c a n c i e s . The p e a k b e c o m e s l a r g e in both width and height a s the d e n s i t y of oxygens o r d i s l o c a t i o n s i n c r e a s e s . In the c a s e of oxygens, h o w e v e r , the peak height s e e m s to s a t u r a t e to a c e r t a i n value. In the following it will be studied why they ap p e a r at Hc2. As the e x t e r n a l f i e l d i n c r e a s e s the l a t t i c e p a r a m e t e r of the A b r i k o s o v s t r u c t u r e b e c o m e s s m a l l and r e a c h e s the t e r m i n a l length eq u al to the c o h e r e n c e length [4]. The A b r i k n s o v l a t t i c e then b e c o m e s m o r e rigid. At t h i s s t a t e , the above o b s t a c l e s such a s d i s l o c a t i o n s r e s i s t v e r y e f f e c t i v e l y a g a i n s t the c o m p l e t i o n of the rigid lattice.
PHYSICS LETTERS
HALL-EFFECT
1 September 1966
ON PROTONS
IN ICE
B. B U L L E M E R and N. RIEHL Physik Department der Technischen Hochschule Mi~nchen
Received 25 July 1966 A positive sign of the Hall-effect indicates protonic c a r r i e r s . The mobility is 1.4 cm2/V sec at -8oc and about 20 times the value found elsewhere, due to trapping. Protons should be "free" longer than 4.2 x 10 -12 sec.
The c o n s i d e r a b l e m o b i l i t y of c h a r g e c a r r i e r s in ice (N0.1 c m 2 / V sec) [1] s u g g e s t s that a H a l l effect due to p r o t o n i c c u r r e n t s should be d e t e c t a b l e [1-5], but no m e a s u r e m e n t s w e r e r e p o r t e d . In i c e , the p r o b l e m s r e l a t e d to h i g h - r e s i s t a n c e H a l l - p r o b e s a r e c o m p o u n d e d by p o l a r i z a t i o n e f f e c t s and a v e r y u n f a v o u r a b l e s i g n a l - t o - n o i s e r a tio c a u s e d by p r o t o n i c d i s c h a r g e at the e l e c t r o d e s . The n o i s e p r o b l e m c a n be a m e l i o r a t e d by s u i t a b l e s a m p l e g e o m e t r y [3]. But f u r t h e r m o r e , above - 2 0 o c , the s u r f a c e c o n d u c t i v i t y of the i c e s a m p l e t e n d s to s h o r t - c i r c u i t the g e n e r a t e d H a l l - v o l t a g e . It a p p e a r s p r e f e r a b l e , t h e r e f o r e , to m e a s u r e the H a l l - current. The s a m p l e s w e r e cut f r o m p u r e i c e s i n g l e c r y s t a l s (of the s a m e t y p e d e s c r i b e d in [6]) in f o r m of r e c t a n g u l a r p l a t e s (86 × 39 × 7.6 m m 3) with the c - d i r e c t i o n along the l a r g e s t d i m e n s i o n . Two i d e n t i c a l e l e c t r o d e s y s t e m s w e r e a p p l i e d to the l a r g e s a m p l e f a c e s . T h e s e e l e c t r o d e s w e r e p r e p a r e d with " p r i n t e d c i r c u i t " m e t h o d s f r o m c o p p e r - c l a d epoxy l a m i n a t e s . The c o p p e r s u r f a c e s , g a l v a n i z e d in a c i d i c P d C 1 2 - s o l u t i o n and f i n a l l y c o v e r e d with P d - b l a c k p r o v i d e d r e l i a b l e c o n t a c t s without b e i n g f r o z e n to the c r y s t a l . A g u a r d - e l e c t r o d e p r o t e c t e d the H a l l - c u r r e n t JH f r o m being a f f e c t e d by s u r f a c e c u r r e n t s a n d f r o m a z e r o d r i f t which would o t h e r w i s e be c a u s e d by n o n - s y m m e t r i c p o l a r i z a t i o n in the c i r cuits driving Jd' When the m a g n e t i c f i e l d w a s t u r n e d on o r off, the Hall s i g n a l was found to o c c u r a f t e r a definite and t e m p e r a t u r e - d e p e n d e n t r e s p o n s e t i m e 7 r of the o r d e r of s o m e 10 s e c . Having p a s s e d a m a x i m u m , JH d e c a y e d s l o w l y (due to i m p e r f e c t d i s c h a r g e ) and d r o p p e d to z e r o a f t e r 50 s e c . The t i m e r r i s c o n s u m e d in r o t a t i n g the J d c u r r e n t l i n e s t h r o u g h the Hall a n g l e ~ in a p l a n e n o r m a l to the m a g n e t i c field. We t h e r e f o r e c o n c l u d e d that 1/~ r should v a r y with t e m p e r a t u r e l i k e the
s u r f a c e c o n d u c t i v i t y of ice [7] and t h i s was c o n f i r m e d by o b s e r v a t i o n ( a c t i v a t i o n e n e r g y ~30 kcal/mole). The r e l a t i v e d i r e c t i o n s of J H , J d and H r e s u l t in a p o s i t i v e s i g n f o r the m a j o r i t y c a r r i e r s in ice. At - 8 o c , the o b s e r v e d H a l l - c u r r e n t was (6 ± 1.6)× × 1012 A in one d i r e c t i o n of the d r i v i n g c u r r e n t and (5± 2)× 10 -12 A a f t e r c u r r e n t r e v e r s a l . A p p l i e d d r i v i n g v o l t a g e and m a g n e t i c f i e l d w e r e Ud = = 105 V and H = 8.5 kG. The f i g u r e s e e m s to i n d i c a t e a g r a t i f y i n g l i n e a r d e p e n d e n c e of H a l l - c u r r e n t on d r i v i n g v o l t a g e at - 2 o c . The d r i v i n g c u r r e n t , b e i n g g r e a t l y a f f e c t e d by s u r f a c e c o n d u c t i v i t y , a p p e a r s to be a p o o r s t a r t ing point f o r f u r t h e r a n a l y s i s . R a t h e r , the H a l l c o e f f i c i e n t R = 1/e n H was e v a l u a t e d u s i n g the r e l a t i o n R = (~H/aZF., w h e r e ~E and ~ a r e defined b y J : J d + J H : ~ / ~ + ~H(/ffXE), and w h e r e e the e l e m e n t a r y c h a r g e and n H the Hall c o n c e n t r a t i o n . I n s e r t i o n of n u m e r i c a l v a l u e s f o r J H , Ud and the s a m p l e d i m e n s i o n s r e s u l t e d in the following v a l u e s a t - 2 o c ( r e sp. - 8 ° C ) : ~H = 1.1 ( r e s p . 1.2) × × 10 -9 A c m / V z s e c , n H = 1 ( r e s p . 0.4)× 1010 c m -3. The v a l u e s of (~E w e r e obtained f r o m [4] 0 H IO"~A "5 -r i i
-4
I uf
-3
I u
o,o f f
! ! !
~2
-,-! / f
!
60
Ud
Fig. 1. Hall-current versus driving voltage at -2oc with 8.5 kG applied for pure ice single crystal. 411
Volume 22, number 4
PHYSICS LETTERS
with a s m a l l c o r r e c t i o n a c c o r d i n g to [7]. F o r the d r i f t m o b i l i t y of the c u r r e n t c a u s i n g the H a l l - e f f e c t we obtained PdH=0.8 (resp. 1.4) c m 2 / V sec. Thus we found a c a r r i e r c o n c e n t r a t i o n l o w e r by a f a c t o r 20 and d r i f t m o b i l i t i e s h i g h e r by a s i m i l a r f a c t o r than the v a l u e s d e r i v e d f r o m d i s s o c i a t i o n f i e l d e f f e c t [4]. Indeed, as the m e c h a n i s m of conductivity in i c e i n v o l v e s a t r a p p i n g p r o c e s s , the a c t u a l v e l o c i t y o b s e r v e d in a g a l v a n o m a g n e t i c e x p e r i m e n t has to e x c e e d the ( a v e r a g e ) d r i f t v e l o c i t y . T h e r e f o r e , the o b s e r v e d f a c t o r of 20 should indicate the r a t i o of t i m e t r a p p e d to t i m e f r e e f o r the c a r r i e r . This a r g u m e n t is supp o r t e d by o b s e r v a t i o n of the e x i s t e n c e of a t r a p f i l l e d l e v e l with s p a c e - c h a r g e - l i m i t e d c u r r e n t s in i c e [6]. C a l c u l a t i o n on a s i m p l e m o d e l b a s e d on t h e s e i d e a s p e r m i t to deduce a m i n i m u m f r e e c a r r i e r life t i m e of 2.6 r e s p . 4 . 2 × 1 0 -12 sec at -2 r e s p . - 8 ° C f r o m the Hall angle ~o = ~HH/C;E. And if we
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EFFECT
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MAGNETIZATION
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a d m i t s o m e s p e c u l a t i o n , t h i s m i g h t e x p l a i n the o b s e r v a t i o n of i n c r e a s i n g m o b i l i t y with d e c r e a s ing t e m p e r a t u r e [6, 7] (e.g. a supply of t h e r m a l e n e r g y would tend to d e c r e a s e the c o r r e l a t i o n b e t w e e n s u c c e s s i v e p r o t o n jumps).
References 1. M. Eigen and L. De Maeyer, Proc. Roy. Soc.A 247 (1958) 505. 2. J.M. Ziman, Electrons and Phonons (Oxford 1963) p. 486. 3. H. Gobrecht. A. Tausend and G. Clauss, Z. Physik 176 (1963) 155. 4. M.Eigen and L.De Maeyer, H. -Ch.Spatz, Ber. Bunsengesell. Phys. Chem. 68 (1964) 19. 5. E.W. Saunders, ERL-64-16 Res. Rep. Univ.Calif. (1964) ; AD-601050.
6. H.Engelhardt and N.Riehl, Physics Letters 14 (1965) 20; Phys. Kondens. Materie 5 No. 2 (1966). 7. B.Bullemer and N.Riehl, submitted to Solid State Commun.
OF
SUPERCONDUCTING
NIOBIUM
N. TSUDA, S. KOIKE * and T. SUZUKI
Institute f o r Solid State Physics, University of Tokyo, Tokyo, Japan Received 26 July 1966
The peak effect in dB/dH at Hc2 was observed. This is explained in terms of the interaction of the Abrikosov lattice with dislocations using the two fluid model. The interaction energy is estimated to be about 3 x 10-8 erg/cm.
It i s well known that a peak a p p e a r s n e a r the u p p e r c r i t i c a l f i e l d in the c u r v e of r e s i s t i v i t y plott e d a g a i n s t m a g n e t i c f i e l d [1-3]. It o r d i n a r i l y a p p e a r s as a r e s u l t of the e x i s t e n c e of g a s e o u s i m p u r i t i e s such a s oxygen o r cold w o r k and it s shape depends on the t r a n s p o r t c u r r e n t density. In the p r e s e n t note, a s h a r p peak in the m a g n e t i z a t i o n found in a single c r y s t a l of niobium will be d e s c r i b e d . A s a m p l e of about 6 m m d i a m . and 10 m m long was d e g a s s e d in 5 x 10-9 m m H g at 1700°C until the peak d i s a p p e a r s at 4.2OK. Then it was c o m p r e s s e d . T h e r e s i s t a n c e r a t i o P300/P4..2 of the s a m p l e d e f o r m e d by 9% was about 340. The m a g n e t i z a t i o n was obtained by m e a s u r i n g the f i r s t d e r i v a t i v e of the m a g n e t i c induction, that i s , the induced v o l t a g e in the coil * On leave from Tokyo College of Science.
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a r o u n d the s a m p l e by the a p p l i c a t i o n of m a g n e t i c f i e l d sweeping at a c o n s t a n t sp eed w as r e c o r d e d . It was found that the p e a k a s shown in fig. 1 w as due to the i m p u r i t i e s such a s o x y g en s o r d i s l o c a t i o n s and not due to s u r f a c e s t a t e s o r v a c a n c i e s . The p e a k b e c o m e s l a r g e in both width and height a s the d e n s i t y of oxygens o r d i s l o c a t i o n s i n c r e a s e s . In the c a s e of oxygens, h o w e v e r , the peak height s e e m s to s a t u r a t e to a c e r t a i n value. In the following it will be studied why they ap p e a r at Hc2. As the e x t e r n a l f i e l d i n c r e a s e s the l a t t i c e p a r a m e t e r of the A b r i k o s o v s t r u c t u r e b e c o m e s s m a l l and r e a c h e s the t e r m i n a l length eq u al to the c o h e r e n c e length [4]. The A b r i k n s o v l a t t i c e then b e c o m e s m o r e rigid. At t h i s s t a t e , the above o b s t a c l e s such a s d i s l o c a t i o n s r e s i s t v e r y e f f e c t i v e l y a g a i n s t the c o m p l e t i o n of the rigid lattice.